CN111598697A

CN111598697A - Option information processing method and related device

Info

Publication number: CN111598697A
Application number: CN202010429818.0A
Authority: CN
Inventors: 王稼豪; 李涛
Original assignee: Hundsun Technologies Inc
Current assignee: Hundsun Technologies Inc
Priority date: 2020-05-20
Filing date: 2020-05-20
Publication date: 2020-08-28
Anticipated expiration: 2040-05-20
Also published as: CN111598697B

Abstract

The embodiment of the application discloses an option information processing method and related equipment, wherein one of core elements of option trading is implicit fluctuation rate, and the implicit fluctuation rate is a key element of an option information processing core. An important innovation of the embodiment of the application is the calculation of the implied fluctuation rate, which is not limited to the calculation of the implied fluctuation rate of a single option contract, but is considered to be taken into all option contracts under different deadline structures, and the information of the option contracts is modified according to the investment arbitrage strategy conditions to realize denoising processing, so that the trading element information of options under the non-arbitrage suite is obtained, and the target implied fluctuation rate of the target option can be calculated according to the trading element information of the options under the non-arbitrage suite and a preset model, so that the accuracy of the information processing of the target option is improved by the basic calculation.

Description

Option information processing method and related device

Technical Field

The present invention relates to the field of computers, and in particular, to an option information processing method and related apparatus.

Background

Options are financial instruments whose value is a function of the subject asset.

Specifically, option buyers or holders own options in a manner that pays an option price (equal to the option price), which gives the holder the right to buy (buy) or sell (sell) a subject asset at a fixed price before the option expiration time, while option sellers or stakeholders collect the option, and when a buyer wishes to execute an option, obligations must be fulfilled. The subject assets of the option may include, among other things, stocks, government bonds, currencies, stock indices, commodity futures, and the like. Before the option expiration time, the holder of the option may determine whether to buy or sell the subject asset (exercise option, referred to simply as a right) according to the right contract according to the spot price of the subject asset, and the fixed price agreed upon in the option at which the option holder buys or sells the subject asset is referred to as the option execution price (right price).

For example, if the spot price at expiration is lower than the exercise price, the holder will choose not to exercise the buy option but only lose the cost of the option itself, i.e., the option gold, whereas if the exercise price is lower than the spot price, the holder of the buy option will exercise the right to purchase the subject asset at the exercise price, gaining a profit equal to the difference between the spot price and the exercise price.

Because the types of options trading products are many, the processing methods of option information are different, for example, the option price is affected by various factors, and in addition, the option trading occurs in real time, the price information always changes in real time and rapidly, so how to process the option information efficiently is a problem to be solved urgently.

Disclosure of Invention

In order to solve the above technical problem, embodiments of the present application provide an option information processing method and related apparatus, so as to efficiently determine a reasonable price for an option.

The embodiment of the application provides an option information processing method, which comprises the following steps:

correcting the trading element information of a plurality of options to be analyzed according to the arbitrage limiting conditions; the hook targets of the plurality of options to be analyzed are target assets;

calculating market hidden fluctuation rates of the options to be analyzed according to the corrected trading element information of the options to be analyzed;

obtaining a corresponding relation between the right price and the market implicit fluctuation rate according to the right price of the option to be analyzed and the market implicit fluctuation rate of the option to be analyzed;

fitting the corresponding relation between the row weight price and the market implicit fluctuation rate based on a preset model to obtain the corresponding relation between the row weight price and the theoretical implicit fluctuation rate;

obtaining a target hidden fluctuation rate corresponding to the right-of-way price of the target option according to the right-of-way price of the target option and the corresponding relation between the right-of-way price and the theoretical hidden fluctuation rate; the hook target of the target option is a target asset;

and calculating the theoretical price of the target option according to the target implicit fluctuation rate.

Optionally, the calculating, according to the revised trading element information of the plurality of options to be analyzed, a market implicit fluctuation rate of the plurality of options to be analyzed includes:

calculating the forward predicted price of the target asset on each due date according to the corrected trading element information of the option to be analyzed based on a forward price fitting algorithm;

and calculating the market implicit fluctuation rate of the option to be analyzed according to the forward predicted price of the target asset on each expiration date.

Optionally, the modifying the trading element information of the plurality of options to be analyzed according to the arbitrage limiting condition includes:

ordering the options to be analyzed with the same due dates according to the row option price of the options to be analyzed to obtain an initial option price sequence corresponding to each due date;

fitting the initial option price sequence according to a arbitrage limiting condition to obtain a fitted option price sequence;

and determining the transaction element information of the corrected option to be analyzed based on the fitting option price sequence.

Optionally, the method further includes:

and screening out the option to be analyzed which does not accord with the arbitrage limiting condition according to the initial option price sequence and the fitting option price sequence, and taking the option to be analyzed which does not accord with the arbitrage limiting condition as the target option.

Optionally, the obtaining a corresponding relationship between the right price and the market implicit fluctuation rate according to the right price of the option to be analyzed and the market implicit fluctuation rate of the option to be analyzed includes:

calculating the real and imaginary degrees of the option to be analyzed;

screening the option to be analyzed based on the excess and deficiency degrees;

and carrying out interpolation operation according to the selected row right price and the market hidden fluctuation rate of the option to be analyzed to obtain the corresponding relation between the row right price and the market hidden fluctuation rate.

Optionally, the method further includes:

identifying a flat-valued option from the options to be analyzed;

obtaining a flat value implied fluctuation rate corresponding to the row option price of the flat value option according to the row option price of the flat value option and the corresponding relation between the row option price and the theoretical implied fluctuation rate;

adjusting the target hidden fluctuation rate according to the comparison result of the flat value hidden fluctuation rate and the historical fluctuation rate of the target asset or the comparison result of the flat value hidden fluctuation rate and the predicted fluctuation rate of the target asset;

the calculating the theoretical price of the target option according to the target implicit fluctuation rate includes:

and calculating the theoretical price of the target option according to the adjusted target implicit fluctuation rate.

Optionally, the arbitrage limiting condition includes at least one of: option convexity condition, option monotonicity, option upper and lower limits, option butterfly arbitrage, option bear price difference arbitrage.

