Numerical Computation of an Integral Representation for Arithmetic-Average Asian Options

The integrands in M. Schröder’s integral representation for the price of Asian options are highly oscillatory yielding cancellations of many digits in the integration. Furthermore, obtaining multiple precision function values is costly. Numerical integration is nevertheless possible by using Hermitian quadrature formulas, techniques of automatic differentiation and explicit error bounds combined with interval arithmetic.

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

[2]  Andreas Griewank,et al.  Evaluating derivatives - principles and techniques of algorithmic differentiation, Second Edition , 2000, Frontiers in applied mathematics.

[3]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[4]  N. N. Lebedev,et al.  Spezielle Funktionen und ihre Anwendung , 1973 .

[5]  Louis B. Rall,et al.  Automatic Differentiation: Techniques and Applications , 1981, Lecture Notes in Computer Science.

[6]  Harald Niederreiter,et al.  Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.

[7]  Y. Kwok.  Mathematical models of financial derivatives , 2008 .