CN111507838A - Value evaluation system and method capable of converting bonds - Google Patents
Value evaluation system and method capable of converting bonds Download PDFInfo
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Abstract
The invention discloses a value evaluation system of convertible bonds, which relates to the technical field of convertible bonds and comprises a parameter initialization module, a stock price fluctuation rate calculation module, a standard American convertible bond value calculation module, a singular option value calculation module, a stock price path analysis module, a convertible bond pricing module and a result output module. The invention adopts the algorithm design of the partial differential equation pricing model, has higher calculation efficiency, and can quickly obtain the value of the convertible bond and the optimal conversion execution boundary.
Description
Technical Field
The invention belongs to the technical field of convertible bonds, and particularly relates to a value evaluation system and method of a convertible bond.
Background
A convertible bond is a bond that the bond holder has the right to convert to stock before the bond expires according to the price of the conversion agreed upon when the bond was issued. If the convertible bond holder does not choose to convert the convertible bond to stock, holding of the convertible bond may continue until the convertible bond's life cycle ends to obtain bond face value and interest agreement. Convertible bonds are an important enterprise financing tool. With the continuous development of the financial market, financial innovation tools are continuously emerging, and convertible bonds containing different terms are continuously released in the capital market. In recent years, a convertible bond having a term of a resettable bargaining price, which is set to a term of a reset bargaining price, is popular with the capital market, and when the stock price does not reach the excess bargaining execution price within the lifetime of the convertible bond and falls to a trigger price of the reset bargaining price, the bargaining execution price of the convertible bond is adjusted down to a prearranged bargaining price, which is advantageous for a holder of the convertible bond to convert the bond into a stock.
Convertible bonds have both bond attributes and option attributes, and contain both bond value and option value. Convertible bonds can be selected to be converted into stocks at any time before the bond duration expires, so the options contained in the convertible bonds are American options; the resettable stock price terms indicate that the american option is a path dependent option. Resettable bargaining terms complicate the value assessment of the convertible bond.
Common convertible bond value evaluation methods include binary tree methods, Monte Carlo simulation methods, and partial differential equation methods. Binary tree methods are less suitable for pricing path dependent options; the Monte Carlo simulation method can price the option-dependent option of the path, but is not good at pricing American option, and needs longer calculation time. Options contained in convertible bonds with resettable bargaining terms are both american and path-dependent options, binary tree methods are not suitable for calculation, and the algorithm of monte carlo simulation method is complicated, resulting in a long calculation time.
Accordingly, those skilled in the art have endeavored to develop a value assessment system and method that can convert bonds.
Disclosure of Invention
In view of the above-mentioned drawbacks of the prior art, the present invention is to design a value evaluation system and method for convertible bonds with restorable equity terms, which constructs a partial differential equation pricing model and a design algorithm for the convertible bond pricing problem with complex terms to achieve fast and accurate evaluation.
The inventor has found through analysis that the partial differential equation method can be used as a method for convertible bond value evaluation because the partial differential equation method has higher calculation efficiency and can also process American options and path-dependent options. Resettable tranche price terms complicate the differential equation pricing model construction of convertible bonds. The stock price rise is beneficial to converting bonds into stocks, thereby improving the value of the convertible bonds; the stock price drop is beneficial to the restitution of the conversion price of the convertible bond (namely, the conversion price is adjusted downwards), so that the value of the convertible bond amount can be improved. In addition, the partial differential equation method calculates both the value of convertible bonds and the optimal equity conversion enforcement boundary.