Optionally, fitting the corresponding relationship between the row weight price and the market hidden fluctuation rate based on a preset model to obtain the corresponding relationship between the row weight price and the theoretical hidden fluctuation rate includes:

fitting the corresponding relation between the right-of-way price and the market implicit fluctuation rate based on a preset model to obtain model parameters of the preset model; the preset model with model parameters is used for reflecting the corresponding relation between the row weight price and the theoretical implicit fluctuation rate.

Optionally, the method further includes:

and calculating the risk indicator of the target option according to the target implicit fluctuation rate.

An embodiment of the present application further provides an option information processing apparatus, including:

the correcting unit is used for correcting the trading element information of the options to be analyzed according to the arbitrage limiting conditions; the hook targets of the plurality of options to be analyzed are target assets;

a market implicit fluctuation rate calculation unit, configured to calculate market implicit fluctuation rates of the plurality of options to be analyzed according to the revised trading element information of the plurality of options to be analyzed;

a corresponding relation obtaining unit, configured to obtain a corresponding relation between the right price and the market implicit fluctuation rate according to the right price and the market implicit fluctuation rate of the right to be analyzed;

the fitting unit is used for fitting the corresponding relation between the row weight price and the market implicit fluctuation rate based on a preset model to obtain the corresponding relation between the row weight price and the theoretical implicit fluctuation rate;

the target implicit fluctuation rate calculation unit is used for obtaining a target implicit fluctuation rate corresponding to the row option price of the target option according to the row option price of the target option and the corresponding relation between the row option price and the theoretical implicit fluctuation rate; the hook target of the target option is a target asset;

and the theoretical price calculating unit is used for calculating the theoretical price of the target option according to the target implicit fluctuation rate.

Optionally, the market implicit fluctuation rate calculating unit includes:

a forward predicted price calculating unit, configured to calculate a forward predicted price of the target asset on each due date according to the corrected trading element information of the option to be analyzed based on a forward price fitting algorithm;

and the market implicit fluctuation rate calculation subunit is used for calculating the market implicit fluctuation rate of the option to be analyzed according to the forward predicted price of the target asset on each expiration date.

Optionally, the modifying unit includes:

an initial option price sequence obtaining unit, configured to sort the to-be-analyzed options with the same due date according to the row option price of the to-be-analyzed option, so as to obtain an initial option price sequence corresponding to each due date;

a fitting option price sequence obtaining unit, configured to fit the initial option price sequence according to a arbitrage limiting condition to obtain a fitting option price sequence;

and the correcting subunit is used for determining the corrected trading element information of the option to be analyzed based on the fitting option price sequence.

Optionally, the apparatus further comprises:

and the option screening unit is used for screening the option to be analyzed which does not accord with the arbitrage limiting condition according to the initial option price sequence and the fitting option price sequence, and taking the option to be analyzed which does not accord with the arbitrage limiting condition as the target option.

Optionally, the correspondence obtaining unit includes:

the real and imaginary degree acquisition unit is used for calculating the real and imaginary degree of the option to be analyzed;

the screening unit is used for screening the option to be analyzed based on the real and imaginary degrees;

and the corresponding relation obtaining subunit is used for carrying out interpolation operation according to the screened row right price and the market implicit fluctuation rate of the option to be analyzed to obtain the corresponding relation between the row right price and the market implicit fluctuation rate.

Optionally, the apparatus further comprises:

a flat-valued option identification unit, configured to identify a flat-valued option from the options to be analyzed;

a flat value implied fluctuation rate obtaining unit, configured to obtain a flat value implied fluctuation rate corresponding to the row weight price of the flat value option according to the row weight price of the flat value option and a corresponding relationship between the row weight price and a theoretical implied fluctuation rate;

the fluctuation rate adjusting unit is used for adjusting the target hidden fluctuation rate according to the comparison result of the flat value hidden fluctuation rate and the historical fluctuation rate of the target asset or the comparison result of the flat value hidden fluctuation rate and the predicted fluctuation rate of the target asset;

the theoretical price calculating unit is specifically configured to:

Optionally, the fitting unit is specifically configured to:

Optionally, the apparatus further comprises:

and the risk index calculation unit is used for calculating the risk index of the target option according to the target implicit fluctuation rate.

An embodiment of the present application further provides an option information processing apparatus, including: a memory and a processor;

the memory for storing program code;

the processor is configured to read the program code in the memory, and execute the program code to implement the option information processing method.

An embodiment of the present application further provides a computer-readable storage medium, where the computer-readable storage medium is used for storing a program code, and the program code is used for executing the option information processing method.

The embodiment of the application provides an option information processing method and related equipment, which can firstly correct trading element information of a plurality of options to be analyzed according to arbitrage limiting conditions, wherein the hook marks of the options to be analyzed are target assets, the market implicit fluctuation rates of the options to be analyzed are obtained through calculation according to the corrected trading element information of the options to be analyzed, the corresponding relation between the option price and the market implicit fluctuation rate of the target asset is obtained according to the option price of the options to be analyzed and the market implicit fluctuation rate of the options to be analyzed, and the corresponding relation between the option price and the market implicit fluctuation rate is fitted based on a preset model to obtain the corresponding relation between the option price and the theoretical implicit fluctuation rate.

One of the core elements of option trading is an implicit fluctuation rate, which is a key element of the option information processing core. An important innovation of the embodiment of the application is the calculation of the implied fluctuation rate, which is not limited to the calculation of the implied fluctuation rate of a single option contract, but is considered to be taken into all option contracts under different deadline structures, and the information of the option contracts is modified according to the investment arbitrage strategy conditions to realize denoising processing, so that the trading element information of options under the non-arbitrage suite is obtained, and the target implied fluctuation rate of the target option can be calculated according to the trading element information of the options under the non-arbitrage suite and a preset model, so that the accuracy of the information processing of the target option is improved by the basic calculation.

Drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments described in the present application, and other drawings can be obtained by those skilled in the art according to the drawings.

Fig. 1 is a flowchart of an option information processing method according to an embodiment of the present application;

fig. 2 is a schematic diagram illustrating convergence of a method for processing option information according to an embodiment of the present application;

fig. 3 is a block diagram of an option information processing apparatus according to an embodiment of the present application.

