Data processing: financial – business practice – management – or co – Automated electrical financial or business practice or... – Finance
Reexamination Certificate
1998-12-10
2002-04-30
Stamber, Eric W. (Department: 2162)
Data processing: financial, business practice, management, or co
Automated electrical financial or business practice or...
Finance
C705S035000
Reexamination Certificate
active
06381586
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention generally relates to computer implemented methods for pricing derivative securities (for example, options) in the finance industry and, more particularly, to such methods having improved efficiency and that select an importance sampling (IS) distribution and combining the selected IS distribution with stratified sampling or Quasi-Monte Carlo (QMC) in novel ways to price financial instruments.
2. Background Description
Monte Carlo simulation is widely used in the finance industry to price derivative securities. However, the method can be quite inefficient because of large variances associated with the estimates. Variance reduction techniques are therefore required. While a large number of such techniques have been developed, more efficient methods are needed for a variety of financial instruments.
A basic survey on general variance reduction techniques, including both the techniques of importance sampling (IS) and stratified sampling, is found in
Monte Carlo Methods
by J. Hammersley and D. Handscomb, Methuen & Co. Ltd., London (1964), pp. 55-61. A survey on the use of Monte Carlo methods in finance is described by P. Boyle, M. Broadie, and P. Glasserman in “Simulation Methods for Security Pricing”,
J. Economic Dynamics and Control,
Vol. 21, pp. 1267-1321 (1998). A survey and description of the state-of-the-art for variance reduction in finance applications is included in the article entitled “Asymptotically Optimal Importance Sampling and Stratification for Pricing Path-Dependent Options” by P. Glasserman, P. Heidelberger and P. Shahabuddin.
IBM Research Report RC
21178, Yorktown Heights, N.Y. (1998). The use of Quasi-Monte Carlo (QMC) sequences (see, for example, H. Niederreiter, “Random Number Generation and Quasi-Monte Carlo Methods”, CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics (1992)) as a variance reduction technique in finance applications has also been considered (see, for example, P. Acworth, M. Broadie and P. Glasserman, “A Comparison of Some Monte Carlo and Quasi Monte Carlo Techniques for Option Pricing”, in
Monte Carlo and Quasi-Monte Carlo Methods
1996, Lecture Notes in Statistics, Vol. 127, Sringer-Verlag, pp. 1-18 (1998), and W. J. Morokoff and R. Caflisch, “Quasi Monte Carlo Simulation of Random Walks in Finance”, in
Monte Carlo and Quasi-Monte Carlo Methods
1996, Lecture Notes in Statistics, Vol. 127, Sringer-Verlag, pp. 340-352 (1998), and the references therein). The effectiveness of quasi-Monte Carlo (QMC) sequences decreases as the dimension of the problem increases. Therefore, as described in the above references, it is important to assign the lowest dimensions of the QMC sequence to the most “important” dimensions, or directions.
As described in the above references, the prior art identifies a zero variance estimator; however, it is not practical to implement since it typically requires both knowing the option's price in advance and sampling from non-standard distributions. In the less general setting of estimating the probability of an event, the prior art also identifies an IS distribution by maximizing a “rate function” over the event.
SUMMARY OF THE INVENTION
It is therefore an object of the invention to provide a computer implemented method for pricing derivative securities, e.g., options, that selects an importance sampling (IS) distribution combined with stratified sampling or quasi-Monte Carlo (QMC) sequences.
According to the invention, there is provided a process with which securities may be priced. This process consists of the steps of choosing an importance sampling distribution and combining the chosen importance sampling with stratification or quasi-Monte Carlo (QMC) simulation. In the first step, an importance sampling distribution is chosen. In the second step, the chosen importance sampling is combined with stratification or Quasi-Monte Carlo sequencing.
The present invention improves upon earlier methods by selecting an importance sampling distribution in a general, novel and effective way. Furthermore, it also combines importance sampling with stratified sampling in a general, novel and effective way. The pricing of many types of securities reduces to one of estimating an expectation of a real-valued function of some random variables.
REFERENCES:
patent: 5844415 (1998-12-01), Gershenfeld et al.
patent: 6061662 (2000-05-01), Makivic
patent: 6178384 (2001-01-01), Kolossvary
patent: WO 97/07475 (1997-02-01), None
IBM TDB NN9609215, “Quasi-Monte Carlo Rendering with Adaptive Sampling”, vol. 39 No. 9: 215-244, Sep. 1, 1996.*
by J. Hammersley and D. Handscomb; Monte Carlo Methods; London: Methuen & Co. Ltd. (1964); pp. 55-61.
by P. Boyle, M. Broadie and P. Glasserman; “Monte Carlo Methods for Security Pricing”; J. Economic Dynamics and Control; (1997); vol. 21, pp. 1267-1321.
by P. Glasserman, P. Heidelberger and P. Shahabuddin; “Asymptotically Optimal Importance Sampling and Stratification for Pricing Path-Dependent Options”; IBM Research Report RC 21178; IBM, Yorktown Heights, NY, (May 11,1998).
by H. Niederreiter; “Random Number Generation and Quasi-Monte Carlo Methods”; CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics, Philadelphia PA (1992): 1-12.
by P. Acworth, M. Broadie and P. Glasserman; “A Comparison of Some Monte Carlo and Quasi Monte Carlo Techniques for Option Pricing”; Monte Carlo and Quasi-Monti Carlo Methods 1966; Lecture Notes in Statistics, vol. 127; Springer-Verlag, NY; pp. 1-18 (1998).
by W. J. Morokoff and R. Caflisch; “Quasi Monte Carlo Simulation of Random Walks in Finance”; Monte Carlo and Quasi-Monte Carlo Methods 1996; Lecture Notes in Statistics, vol. 127; Springer-Verlag NY; pp. 340-352; (1998).
Glasserman Paul
Heidelberger Philip
Shahabuddin Nayyar P.
Champagne Donald L.
Stamber Eric W.
Tassinari, Jr. Robert P.
Whitham Curtis & Christofferson, P.C.
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