The inventor firstly decomposes the convertible bond containing the resettable conversion price terms into two standard American convertible bonds and one embedded singular option according to the difference of the stock price paths: (1) if the stock price is always larger than the trigger price for resetting the transfer price and the initial transfer price is reached, the convertible bond can not be reset at a later time, which means that the convertible bond can be regarded as a standard American convertible bond with the initial transfer price as the transfer price, and the value of the convertible bond is recorded as V1(ii) a (2) If the stock price is always smaller than the initial transfer price and the trigger price for resetting the transfer price is reached, the convertible bond resets the transfer price immediately according to the terms agreed at the time of issuance, which means that the convertible bond can be regarded as a standard American type convertible bond with the reset transfer price as the transfer price after resetting the transfer price, and the value of the convertible bond is recorded as V2(ii) a (3) If the stock price has not reached the initial transfer price and the trigger price to reset the transfer price is not reached, then the value of this convertible bond is the sum of two partial values: part of standard American option value V using initial stock-change price as stock-change price1Another part is the opportunity to reset the turn price so as to reduce the value V brought by the turn price3Then the convertible bond value in this case is V1+V3。
And secondly, respectively establishing a value evaluation model for two standard American convertible bonds with different conversion rates and one embedded singular option. Therein is directed toThe value evaluation models of the two standard American convertible bonds are partial differential equations with free boundaries, and the difference between the two convertible bonds is different in stock conversion price; the value of the embedded singular options satisfies a partial differential equation whose boundary conditions depend on the solution V of the aforementioned free boundary problem1And V2。
Finally, inputting parameters in the model, solving the pricing model by using a numerical calculation method, and respectively obtaining corresponding values V of two standard American convertible bonds and one embedded singular option1、V2And V3And finally obtaining convertible bond value V containing the term of the resettable conversion price by combining the historical path of the stock price.
In one embodiment of the present invention, there is provided a value evaluation system of convertible bonds, including: the system comprises a parameter initialization module, a stock price fluctuation rate calculation module, a standard American convertible bond value calculation module, a singular option value calculation module, a stock price path analysis module, a convertible bond pricing module and a result output module; the parameter initialization module inputs initialization parameters; the stock price fluctuation rate calculation module calculates a stock price fluctuation rate sigma; the standard American convertible bond value calculation module calculates to obtain a standard American convertible bond value and an optimal conversion execution boundary; the singular option value calculation module calculates the value of the singular option; the stock price path analysis module inputs stock price historical data of the convertible bond between the initial day and the convertible bond value evaluation day, and analyzes and obtains price path characteristics of the stock; the convertible bond pricing module calculates to obtain convertible bond pricing; and the result output module outputs a calculation result and a graph.
Optionally, in the convertible bond value evaluation system in the above embodiment, the initialization parameters include the risk free rate r, the continuous share rate q of the stock, the initial conversion price E, and the reset conversion price E1Resetting the trigger price S of the stock pricerThe expiration time T of the convertible bond, the face value Z of the convertible bond and the face interest rate k of the convertible bond.
Optionally, in the convertible bond value evaluation system according to any of the above embodiments, the stock price fluctuation rate calculation module includes a first stock price fluctuation rate calculation unit that selects to directly input a stock price fluctuation rate σ value, and a second stock price fluctuation rate calculation unit that inputs stock historical trading price data for a period of time in a format of EXCE LL, the unit providing a stock price fluctuation rate calculation function to obtain the stock price fluctuation rate σ.
Optionally, in the value evaluation system for convertible bonds in any of the above embodiments, the standard american type convertible bond value calculation module calculates a standard american type convertible bond value and an optimal conversion execution boundary.
Optionally, in the convertible bond value evaluation system according to any of the above embodiments, the standard american convertible bond value calculation module includes a convertible bond value calculation first unit and a convertible bond value calculation second unit, the convertible bond value calculation first unit calculates a standard american convertible bond value with an initial equity conversion price as an equity conversion price, and obtains a corresponding optimal equity conversion execution boundary; the convertible bond value calculation second unit calculates a standard american type convertible bond value with the converted stock price after the resetting as the converted stock price, and obtains a corresponding optimum converted stock execution boundary.
Optionally, in the convertible bond value evaluation system in any of the above embodiments, the convertible bond pricing module calculates two standard american convertible bonds and one embedded singular option value, i.e., V, based on the price path characteristics of the stock during the convertible bond lifetime and the calculated price path characteristics of the stock1、V2And V3。
Optionally, in the convertible bond value evaluation system in any of the above embodiments, the convertible bond pricing includes bond value V corresponding to time t, stock price S, and an optimal conversion execution boundary.
Optionally, in the value evaluation system for convertible bonds in any of the above embodiments, the result output module outputs the calculation result and the graph including the bond value V corresponding to the time t and the stock price S and the optimal conversion execution boundary graph.