Detailed Description

In order to make the technical solutions of the present application better understood, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.

Reference to "options" in the context of this application is a standardized contract, made uniformly by an exchange, that specifies subject matter that a buyer has the right to buy or sell a contracted hooked-up subject asset at a particular price at a particular time in the future. Options are contracts that the counterparty has agreed upon regarding future options. Options referred to in this application are primarily option standardized in-field contracts issued by domestic exchanges. At present, domestic exchanges related to standardized option contracts mainly include: shanghai stock exchange, Shenzhen stock exchange, Shanghai futures exchange, Dalian futures exchange, Zhengzhou option exchange, and Chinese financial futures exchange. The standardized option contracts that have been marketed for different trades mainly include: 50ETF options, soybean meal options, corn options, white sugar options, cotton options, Hu Cu options, rubber options, and the like.

At present, the options provided by different exchanges are relatively more in types, and with the development of the option derivative market, the options of different varieties are also gradually introduced. Assets based on different kinds of hooking labels, including ETF, stocks, futures, and indices, etc. Due to the comprehensive effect of the influence factors such as various target assets, rapid price change, inventory and the like, the method has great significance for reasonable processing of option information and building of option information processing flow devices. The currently popular blake-scoles (BS) model is a wide option estimation method, and also includes various calculation methods such as monte carlo simulation. These models have many advantages, but in general, the assumption conditions of the models are too harsh, and factors such as actual trading strategies are not included, which may result in some degree of inaccuracy or stability in option information processing.

In addition, because option contracts are issued on market trades by different exchanges, market participants are different, and organizations, individual investors, market makers and the like; the investment transaction types are not limited to arbitrage, stock enhancement, hedging, directional trading and the like, the price of the option market is formed, the range of the investment option series contracts is different due to the existence of different participant main bodies in the market and the difference of investment modes and schemes of different transaction types, the price forming mechanisms of different option contracts have noises of different degrees, and option information processing is not accurate to a certain extent.

Based on this, the embodiment of the present application provides an option information processing flow system and related devices, first, by obtaining trading element information of an option to be analyzed belonging to an asset with a hook target, where the trading element information specifically includes an option market price, a right-of-way price, an expiration time, and the like, performing denoising processing on the option market price to be analyzed based on a arbitrage limiting condition to obtain an option price under an arbitrage-free condition, calculating to obtain market hidden fluctuation rate of the option contract according to the corrected trading element information of the options to be analyzed, based on a preset model, fitting the corresponding relation between the right-of-way price and the market implicit fluctuation rate to determine the target implicit fluctuation rate of the target option, and calculating to obtain the theoretical price of the target option according to the target implicit fluctuation rate, wherein the calculated option implicit fluctuation rate and the theoretical price of the option have the characteristics of stability and accuracy.

In addition, in the embodiment of the application, the corresponding relation between the right price and the theoretical implicit fluctuation rate of the target asset can be obtained according to the option to be analyzed, so that the method is used for calculating the theoretical prices of other options of the target asset, the process is simple and easy to operate, certain universality is achieved, and the option information processing efficiency is improved to a certain extent.

The following describes in detail a specific implementation manner of an option information processing method and apparatus provided in the embodiments of the present application by using embodiments with reference to the accompanying drawings.

Referring to fig. 1, a flowchart of an option information processing method provided in an embodiment of the present application may include the following steps.

And S101, correcting the trading element information of the plurality of options to be analyzed according to the arbitrage limiting conditions.

The option to be analyzed is an option that has been put on the market and is a tradable option, and the option to be analyzed may be an option standardization floor contract issued by a domestic exchange. In the embodiment of the present application, the options to be analyzed are options having the same hooked mark, for example, the hooked marks of the options to be analyzed may all be target assets. The target asset may be a stock, government bond, currency, stock index, commodity future, etc.

The options to be analyzed may be in the form of euros or americas, where euros can only be exercised on their due date and americas can be exercised at any time after purchase and before expiration.

The trading element information of the option can be known by being issued by a trading exchange or other ways, and can include the price, the right price, the type, the hook mark, the due date and the like of the option to be analyzed, and can also include the real-time price and the like of the hook mark.

The market characteristics of the subject asset may be reflected to some extent by trading element information for options to be analyzed, such as a copper right at $ 2000/ton for options to be analyzed that expire at day 4-month-18, and a copper right at $ 1900/ton for options to be analyzed that expire at day 5-month-18, considering that copper will be increasing in value within one month after day 4-month-18.

Because the option contracts are issued on the market by different exchanges, market participants are different, and organizations, individual investors, market makers and the like; the investment transaction types are not limited to arbitrage, stock enhancement, hedging, directional trading and the like, the prices of the option market are formed, the range of the investment option series contracts is different due to the existence of different participant bodies in the market and the difference of investment modes and schemes of different transaction types, and the price forming mechanisms of different option contracts have different degrees of noise.

Therefore, in the embodiment of the present application, the trading elements of the option to be analyzed may also be corrected, and specifically, the right price of the option to be analyzed may be corrected.

Specifically, the multiple options to be analyzed may have different due dates, the options to be analyzed that expire on the same day may have a right price, and the options to be analyzed that expire on the same day may be sorted based on the right prices of the options to be analyzed, so as to obtain initial right price sequences corresponding to the respective due dates, that is, each initial right price sequence is a sequence of right prices corresponding to the same due date.

Before the options to be analyzed that expire on the same day are sorted according to the option price, the options to be analyzed may be further divided into a call option and a call option, where generally speaking, the higher the option price is, the lower the price of the option is, and generally speaking, the lower the price of the option is, the higher the price of the option is, so that the trading element information of the options to be analyzed can be corrected through the initial option price sequence.

Specifically, the initial option price sequence may be fitted according to the arbitrage constraint to obtain a fitted option price sequence, and the revised trading element information of the option to be analyzed is determined based on the fitted option price sequence. Wherein, the arbitrage limiting condition may include at least one of option convexity condition, option butterfly arbitrage, option bear price difference arbitrage, option monotonicity, option upper and lower limits, etc.

