WO2009006872A1 - Verfahren zur ableitung eines zustandsraumes zur berechnung szenariobedingter, stochastischer kenngrössen - Google Patents
Verfahren zur ableitung eines zustandsraumes zur berechnung szenariobedingter, stochastischer kenngrössen Download PDFInfo
- Publication number
- WO2009006872A1 WO2009006872A1 PCT/DE2008/001054 DE2008001054W WO2009006872A1 WO 2009006872 A1 WO2009006872 A1 WO 2009006872A1 DE 2008001054 W DE2008001054 W DE 2008001054W WO 2009006872 A1 WO2009006872 A1 WO 2009006872A1
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- actions
- stochastic
- state space
- eur
- chronological sequence
- Prior art date
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
Definitions
- the invention relates to a method for deriving a state space for the calculation of stochastic parameters.
- the challenge consists in a precise notation that is understandable to a wide audience and clearly describes the timing of the strategy or the derivative.
- the presentation should be suitable for capturing as far as possible all quantitative aspects, for automated processing and storage. In addition, the presentation should minimize the manual effort required to calculate parameters such as risk metrics, optimal amounts of traded good, or the economic benefits of the trading strategy.
- the invention is based on the object to find a method that avoids the disadvantages described above and is easy to apply.
- This task is solved by a method of deriving a state space in which the problem is entered as a chronological sequence of actions in a memory, then an analysis of the chronological sequence of actions is performed on dependencies of the actions of each other and then the chronological sequence is converted into at least one sequentially calculable sequence of actions and from this scenario-related, stochastic parameters are calculated.
- the new programming concept represents a departure from this strict requirement because it allows access to a future value of a variable without losing the original chronological order.
- the method does not involve merely resorting the instructions to a sequentially calculable order, but the use of the original order for the calculation of stochastic parameters such as risk parameters and prices for the described processes.
- stochastic properties such as the expectation value are calculated on the basis of the set of all known variable values in the respective scenario - or an equivalent subset of these.
- the method extends precisely to the automatic use of this chronological information for the derivation of the stochastic values to be calculated.
- a pure permutation of the order in which first y and then x is calculated as the average of y would deviate from the methods.
- the method according to the invention can be used for different derivations of occupied rooms.
- the method can be used particularly advantageously if the problem is a financial mathematical problem.
- the chronological sequence is embedded in a procedural programming language.
- the procedural programming language specifies the chronological sequence of the actions as a command sequence.
- the chronological sequence can also be expressed as a markup language. This is understood to mean any markup language including XML and XML dialects. [25] Furthermore, the chronological sequence can be expressed as graphical notation. Such a graphical notation represents the chronological sequence of actions as flow or sequence diagram. Finally, the chronological sequence can also be expressed as UML or UML dialect.
- This state space contains at most all information that is known at the model time and minimally all information that is necessary to correctly calculate this conditional stochastic parameter.
- the procedure facilitates the modeling and analysis of financial mathematical problems and the procedure for using this technology includes the following steps in practice: 1. Reading the model of a financial mathematical problem in a domain-specific description language, which is based in their form on a sequentially evaluated programming language.
- storage may be a directed graph (dependency graph) in which actions are represented by nodes and dependencies by edges.
- Domain-specific descriptive languages in step 1 are markup languages such as XML, graphical description languages such as UML, and programming languages that list action by action in a chronological order using this chronological order to determine conditional stochastic size constraints.
- Possible actions in step 2 include evaluating formulas and assigning the result to a variable, as well as all other programming constructs for structuring the calculation sequence, such as modularization, function calls, loops, conditional branches, parallelization, and process synchronization.
- the described method leads to a reordering of the calculation order and the automatic determination of the condition for stochastic quantities.
- the possible stochastic function in step 3 are all functions that have a stochastic size on a measurable, ie at model time and taking into account the added Standsraumes determinable, depict value. Examples include: all central stochastic moments (expected value, variance, 7), skewness, kurtosis, quantiles, covariance, value at risk, conditional value at risk, and sharpe ratio.
- the invention relates to automatic conversion to corresponding conditional stochastic quantities.
- the invention includes the description of chronological processes, such as trading strategies based on stochastic functions. It also includes the resorting of computation instructions to a predictable order while using the original order for stochastic conditions. The arrangement of unsorted or in a for the calculation not relevant original order is not meant here.
- the method according to the invention involves the automatic derivation of relevant conditions for stochastic measures such as expected values or correlations due to the respective state space (state-space). Less relevant are descriptions with stochastic functions on explicitly specified conditions.
- the invention thus provides a technology for describing sequential operations in a manner that can be easily understood and easily converted into a numerical algorithm.
- Figure 1 is a flow chart of the analysis of a financial model
- Figure 3 is a complete dependency graph of the model variable
- Figure 4 shows a dependency graph for the calculation of the value of the variable V1, in which the variables known at time 1 are highlighted in gray and the other variables are still stochastic at that time
- Figure 5 shows a dependency graph for the calculation of the value of the variable V1, in which the information necessary for the calculation of the value of the variable V1 can be reduced to S1.
- This option refers to the average a of the respective share price S.
- the fair value of the financial mathematics results from the consideration of so-called risk-neutral scenarios with optimal exercise strategy of the option holder.
- the optimal strategy is to exercise the option as soon as the expected present value of option E (V) is less than the present value at immediate exercise max (a - K, 0) * EUR.
- V max (a * EUR - K * EUR, 0)% Exercise of the maturity date option [46]
- the financial product is synchronized with the stochastic model in ThetaScript via the theta function.
- the following example shows the definition of the processes of two variables EUR and S.