In another embodiment of the present invention, based on any one of the above embodiments, there is provided a convertible bond value evaluation method, including the steps of:
step S100, initializing parameters;
step S200, determining the fluctuation rate of the stock price;
step S300, calculating the value of the standard American convertible bond;
s400, calculating the value of the embedded singular option;
step S500, analyzing a stock price historical path;
step S600, calculating pricing of bonds can be converted;
and S700, outputting a calculation result and a graph.
Optionally, in the convertible bond value evaluation method in the above embodiment, the parameter initialization in step S100 refers to inputting initialization parameters, including the risk-free interest rate r, the continuous share percentage q, the initial conversion price E, and the reset conversion price E1Resetting the trigger price S of the stock pricerThe expiration time T of the convertible bond, the face value Z of the convertible bond and the face interest rate k of the convertible bond.
Alternatively, in the convertible bond value evaluation method in any of the above embodiments, the stock price fluctuation rate σ is calculated in step S200 by acquiring stock closing price data for a period of time.
Optionally, in the value evaluation method of convertible bonds in any of the above embodiments, step S200 includes:
s201, obtaining stock closing price data S in a period of timei(i ═ 0,1, …, n), where SiIndicating the stock closing price of the ith day;
s202, calculating the logarithmic yield of the stock price
S203, calculating viStandard deviation of (2)
S204, calculating to obtain the fluctuation rate of the stock price
Optionally, in the value evaluation method of convertible bonds in any of the above embodiments, step S300 includes:
s301, obtaining initialization parameters;
s302, calculating standard American convertible bond value V by applying prediction-correction finite difference algorithm1And V2；
S303, calculating V1And V2The corresponding optimal turn execution boundary.
Further, in the value evaluation method of convertible bonds in the above embodiment, the model solved by the prediction-correction finite difference algorithm in S302 is as follows:
wherein, V1For the standard American convertible bond value with initial converted stock price as converted stock price, V2The standard American convertible bond value using the converted stock price after the replacement as the converted stock price is that r is the risk-free interest rate, q is the continuous dividend rate of the stock, E is the initial converted stock price, E1The converted stock price after reset, T the convertible bond expiration time, Z the convertible bond face value, k the convertible bond face interest rate,
And
is equal to V1And V2The corresponding optimal turn execution boundary.
Optionally, in the value evaluation method of convertible bonds in any of the above embodiments, step S400 includes:
s401, obtaining initialization parameters and standard American convertible bond value V1And V2；
S402, calculating to obtain the value V of the embedded singular option by applying an implicit central difference algorithm3。
Further, in the value evaluation method of convertible bonds in the above embodiment, the model solved by the implicit central difference algorithm in S402 is as follows:
wherein, V3For the value of the embedded singular option, r is the risk free interest rate, q is the stock continuous dividend rate, E is the initial turn-to-stock price, T is the expiration time of the convertible bond, SrTo reset the trigger price for the change of stock price, V1For the standard American convertible bond value with initial converted stock price as converted stock price, V2The bond value can be converted for the standard American style taking the converted stock price after reset as the converted stock price.
Optionally, in the value evaluation method of convertible bonds in any of the above embodiments, step S500 includes:
s501, analyzing historical paths of bonds, namely analyzing historical price data between the initial day of the bonds and the evaluation day of the bond value;
s502, judging whether the historical price reaches the initial stock conversion price;
s503, judging whether the historical price reaches the trigger price for resetting the transfer price.
Alternatively, in the convertible bond value evaluation method in any of the above embodiments, step S600 obtains three values V from historical path analysis and calculation of stock prices1、V2And V3The calculation of convertible bond pricing includes calculation of bond value V and optimal conversion execution boundaries for time t, stock price S.
Optionally, in the value evaluation method of convertible bonds in any of the above embodiments, the value formula V (S, t) of the convertible bonds in step S600 is:
wherein
τ1Is the time, tau, at which the stock price first reaches the initial turn-to-stock price E2It is the time when the stock price first reaches the trigger price Sr that resets the transfer price.
Optionally, in the value evaluation method of convertible bonds in any of the above embodiments, the calculation result and graph of step S700 includes bond value V corresponding to time t and stock price S and an optimal conversion execution boundary diagram.