The option prices of the options to be analyzed that satisfy the arbitrage constraint condition are in the fitted option price sequence after fitting, and the option prices of the options to be analyzed that do not satisfy the arbitrage constraint condition are corrected and then in the fitted option price sequence after fitting, that is, the option prices of the options to be analyzed that satisfy the arbitrage constraint condition are the same in the initial option price sequence and the fitted option price sequence, and the option prices of the options to be analyzed that do not satisfy the arbitrage constraint condition are different in the initial option price sequence and the fitted option price sequence, so that whether the options to be analyzed satisfy the arbitrage constraint condition can be identified.

It is understood that the option price of the option to be analyzed that does not satisfy the arbitrage limiting condition may not be reasonable, and thus the theoretical price of the option can be re-determined by using the option information processing method provided in the embodiment of the present application as the target option.

The arbitrage limiting conditions are briefly described below.

Specifically, the option convexity condition may be represented by the following formula:

option monotonicity may be expressed by the following equation:

the option upper and lower limits can be expressed by the following formula:

wherein i represents an option index in the initial option price sequence, i is a positive integer, and m is an option price; x is the option price, r is the market risk-free interest rate; t is the remaining expiration time of the option to be analyzed.

The option butterfly arbitrage is to use the price difference of different delivery months to make arbitrage, and is formed from two cross-period arbitrages which are opposite in direction and share the contract of intermediate delivery months. The option strategy is limited in risk and limited in profit, and is formed by combining a bull market arbitrage with a bear market arbitrage. It is a synthetic form in arbitrage trading, where the whole arbitrage involves three contracts. As the name suggests, the butterfly-type condom is like a butterfly, and the wings are symmetrical on two sides of the body. Three contracts in futures arbitrage are the closer month contract, the forward contract and the further contract, which we call the near end, the middle, the far end.

The option butterfly arbitrage and the option bear price difference arbitrage can be represented by the following formulas:

m_i+2-2*m_i+1+m_i≥0；

wherein i represents the option index in the initial option price sequence, i is a positive integer, and m is the option price.

In the embodiment of the application, the options to be analyzed are corrected by arbitrage limiting conditions, so that unreasonable options can be corrected according to the association between the options to be analyzed, subsequent operation is performed according to reasonable options, and the reliability of a theoretical price calculation program is improved.

And S102, calculating market implicit fluctuation rates of the options to be analyzed according to the corrected trading element information of the options to be analyzed.

The volatility is a measure of the volatility of the profit realized by the asset, and the implicit volatility of the option is a specific attribute of the option, which means the standard deviation of the rate of return of the option before the arrival date, and is the volatility capable of showing the market prospect. Generally speaking, the greater the implied volatility of the option, the greater the risk, the greater the benefit, and the greater the entitlement.

After the trading element information of the options to be analyzed is corrected, the market implicit fluctuation rates of the options to be analyzed can be calculated according to the corrected trading element information of the options to be analyzed. Where the due date and the right price of the option to be analyzed may reflect, to some extent, the price of the target asset in the market, for example, in the option to be analyzed with a 4-month-18-day due, the right price of copper is $ 2000/ton, in the option to be analyzed with a 5-month-18-day due, the right price of copper is $ 1900/ton, and copper is considered to be increasing in value within one month after 4-month-18-day.

Therefore, the forward predicted price of the target asset on the due date can be calculated according to the corrected trading element information of the option to be analyzed based on the forward price fitting algorithm.

According to the forward price fitting algorithm, the due date and the right price of the option to be analyzed can be analyzed, the option flat price arbitrage space is removed, and the forward predicted price corresponding to each due date is obtained. The forward price fitting algorithm can be referred to the following equation:

wherein, K_iThe right price of the row of the ith option to be analyzed; c_iThe price of the call option for the ith option to be analyzed; p_iA drop option price for the ith option to be analyzed; r is the market risk-free interest rate; t is the remaining expiration time of the option to be analyzed; d is the market correction price rising water sticking rate; the trading cost can be set according to the situation, in the scheme, the trading cost is assumed to be 0, N is the number of options to be processed, and here, the option contract to be analyzed can be arbitrarily set by itself and does not need to be included in all option contracts to be analyzed for calculation. And d is obtained by eliminating the flat price arbitrage space algorithm, and the reference formula is as follows:

that is, the price of the target asset from which the option market forecast can be calculated, ForwardPrice ═ S ^ (T (r-d)), that is, ForwardPrice, is the forward forecast price of the corrected target asset under the excluded flat price arbitrage space.

The flat price arbitrage space is that arbitrage opportunities are generated due to the fact that price balance between original options is damaged when the option prices deviate from theoretical prices, and long-term predicted prices obtained through calculation after the flat price arbitrage space is removed are more accurate.

According to the forward predicted price of the target property on the due date, the market implicit fluctuation rate of the option to be analyzed can be calculated, the European option is calculated through the European implicit fluctuation rate algorithm, and the American option is calculated through the American implicit fluctuation rate algorithm.

S103, obtaining the corresponding relation between the right price and the market implicit fluctuation rate according to the right price of the right to be analyzed and the market implicit fluctuation rate of the right to be analyzed.

After the market hidden fluctuation rate of the option to be analyzed is obtained through calculation, the option to be analyzed has the option price, so that the corresponding relation between a plurality of option prices and the market hidden fluctuation rate can be obtained. For example, if the first option to be analyzed has a first right price and a first market hidden fluctuation rate, and the second option to be analyzed has a second right price and a second market hidden fluctuation rate, the first right price and the first market hidden fluctuation rate have a corresponding relationship, and the second right price and the second market hidden fluctuation rate have a corresponding relationship.

The market implicit fluctuation rate of the option to be analyzed is obtained according to the trading element information of the option to be analyzed, so that the option to be analyzed is the option really existing in the market and can reflect the characteristics of the market, the market implicit fluctuation rate of the option to be analyzed can also reflect the characteristics of the market and has certain reliability, and the corresponding relation between the obtained price of the option and the market implicit fluctuation rate also has reliability.

In the embodiment of the application, the real and imaginary degrees of the option to be analyzed can be further calculated, the option to be analyzed is screened based on the calculated real and imaginary degrees, and interpolation calculation is performed according to the row right price and the market implicit fluctuation rate of the option to be analyzed, which are obtained through screening, so as to obtain the corresponding relationship between the row right price and the market implicit fluctuation rate.

