Parallel computing in Asian option pricing

We discuss the use of parallel computing in Asian option pricing and evaluate the efficiency of various algorithms. We only focus on ''backward-starting fixed strike'' Asian options that are continuously averaged. We implement a partial differential equation (PDE) approach that involves a single state variable to price the Asian option, and implement the same methodology to price a standard European option to check for accuracy. A parabolic PDE is solved by using both explicit and Crank-Nicolson's implicit finite-difference methods. In particular, we look for algorithms designed for implementing the computations in massively parallel processors (MPP). We evaluate the performance of the algorithms by comparing the numerical results with respect to accuracy and wall-clock time of code executions. Codes are executed on a Linux PC cluster.

[1]  Eduardo S. Schwartz.  The valuation of warrants: Implementing a new approach , 1977 .

[2]  Timothy J. Williams,et al.  Algorithm for Solving Tridiagonal Matrix Problems in Parallel , 1995, Parallel Comput..

[3]  Tiong Wee Lim.  Performance of recursive integration for pricing European-style Asian options , 2002 .

[4]  A. Kemna,et al.  A pricing method for options based on average asset values , 1990 .

[5]  Hai-Xiang Lin,et al.  A unifying graph model for designing parallel algorithms for tridiagonal systems , 2001, Parallel Comput..

[6]  Georges Courtadon,et al.  A More Accurate Finite Difference Approximation for the Valuation of Options , 1982, Journal of Financial and Quantitative Analysis.

[7]  Eduardo S. Schwartz,et al.  Finite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims: A Synthesis , 1977 .

[8]  Henk A. van der Vorst,et al.  Developments and trends in the parallel solution of linear systems , 1999, Parallel Comput..

[9]  L. Rogers,et al.  The value of an Asian option , 1995, Journal of Applied Probability.

[10]  P. Glasserman,et al.  Monte Carlo methods for security pricing , 1997 .

[11]  P. Koehl,et al.  A P.D.E. Approach to Asian Options: Analytical and Numerical Evidence , 1997 .

[12]  Dawn Hunter.  Robust numerical methods for PDE models of Asian options , 2000 .

[13]  P. Amodio,et al.  Parallel factorizations and parallel solvers for tridiagonal linear systems , 1992 .

[14]  Harold S. Stone,et al.  An Efficient Parallel Algorithm for the Solution of a Tridiagonal Linear System of Equations , 1973, JACM.

[15]  Eduardo S. Schwartz,et al.  An Equilibrium Model of Bond Pricing and a Test of Market Efficiency , 1982, Journal of Financial and Quantitative Analysis.

[16]  H. H. Wang,et al.  A Parallel Method for Tridiagonal Equations , 1981, TOMS.

[17]  Alan G. White,et al.  Valuing Derivative Securities Using the Explicit Finite Difference Method , 1990, Journal of Financial and Quantitative Analysis.

[18]  Yike Guo,et al.  Design of high performance financial modelling environment , 2000, Parallel Comput..

[19]  J. Crank,et al.  A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type , 1947 .

[20]  G. Hedstrom,et al.  Numerical Solution of Partial Differential Equations , 1966 .