- the stochastic model does not necessarily have to be described in the same programming language as the structural model.
- the following code shows an implementation using the Matlab function Theta.m:
- the next step is breaking up into actions and finding a calculable action.
- V (I) max (a [248] * EUR [248] - K * EUR [248], 0)
- V in line 17 depends on: V [250], that is, on a [250], EUR [250], K, where K is deterministic.
- the time in line 17 is 249. At this time a [250] and EUR [250] are still unknown.
- Line 15 reveals that a [250] depends on a [249], S [250] and EUR [250].
- S [250] depends on S [249] and EUR [250] on EUR [249].
- three quantities are calculated, which are known at time 249 and are needed for the state space. That is, the conditional expected value to be calculated is E (Vla [249], S [249], EUR [249]).
- V in line 19 depends on: V [250] and V [249].
- V (I) max (a [248] * EUR [248] - K * EUR [248], 0)
- randn 1000,1 returns a vector with 1000 normally distributed random numbers.
- Theta.m The conditional expectation values are then calculated using regressions (E_regress (x, y)), as usual in the least-squares Monte-Carlo method [LS].
- the following insurance product is a simple financial product whose characteristics are also found in capital market life insurance policies.
- the product has a term of two years. At the end of each year, the customer receives a credit note (Variable P) in accordance with the capital market development (Variable S). The credit increases slightly by 4% of the stock index at the beginning of the year.
- the present model includes both sides, both payments to the customer and the portfolio value of the insurer (variable V). To minimize its risk, the insurer invests in the capital market. This strategy leads to a minimal variance in the payments to be made.
- Beta (X, Y) COV (X, Y) / VAR (Y)
- Beta (X, Y) argmin (VAR (X + ⁇ Y)) ⁇
- V V 1 + 1 - Beta (V t + 1 , S 1 + 1 ) * (S 1+ IS)
- V V 1 + 1 - Beta (V t + 1 , S 1 + 1 ) * (S 1 + 1 -S)
Landscapes
- Business, Economics & Management (AREA)
- Engineering & Computer Science (AREA)
- Accounting & Taxation (AREA)
- Development Economics (AREA)
- Economics (AREA)
- Finance (AREA)
- Marketing (AREA)
- Strategic Management (AREA)
- Technology Law (AREA)
- Physics & Mathematics (AREA)
- General Business, Economics & Management (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Financial Or Insurance-Related Operations Such As Payment And Settlement (AREA)
Abstract
Description
Claims
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
DE112008002476T DE112008002476A5 (de) | 2007-07-06 | 2008-06-26 | Verfahren zur Ableitung eines Zustandsraumes zur Berechnung szenariobedingter, stochastischer Kenngrößen |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
DE102007031643.9 | 2007-07-06 | ||
DE200710031643 DE102007031643A1 (de) | 2007-07-06 | 2007-07-06 | Verfahren zur Ableitung eines Zustandsraumes |
Publications (1)
Publication Number | Publication Date |
---|---|
WO2009006872A1 true WO2009006872A1 (de) | 2009-01-15 |
Family
ID=39869980
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
PCT/DE2008/001054 WO2009006872A1 (de) | 2007-07-06 | 2008-06-26 | Verfahren zur ableitung eines zustandsraumes zur berechnung szenariobedingter, stochastischer kenngrössen |
Country Status (2)
Country | Link |
---|---|
DE (2) | DE102007031643A1 (de) |
WO (1) | WO2009006872A1 (de) |
Family Cites Families (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPH1063634A (ja) * | 1996-04-05 | 1998-03-06 | Nec Corp | 時系列予測・分類のための方法及び装置 |
DE19837871C2 (de) * | 1998-08-20 | 2000-06-08 | Manfred Broy | Verfahren zum automatischen Erzeugen eines Programms |
WO2001057648A2 (de) * | 2000-01-31 | 2001-08-09 | Siemens Aktiengesellschaft | Anordnung miteinander verbundener rechenelemente und verfahren zur rechnergestützten ermittlung eines zweiten zustands eines systems in einem ersten zustandsraum aus einem ersten zustand des systems in dem ersten zustandsraum |
-
2007
- 2007-07-06 DE DE200710031643 patent/DE102007031643A1/de not_active Withdrawn
-
2008
- 2008-06-26 WO PCT/DE2008/001054 patent/WO2009006872A1/de active Application Filing
- 2008-06-26 DE DE112008002476T patent/DE112008002476A5/de not_active Ceased
Non-Patent Citations (1)
Title |
---|
"STATEMENT IN ACCORDANCE WITH THE NOTICE FROM THE EUROPEAN PATENT OFFICE DATED 1 OCTOBER 2007 CONCERNING BUSINESS METHODS - PCT / ERKLAERUNG GEMAESS DER MITTEILUNG DES EUROPAEISCHEN PATENTAMTS VOM 1.OKTOBER 2007 UEBER GESCHAEFTSMETHODEN - PCT / DECLARATION CONFORMEMENT AU COMMUNIQUE DE L'OFFICE EUROP", JOURNAL OFFICIEL DE L'OFFICE EUROPEEN DES BREVETS.OFFICIAL JOURNAL OF THE EUROPEAN PATENT OFFICE.AMTSBLATTT DES EUROPAEISCHEN PATENTAMTS, OEB, MUNCHEN, DE, 1 November 2007 (2007-11-01), pages 592 - 593, XP007905525, ISSN: 0170-9291 * |
Also Published As
Publication number | Publication date |
---|---|
DE112008002476A5 (de) | 2010-06-17 |
DE102007031643A1 (de) | 2009-01-08 |
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