Among them, The real option (In The Money, ITM) can also be called The price option. For a call option, the real-valued option is an option contract with a right price that is lower than the hooked-up asset price. For a put option, the real-valued option is an option contract with a right price higher than the hooked-up asset price.

Out of The Money, OTM, can also be called extra-price options. For a call option, the null option is an option contract with a row price hook higher than the underlying asset price. For a yield option, the null option is an option contract with a right of way price lower than the hooked-up asset price.

The flat option (At The Money, ATM) is The option contract with The highest running price and The highest hooked-up asset price. Usually, in most cases, no real flat option contracts exist on the market, i.e. the option price is exactly equal to the hook mark asset price.

The option buyer purchases the option because the option buyer has a rising trend to the price of the subject matter; the option is also called a sell option, which means that the buyer of the option has the right to sell a certain amount of target objects to the seller of the sell option according to the price of the right of way in the validity period of the option, and the option buyer purchases the option because the price of the target objects is considered to have a tendency to drop.

The option to be analyzed is screened through the real and imaginary values of the option to be analyzed, the option to be analyzed which is not interested by the user or the exchange can be removed to a certain extent, so that the interested option to be analyzed is screened out, and then interpolation operation is carried out according to the option price and the market hidden fluctuation rate of the option to be analyzed, which are obtained through screening, so as to obtain the corresponding relation between the option price and the market hidden fluctuation rate. In other words, the method and the device assign values to uninterested options to be analyzed according to interpolation operation to obtain the market implicit fluctuation rate of the options, so that the market implicit fluctuation rate of the options converges towards the interested direction of the user or the exchange.

And S104, fitting the corresponding relation between the market implicit fluctuation rate and the row weight price based on a preset model to obtain the theoretical implicit fluctuation rate corresponding to the row weight price.

In the embodiment of the application, the market implicit fluctuation rate is a value corresponding to the row weight price, and the values are finite and scattered, so that the corresponding relation between the row weight price and the market implicit fluctuation rate can be fitted based on the preset model, and the corresponding relation between the row weight price and the implicit fluctuation rate according with the preset model is obtained. For the purpose of distinction, the implicit fluctuation rate before fitting is referred to as market implicit fluctuation rate, and the implicit fluctuation rate after fitting is referred to as theoretical implicit fluctuation rate.

The preset model can be provided by a user or a trading exchange, and the preset model can exist in the form of a function, such as a function of Nealder-Mead, LM, LP, and the like. The preset model is generally a function with model parameters, and the model parameters of the preset model can be obtained by fitting the corresponding relation between the right-of-way price and the market hidden fluctuation rate, so that the model parameters can be brought into the preset model to obtain the preset model with the model parameters, and the preset model can be matched with the corresponding relation between the right-of-way price and the market hidden fluctuation rate.

Of course, after the theoretical implicit fluctuation rate is obtained, the theoretical implicit fluctuation rate can be adjusted according to the historical fluctuation rate. This is because, if the theoretical implicit fluctuation rate is greater than the historical fluctuation rate, the theoretical implicit fluctuation rate may be overestimated, and the theoretical implicit fluctuation rate may be adjusted down appropriately, and if the theoretical implicit fluctuation rate is less than the historical fluctuation rate, the theoretical implicit fluctuation rate may be underestimated, and the theoretical implicit fluctuation rate may be adjusted up appropriately. Specifically, an adjustment value VolRange may be added to the function f (k) of the preset model, where k is the row weight value, and the adjustment value VolRange may be determined according to the situation, and the adjusted function of the preset model may be f (k) + VolRange.

In the embodiment of the application, the value of VolRange is determined by comparing the average value of the values of f (k) + VolRange under each row weight value with the historical fluctuation rate; the value of VolRange may also be determined by comparing a weighted average of the values of f (k) + VolRange at each row weight value to the historical volatility. Of course, the VolRange value may also be determined by comparing the values of the features of other functions that can embody the preset model with the historical fluctuation rate.

The corresponding relation between the right-of-way price and the market implicit fluctuation rate has reliability, the corresponding relation between the right-of-way price and the theoretical implicit fluctuation rate obtained based on the preset model fitting also has reliability, and meanwhile, the characteristics of the preset model are met, so that the expectation of a user or a trading exchange can be met.

And S105, obtaining a target hidden fluctuation rate corresponding to the right-of-way price of the target option according to the right-of-way price of the target option and the corresponding relation between the theoretical hidden fluctuation rate and the right-of-way price.

After the corresponding relationship between the theoretical implicit fluctuation rate and the right-of-way price is obtained, the target implicit fluctuation rate corresponding to the right-of-way price of the target right-of-way can be obtained according to the right-of-way price of the target right-of-way. Of course, the hook target of the target option is also the target asset, which is the same as the option to be analyzed, so that there is a uniform corresponding relationship between the price of the right and the implicit fluctuation rate. Specifically, if the correspondence between the theoretical implicit fluctuation rate and the row option price is expressed by a function, the row option price of the target option can be used as an argument, and the target implicit fluctuation rate corresponding to the row option price of the target option can be obtained by calculation.

Because the corresponding relation between the theoretical implicit fluctuation rate and the right-of-way price has market characteristics and meets the characteristics of the preset model, the determined right-of-way price of the target option also meets the market rules and meets the characteristics of the preset model, and therefore the right-of-way price is accurate.

In the embodiment of the present application, a flat option may also be identified from options to be analyzed, and of course, when calculating real and imaginary values in step S102, a flat option before analysis may be identified, or identification may be performed before or after step S101, without affecting the implementation of the embodiment of the present application.

After the flat-value option is identified, the flat-value implied fluctuation rate corresponding to the row weight price of the flat-value option can be obtained according to the row weight price of the flat-value option and the corresponding relation between the row weight price and the theoretical implied fluctuation rate, and the target implied fluctuation rate is adjusted according to the comparison result of the flat-value implied fluctuation rate and the historical fluctuation rate of the target asset or the comparison result of the flat-value implied fluctuation rate and the predicted fluctuation rate. Specifically, if the flat value implied fluctuation rate is greater than the historical fluctuation rate or the predicted fluctuation rate of the target asset, the implied fluctuation rate may be overestimated, the target implied fluctuation rate may be adjusted downward appropriately, and if the flat value implied fluctuation rate is less than the historical fluctuation rate or the predicted fluctuation rate of the target asset, the theoretical implied fluctuation rate may be underestimated, and the target implied fluctuation rate may be adjusted upward appropriately. Specifically, the adjustment VALUE atmpol _ VALUE may be added to the function σ of the preset model, where the adjustment VALUE atmpol _ VALUE may be determined according to the situation, and the function of the adjusted preset model may be σ + atmpol _ VALUE.