The method is different from a pricing technology based on a Monte Carlo simulation method, the convertible bond value evaluation method adopts value decomposition, so that investors can understand the value composition of convertible bonds containing special terms more deeply, the value connotation of financial investment products is better mastered, and the investors can be helped to select investment products suitable for themselves more pertinently and avoid investment risks; each value after decomposition is simple and easy to calculate, which is beneficial to simplifying model construction and algorithm design and is also beneficial to construction of a hedge strategy; the algorithm design of the partial differential equation pricing model is adopted, the calculation efficiency is high, and the value of convertible bonds and the optimal conversion execution boundary can be quickly obtained.
The conception, the specific structure and the technical effects of the present invention will be further described with reference to the accompanying drawings to fully understand the objects, the features and the effects of the present invention.
Drawings
FIG. 1 is a block diagram illustrating a value evaluation system for convertible bonds in accordance with an exemplary embodiment;
FIG. 2 is a flow chart illustrating a value assessment method of convertible bonds in accordance with an illustrative embodiment;
FIG. 3 is a block diagram illustrating a stock price volatility calculation module in accordance with an illustrative embodiment;
fig. 4 is a block diagram illustrating a standard american convertible bond value calculation module according to an exemplary embodiment.
Detailed Description
The technical contents of the preferred embodiments of the present invention will be more clearly and easily understood by referring to the drawings attached to the specification. The present invention may be embodied in many different forms of embodiments and the scope of the invention is not limited to the embodiments set forth herein.
In the drawings, structurally identical elements are represented by like reference numerals, and structurally or functionally similar elements are represented by like reference numerals throughout the several views. The size and thickness of each component shown in the drawings are arbitrarily illustrated, and the present invention is not limited to the size and thickness of each component. The thickness of the components is exaggerated somewhat schematically and appropriately in order to make the illustration clearer.
The inventor designs a value evaluation system of convertible bonds, as shown in fig. 1, which comprises a parameter initialization module, a stock price fluctuation rate calculation module, a standard American convertible bond value calculation module, a singular option value calculation module, a stock price path analysis module, a convertible bond pricing module and a result output module; the parameter initialization module inputs initialization parameters including risk-free interest rate r, continuous share rate q, initial stock conversion price E and reset stock conversion price E1Resetting the trigger price S of the stock pricerThe expiration time T of the convertible bond, the face value Z of the convertible bond and the face interest rate k of the convertible bond; the stock price fluctuation rate calculation module calculates a stock price fluctuation rate sigma; the standard American convertible bond value calculation module calculates to obtain a standard American convertible bond value and an optimal conversion execution boundary; the singular option value calculation module calculates the value of the singular option; the stock price path analysis module inputs stock price historical data of the convertible bond between the initial day and the convertible bond value evaluation day, and analyzes and obtains price path characteristics of the stock; the convertible bond pricing module calculates convertible bond pricing based on price path characteristics of the stocks in the convertible bond storage period and two calculated standardsAmerican convertible bond and an embedded singular option value, including bond value V corresponding to time t, stock price S and optimal conversion execution boundary, i.e. V1、V2And V3(ii) a And the result output module outputs a calculation result and a graph, wherein the calculation result comprises the bond value V corresponding to the time t and the stock price S and the optimal stock conversion execution boundary graph.
In this embodiment, as shown in fig. 3, the inventor designs that the stock price fluctuation rate calculation module comprises a first unit for calculating the stock price fluctuation rate and a second unit for calculating the stock price fluctuation rate, wherein the first unit for calculating the stock price fluctuation rate selects to directly input the stock price fluctuation rate σ, the second unit for calculating the stock price fluctuation rate inputs the stock historical trading price data for a period of time in the format of EXCE LL, and the second unit for calculating the stock price fluctuation rate provides a function for calculating the stock price fluctuation rate σ to obtain the stock price fluctuation rate σ.
In this embodiment, as shown in fig. 4, the inventor designs a standard american convertible bond value calculation module including: a convertible bond value calculating first unit and a convertible bond value calculating second unit, wherein the convertible bond value calculating first unit calculates standard American convertible bond value with the initial conversion price as the conversion price, and obtains a corresponding optimal conversion execution boundary; the convertible bond value calculation second unit calculates a standard american type convertible bond value with the converted stock price after the resetting as the converted stock price, and obtains a corresponding optimum converted stock execution boundary.
Based on any one of the above embodiments, the inventor provides a value evaluation method for convertible bonds, as shown in fig. 2, comprising the following steps:
step S100, initializing parameters, inputting initialization parameters in a parameter initialization module, wherein the initialization parameters comprise risk-free interest rate r, continuous share rate q of stocks, initial stock conversion price E and reset stock conversion price E1Resetting the trigger price S of the stock pricerConvertible bond expiration time T, convertible bond face value Z and convertible bond face interest rate k;
step S200, determining a stock price fluctuation rate, executing in a stock price fluctuation rate calculation module, selecting a first unit for calculating the stock price fluctuation rate to directly input a stock price fluctuation rate sigma, inputting stock historical trading price data of a period of time in an EXCE LL table format by a second unit for calculating the stock price fluctuation rate, and providing a stock price fluctuation rate calculation function by the second unit for calculating the stock price fluctuation rate to obtain the stock price fluctuation rate sigma, wherein the method specifically comprises the following steps:
s201, obtaining stock closing price data S in a period of timei(i ═ 0,1, …, n), where SiIndicating the stock closing price of the ith day;
s202, calculating the logarithmic yield of the stock price
S203, calculating viStandard deviation of (2)
S204, calculating to obtain the fluctuation rate of the stock price
Step S300, calculating the value of the standard american-style convertible bond, which is executed in the standard american-style convertible bond value calculation module, and specifically includes:
s301, obtaining initialization parameters;
s302, calculating standard American convertible bond value V by applying prediction-correction finite difference algorithm1And V2The solved model is as follows:
wherein, V1For the standard American convertible bond value with initial converted stock price as converted stock price, V2The standard American convertible bond value using the converted stock price after the replacement as the converted stock price is that r is the risk-free interest rate, q is the continuous dividend rate of the stock, E is the initial converted stock price, E1Is heavyThe later converted stock price, T is the expiration time of the convertible bond, Z is the face value of the convertible bond, k is the face interest rate of the convertible bond,
And
performing a boundary for the respective optimal turn;
s303, calculating to obtain V1And V2Corresponding optimal turn execution boundaries
And
step S400, calculating the value of the embedded singular option, specifically comprising:
s401, obtaining initialization parameters and standard American convertible bond value V1And V2；
S402, calculating the value V of the embedded singular option by applying an implicit central difference algorithm3The formula is as follows:
wherein, V3For the value of the embedded singular option, r is the risk free interest rate, q is the stock continuous dividend rate, E is the initial turn-to-stock price, T is the expiration time of the convertible bond, SrTo reset the trigger price for the change of stock price, V1For the standard American convertible bond value with initial converted stock price as converted stock price, V2The bond value can be converted for the standard American style taking the converted stock price after reset as the converted stock price.
Step S500, analyzing a stock price historical path, specifically comprising:
s501, analyzing historical paths of bonds, namely analyzing historical price data between the initial day of the bonds and the evaluation day of the bond value;
s502, judging whether the historical price reaches the initial stock conversion price;
s503, judging whether the historical price reaches the trigger price for resetting the transfer price.
Step S600, calculating bond pricing can be converted, and three values V obtained through analysis and calculation of historical paths of share prices1、V2And V3Finally, the following convertible bond value formula V (S, t) is obtained:
wherein
τ1Is the time, tau, at which the stock price first reaches the initial turn-to-stock price E2The stock price reaches the trigger price S for resetting the stock price for the first timerThe time of (d);
and S700, outputting a calculation result and a graph, wherein the calculation result comprises the bond value V corresponding to the time t and the stock price S and the optimal transfer execution boundary graph.
Taking the Guanghua transformation bond (code 128051) as an example, the value of the convertible bond of 12 months and 14 days in 2019 is calculated, and the relevant parameters are respectively: the expiration time T of the bond is 5, the face value Z of the convertible bond is 100, the fluctuation rate sigma is 0.332, the continuous dividend rate q of the stock is 0.006, the risk-free interest rate r is 0.04, the conversion price E is 16.95, E112.72, the bond face interest rate k is 0.005, and the application value calculation system can calculate the convertible bond value under the corresponding stock price as shown in table 1.
TABLE 1
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.
Claims (10)
1. A value evaluation system of convertible bonds is characterized by comprising a parameter initialization module, a stock price fluctuation rate calculation module, a standard American convertible bond value calculation module, a singular option value calculation module, a stock price path analysis module, a convertible bond pricing module and a result output module; the parameter initialization module inputs initialization parameters; the stock price fluctuation rate calculation module calculates a stock price fluctuation rate sigma; the standard American convertible bond value calculation module calculates to obtain a standard American convertible bond value and a corresponding optimal conversion execution boundary; the singular option value calculation module calculates the value of the singular option; the stock price path analysis module inputs stock price historical data of the convertible bond between the initial day and the convertible bond value evaluation day, and analyzes and obtains price path characteristics of the stock; the convertible bond pricing module calculates to obtain convertible bond pricing; and the result output module outputs a calculation result and a graph.
2. The convertible bond value evaluation system of claim 1, wherein the initialization parameters comprise an inauguration interest rate r, a stock continuous dividend rate q, an initial equity conversion price E, a reset equity conversion price E1Resetting the trigger price S of the stock pricerThe expiration time T of the convertible bond, the face value Z of the convertible bond and the face interest rate k of the convertible bond.
3. The convertible bond value evaluation system of claim 1, wherein the stock price fluctuation rate calculation module comprises a stock price fluctuation rate calculation first unit that selects to directly input the stock price fluctuation rate σ value and a stock price fluctuation rate calculation second unit that inputs the stock historical trading price data for a period of time in the EXCE LL table format, the unit providing the stock price fluctuation rate calculation function to obtain the stock price fluctuation rate value.
4. The convertible bond value evaluation system according to claim 1, wherein the standard american-type convertible bond value calculation module includes a convertible bond value calculation first unit that calculates a standard american-type convertible bond value with an initial equity conversion price as an equity conversion price and obtains a corresponding optimal equity conversion execution boundary; the convertible bond value calculation second unit calculates a standard american type convertible bond value with the converted stock price after the resetting as the converted stock price, and obtains a corresponding optimum converted stock execution boundary.
5. The convertible bond worth assessment system of claim 1, wherein said convertible bond pricing module is based on price path characteristics of stocks over the convertible bond lifetime and two standard american convertible bonds calculated and one embedded singular option value.
6. The convertible bond worth assessment system of claim 1, wherein said convertible bond pricing includes bond value versus time, stock price and optimal conversion enforcement boundaries.
7. A value evaluation method of convertible bonds using the value evaluation system of convertible bonds according to any of claims 1 to 6, characterized by comprising the steps of:
step S100, initializing parameters;
step S200, determining the fluctuation rate of the stock price;
step S300, calculating the value of the standard American convertible bond;
s400, calculating the value of the embedded singular option;
step S500, analyzing a stock price historical path;
step S600, calculating pricing of bonds can be converted;
and S700, outputting a calculation result and a graph.
8. A value evaluation method using the convertible bond of claim 7, wherein said step S200 comprises:
s201, stock closing price data in a period of time is acquired;
s202, calculating the logarithmic yield of the stock price;
s203, calculating the standard deviation of the logarithmic yield;
and S204, calculating to obtain the stock price fluctuation rate sigma.
9. A value evaluation method using the convertible bond of claim 7, wherein said step S300 comprises:
s301, obtaining initialization parameters;
s302, calculating the value of the standard American convertible bond by applying a prediction-correction finite difference algorithm;
and S303, calculating a corresponding optimal stranding execution boundary.
10. A value evaluation method using the convertible bond of claim 7, wherein said step S500 comprises:
s501, analyzing historical paths of bonds, namely analyzing historical price data between the initial day of the bonds and the evaluation day of the bond value;
s502, judging whether the historical price reaches the initial stock conversion price;
s503, judging whether the historical price reaches the trigger price for resetting the transfer price.
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