Of course, if the target option is one or more options in the options to be analyzed, the target implicit fluctuation rate of the target option and the flat implicit fluctuation rate of the flat option form a first-to-last curve, which is called a smile curve, and the smile curve is adjusted in an up-and-down translation manner according to the comparison result of the flat implicit fluctuation rate and the historical fluctuation rate of the target asset or the comparison result of the flat implicit fluctuation rate and the predicted fluctuation rate.

Therefore, the target implicit fluctuation rate of the target option can be adjusted according to the asset fluctuation rate of the target asset, so that the target implicit fluctuation rate is corrected in time, and the accuracy of the target implicit fluctuation rate is improved.

And S106, calculating the theoretical price of the target option according to the target implicit fluctuation rate.

Since the target implicit fluctuation rate corresponds to the row option price of the target option, the target implicit fluctuation rate is the implicit fluctuation rate of the target option, and the theoretical price of the target option can be calculated according to the target implicit fluctuation rate. Generally speaking, the greater the implied volatility of the option, the greater the risk, the greater the benefit, and the greater the entitlement.

As a possible implementation manner, the target option may also be one or more options in the options to be analyzed, and since the market implicit fluctuation rate of the options to be analyzed is fitted to obtain the theoretical implicit fluctuation rate, the obtained target implicit fluctuation rate is not necessarily the same as the market implicit fluctuation rate of the options to be analyzed, so that a more reasonable implicit fluctuation rate and a theoretical price calculated according to the implicit fluctuation rate can be provided for some options to be analyzed with unreasonable trading element information.

In the embodiment of the present application, a risk indicator of the target option may also be calculated according to the implicit fluctuation rate of the target option, and specifically, a greek risk indicator greens of the target option may be calculated.

In the process of calculating the theoretical price and the risk index of the target option, the european option can be calculated by adopting an european algorithm, and the american option can be calculated by adopting an american algorithm.

Referring to fig. 2, a schematic diagram of convergence of option information processing by using an option information processing method according to an embodiment of the present application is shown, where an abscissa is an index (index) of iteration times and an ordinate is an error rate (error), so that it can be seen that the error rate is significantly reduced after ten iterations, and thus the method can have a faster convergence rate and significantly reduce the amount of computation.

The embodiment of the application provides an option information processing method, which can firstly obtain trading element information of a plurality of options to be analyzed, the hook mark of the options to be analyzed is a target asset, market hidden fluctuation rates of the plurality of options to be analyzed are obtained through calculation according to the trading element information, corresponding relations between the option price of the target asset and the market hidden fluctuation rates are obtained according to the option price of the options to be analyzed and the market hidden fluctuation rates of the options to be analyzed, and the corresponding relations between the option price and the market hidden fluctuation rates are fitted based on a preset model to obtain the corresponding relations between the option price and the theoretical hidden fluctuation rates. In the embodiment of the application, trading element information of an option to be analyzed of an asset belonging to a certain hook target is obtained, wherein the trading element information specifically comprises an option market price, a right price, an expiration time and the like, the option market price under the condition of no arbitrage is obtained by performing denoising processing on the option market price based on arbitrage limiting conditions, a market hidden fluctuation rate of an option contract is obtained by calculation according to the revised trading element information of a plurality of options to be analyzed, a corresponding relation between the right price and the market hidden fluctuation rate can be fitted based on a preset model, so that a target hidden fluctuation rate of a target option is determined, and a theoretical price of the target option is obtained by calculation according to the target hidden fluctuation rate.

The embodiment considers the fluctuation rate structure analysis algorithm of the option contract implicit fluctuation rate, the expected factors of the market for the hooked target asset price and the hooked target asset fluctuation rate adjustment factor. The expected factors of the market participation main body for the asset price of the hook targets are brought into, and the tracking effect of option market pricing is improved; the asset fluctuation rate adjustment factor of the hook target is included, so that overlarge deviation amplitude between the option market price and the asset price of the hook target can be corrected, the extreme wrong pricing is prevented, and the option market is effectively associated with the asset of the hook target; the method is incorporated into a fluctuation rate structure analysis algorithm, namely an algorithm engine, can meet the requirements of different fluctuation rate fitting models, and achieves high adaptability, reusability and production application degree.

The following describes in detail the process of modifying the transaction element information in S101, in which a call option denoising algorithm is taken as an example.

The objective of the algorithm is to process the option original quotation, so that the option quotation meets the arbitrage condition limitation, namely market price noise is eliminated, and the data quality of the option quotation is ensured on the premise of ensuring the minimum change of the option quotation. Where y is an n-dimensional vector containing all the option prices, x is a corresponding n-dimensional vector containing the corresponding right prices, and the elements of x are assumed to be arranged in increasing order. m is the n-dimensional vector solution we are looking for, and the mathematical expression is:

(1) parameter-free denoising flow algorithm: and (3) correcting the quotation:

according to the derivation in the theoretical basis, the arbitrage limiting condition 1 is applied at the same time: option monotonicity and option upper and lower limits, for i ═ 1,2 … n-1, there are:

and arbitrage restriction condition 2: option convexity and butterfly arbitrage space, for i ═ 1,2 … n-2, there are:

note that we can optimize constraint 1 according to the arbitrage constraint 2, i.e. the slope of the function is monotonically increasing:

in most cases, the right prices are equidistant, and for the case where the right prices are not equidistant, reference can be made to the following method, whereby we can simplify the constraint 2 as:

m_i+2-2m_i+1+m_i≥0。

to this end, we have obtained a mathematical expression of the problem we are solving:

limited to a cumulative number n of constraints, for i ═ 1,2 … n-1, there are:

the method converts the conditions into a Dykstra projection algorithm, and the conversion model algorithm is as follows:

case where t is 1:

for such a least squares problem, we use a multidimensional mapping, i.e. a least squares solution limited by a convex cone. However, it should be noted that A.m-b.ltoreq.0 is not an n-dimensional convex cone expression and we still need to transform the problem so that the constraint becomes C.u. ltoreq.0.

Note that if we define u, v, z, C as:

thereby, it is possible to obtain:

is limited to

C.u≤0；t＝1。

Note that if we get a solution u ═ (z ═ 1) to this problem, we can get m ═ z × + y from z ═ m-y, and m in this problem meets the previous constraints:

the condition that t is 1 is relaxed to t is more than or equal to 0

However, since we have no restriction condition for obtaining a convex cone due to the presence of t ═ 1, we change the condition for t ≧ 1 to t ≧ 0, and the problem becomes

Limited to C.u ≦ 0; t is more than or equal to 0.

And (3) converting the solution of u under the condition that t is more than or equal to 0 into the solution under the condition that t is 1:

now, all the constraints have been converted into a convex cone form, thereby satisfying the conditions for using the Dykstra algorithm. Let us assume that we have a solution u ═ z, t when t ≧ 0. According to the above, u satisfies C.u ≦ 0, and further

A.z**+(A.y–b)≤0；

A.z**t*+(A.y–b)t*≤0。

Therefore, (z × t, t) also satisfies the constraints of C.u ≦ 0 and t ≧ 0, and we can obtain the optimal solution for u ═ 0 (z × t), which is the most appropriate solution

‖z^*‖²+‖t^*-1‖²≤‖z^**t^*‖²+‖t^*-1‖²，

Namely, it is

‖z^*‖²≤‖z^**t^*‖²。

At the same time, u should correspond to C.u^*Less than or equal to 0, i.e.

A.z*+(A.y–b)t*≤0；

A.z*/t*+(A.y–b)≤0。

Therefore (z × t, 1) should meet the constraints of C.u ≦ 0 and t ≦ 1, and since u ═ 1 is the optimal solution, we can get:

‖z^**t^*‖²≤‖z^*‖²。

in summary z^**t^*＝z^*Thus we can get m ═ z^*/t^*+ y. So far, we have converted the constraints of the original problem into constraints that conform to the multidimensional mapping algorithm.

The constraints may then be converted into a matrix form.

Meanwhile, two limiting conditions of C.u being less than or equal to 0 and t being more than or equal to 0 can be integrated, and when the C is a matrix with n rows and n +1 columns, a new limiting condition t being more than or equal to 0 can be added, so that a matrix with n +1 rows and n +1 columns can be obtained

The new row corresponds to the constraint that t ≧ 0, so according to the definition of u, this behavior (000 … 0-1).

To this end, the entire problem can be expressed as

In the following, we use C as default

The specific solution method is as follows:

let C_jLine j of C.u ≦ 0, therefore, C_jIs defined as one at

Convex cone in space, therefore C.u ≦ 0 is equivalent to ∩_jC_jAnd further the problem can be translated into:

subsequently, we will be in turn at C_jThe projection is carried out, and the specific flow is as follows:

a first set of cycles:

① definition of u_1,1Is v at C₁Projection of_1,1＝u_1,1V, i.e. u_1,1＝v+I_1,1；

② definition of u_1,2Is u_1,1At C₂Projection of_1,2＝u_1,2-u_1,1I.e. u_1,2＝v+I_1,1+I_1,2；

③……

④ definition of u_1,n+1Is u_1,nAt C_n+1Projection of_1,n+1＝u_1,n+1-u_1,nI.e. u_1,2＝v+I_1,1+I_1,2+…+I_1,n+1。

A second set of cycles:

① definition of u_2,1Is u_1,n+1-I_1,1At C₁Projection of_2,1＝u_2,1-(u_1,n+1-I_1,1) I.e. u_2,1＝I_2,1+(u_1,n+1-I_1,1)＝I_2,1+v+I_1,2+…+I_1,n+1；

② definition of u_2,2Is (u)_2,1-I_1,2) At C₂Projection of_2,2＝u_2,2-(u_2,1-I_1,2) I.e. u_2,2＝I_2,2+(u_2,1-I_1,2)＝I_2,1+I_2,2+v+I_1,3+…+I_1,n+1；

③……

For the mth set of cycles, we can use u directly_m,rOf the general formula (II)

u_m,rIs v + I_m,1+I_m,2+…+I_m,r-1+I_m-1,r+1+I_m-1,r+2+…+I_m-1,nAt C_rProjection of_m,r＝u_m,r-(v+I_m,1+I_m,2+…+I_m,r-1+I_m-1,r+1+I_m-1,r+2+…+I_m-1,n)。

When u is_m,r∈∩_jC_jThen, the optimal solution under the limiting condition is obtained, namely, the circulation can be quitted, and then the optimal solution is obtained according to the m-z^*/t^*+ y gives m.

When the number of cycles is m → ∞, u_m,rMust converge and so even if we cannot get the optimal solution directly, a solution with sufficient accuracy can be obtained after enough cycles.

Projection method of vector on convex cone without weight:

P(v|C_j) Is vector v at C_jThe expression for the projection above is:

projection method of vector on convex cone with weight:

now the evaluation function is added with a weight w, i.e.

Note that the constraints do not change with the additional weights, and what we need to change is only the projection formula, which is:

(2) a parametrically-free denoising algorithm: stationary data

In the process preliminary algorithm, the algorithm can ensure that the data accords with the limiting conditions, the option price data corrected by the algorithm is used by the local correction algorithm in the method, the market noise is further reduced, and the purpose of filtering and smoothing secondary noise is achieved.

Assuming the regression equation to be:

we can Taylor expand z around a series of x values, resulting in:

β_k(x)≡m^k(x)/k！。

further we can get a polynomial approximation of m (z) around x, which can take the values of the row option prices in turn for the price to be corrected, so we can get an approximation of the option prices around all the row option prices. For the selection of the expansion order p, it is not better that p is higher, because too large p value can cause the expansion to be unable to effectively filter noise, and too small p value can cause the omission of trend information.

For the fitting evaluation of the regression analysis, it is clear that we should assign higher weights in the vicinity of x, so we will introduce the kernel function K (), bandwidth h, weight defined as K_h(x_i-x)≡K((x_i-x)/h)/h。

There are many choices of kernel functions, such as parabolic, triangular, Gaussian, in this case we will choose a Gaussian kernel, i.e. a normally distributed weight, and we can obtain β_k(x) Is defined as a value that minimizes the following function:

in fact, we can observe β_k(x) Note that when p is equal to 0, this is a local constant fit, equivalent to Nadaraya-Watson fit, β this time_0,0(x) Comprises the following steps:

for other p values, we have a common β_kp(x) The formula:

wherein the content of the first and second substances,

when p is equal to 1, the compound is,

after the actual data verification under different values, the quality of the data can be best guaranteed when p is 1, which is not described herein.

Selecting the bandwidth of the kernel function:

the choice of bandwidth will greatly affect the data we get, for example, when h is very large, the local polynomial fit will become a polynomial fit, when p is equal to 1, we get a straight line, when h approaches 0, we will not make any change to the data, so the complexity of the choice of bandwidth is not inferior to that of our model. The bandwidth function selected by the method is a global bandwidth formula for minimizing mean square error integral, and the integral to be minimized is as follows:

we can thus derive the bandwidth function:

wherein, C_k,pDepending on the choice of kernel function, for a Gaussian kernel function, C_0,10.776. π (x) is the edge density function of the regression object, v (x) is its variance, m^(p+1)(x) The derivative is of order p +1, and none of the three terms is known to be selected. Here we choose a polynomial of order (p +3) to perform a conventional least squares fit to m (x), and the fitting result is expressed as

Furthermore, we can easily find the p +1 order derivative m^(p+1)(x) In that respect In the bandwidth function, we usually choose a weight function w (x) as w (x) ═ w₀(x) f (x), wherein,

where sd is the standard deviation, and we obtained

Further, h is obtained:

where ssr is the sum of the squares of the residuals.

Based on the option information processing method, the embodiment of the present application further provides an option information processing apparatus, and referring to fig. 3, the apparatus is a block diagram of the option information processing apparatus provided in the embodiment of the present application, and the apparatus includes:

a correcting unit 110, configured to correct the trading element information of the options to be analyzed according to the arbitrage limiting condition; the hook targets of the plurality of options to be analyzed are target assets;

a market implicit fluctuation rate calculation unit 120, configured to calculate market implicit fluctuation rates of the options to be analyzed according to the revised trading element information of the options to be analyzed;

a corresponding relationship obtaining unit 130, configured to obtain a corresponding relationship between the right price and the market implicit fluctuation rate according to the right price and the market implicit fluctuation rate of the right to be analyzed;

the fitting unit 140 is configured to fit the corresponding relationship between the row weight price and the market implicit fluctuation rate based on a preset model to obtain a corresponding relationship between the row weight price and the theoretical implicit fluctuation rate;

a target implicit fluctuation rate calculation unit 150, configured to obtain a target implicit fluctuation rate corresponding to the row option price of the target option according to the row option price of the target option and a correspondence between the row option price and the theoretical implicit fluctuation rate; the hook target of the target option is a target asset;

and a theoretical price calculating unit 160, configured to calculate a theoretical price of the target option according to the target implicit fluctuation rate.

Optionally, the market implicit fluctuation rate calculating unit includes:

Optionally, the modifying unit includes:

Optionally, the apparatus further comprises:

Optionally, the correspondence obtaining unit includes:

Optionally, the apparatus further comprises:

the theoretical price calculating unit is specifically configured to:

Optionally, the fitting unit is specifically configured to:

Optionally, the apparatus further comprises:

the memory for storing program code;

The name "first" in the names "first … …", "first … …", etc. mentioned in the embodiments of the present application is only used for name identification, and does not represent the first in sequence. The same applies to "second" etc.

As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that all or part of the steps in the above embodiment methods can be implemented by software plus a general hardware platform. Based on such understanding, the technical solution of the present application may be embodied in the form of a software product, which may be stored in a storage medium, such as a read-only memory (ROM)/RAM, a magnetic disk, an optical disk, or the like, and includes several instructions for enabling a computer device (which may be a personal computer, a server, or a network communication device such as a router) to execute the method according to the embodiments or some parts of the embodiments of the present application.

The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for the apparatus embodiment, since it is substantially similar to the method embodiment, it is relatively simple to describe, and reference may be made to some descriptions of the method embodiment for relevant points. The above-described embodiments of the apparatus and system are merely illustrative, wherein modules described as separate parts may or may not be physically separate, and parts shown as modules may or may not be physical modules, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.

The above description is only a preferred embodiment of the present application and is not intended to limit the scope of the present application. It should be noted that, for a person skilled in the art, several improvements and modifications can be made without departing from the scope of the present application, and these improvements and modifications should also be considered as the protection scope of the present application.

Claims

1. An option information processing method, characterized in that the method comprises:

2. The method according to claim 1, wherein the calculating the market implicit fluctuation rate of the plurality of options to be analyzed according to the revised trading element information of the plurality of options to be analyzed comprises:

3. The method according to claim 1, wherein the modifying the trading element information of the plurality of options to be analyzed according to the arbitrage constraint comprises:

4. The method of claim 3, further comprising:

5. The method according to claim 1, wherein obtaining the correspondence between the right-of-way price and the market implicit fluctuation rate according to the right-of-way price of the option to be analyzed and the market implicit fluctuation rate of the option to be analyzed comprises:

calculating the real and imaginary degrees of the option to be analyzed;

screening the option to be analyzed based on the excess and deficiency degrees;

6. The method of claim 1, further comprising:

identifying a flat-valued option from the options to be analyzed;

7. The method of any one of claims 1-6, wherein the arbitrage limiting conditions comprise at least one of: option convexity condition, option monotonicity, option upper and lower limits, option butterfly arbitrage, option bear price difference arbitrage.

8. The method according to any one of claims 1 to 6, wherein the fitting the corresponding relationship between the row weight price and the market implicit fluctuation rate based on a preset model to obtain the corresponding relationship between the row weight price and the theoretical implicit fluctuation rate comprises:

9. The method of any one of claims 1-6, further comprising:

10. An option information processing apparatus, comprising: