Performance of Gahver-Stehfest Numerical Laplace Inversion Method on Option Pricing Formulas
Keywords:
American call option, Laplace transform, numerical inversion, optimal exercise priceAbstract
In this paper we study the performance of Gahver-Stehfest numerical Laplace inversion method. The method is applied to some simple functions which have analytical Laplace inversion and the option pricing formulas which their analytical inversions are not available. The accuracy and efficiency of the methods for each functions are presented.
References
J. L. Schiff, The Laplace Transform: Theory and Applications. Springer Science & Business Media, October 1999.
G. Davis, “A Laplace transform technique for the analytical solution of a diffusion- convection equation over a finite domain,” Applied Mathematical Modelling, vol. 9, no. 1, pp. 69 – 71, 1985. [Online]. Available: http://www.sciencedirect.com/science/article/pii/0307904X8590143X
H. Eltayeb and A. Klman, “A note on solutions of wave, Laplaces and heat equations with convolution terms by using a double Laplace transform,” Applied Mathematics Letters, vol. 21, no. 12, pp. 1324 – 1329, 2008. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0893965908000761
D. Shah and A. K. Parikh, “Solution of one dimensional wave equation using Laplace transform,” International Journal of Science and Research, vol. 4, no. 2, pp. 2264–2267, February 2015.
S. A. D. Bahuguna and R. K. Shukla, “Laplace transform method for one-dimensional heat and wave equations with nonlocal conditions,” International Journal of Applied Mathematics and Statistics, vol. 16, no. M10, pp. –, March 2010.
Y.-K. Kwok, Mathematical Models of Financial Derivatives, 2nd ed. Springer, 2008.
D. G. Duffy, Transform Methods for Solving Partial Differential Equations, 2nd ed. Chapman and Hall/CRC, 2004.
H. Hassanzadeh and M. P. Darvish, “Comparison of different numerical Laplace inversion methods for engineering applications,” Applied Mathematics and Computation, vol. 189, no. 2, pp. 1966 – 1981, 2007.
Y. A. A. Cheng, P. Sidauruk, “Approximate inversion of the Laplace transform,” The Mathematica Journal, vol. 4, no. 2, pp. 76–81, 1994.
K. L. Kuhlman, “Review of inverse Laplace transform algorithms for Laplace-space numerical approaches,” Numerical Algorithms, vol. 63, no. 2, pp. 339–355, 2013.
S.-P. Zhu, “A new analytical approximation formula for the optimal exercise boundary of American put options,” International Journal of Theoretical and Applied Finance, vol. 7, no. 9, pp. 1141–1177, 2006.
T. W. Yee, Vector Generalized Linear and Additive Models: With an Implementation in R, ser. Springer Series in Statistics. Springer, 2015.
E. R. M. Putri, “Stock loans valuation,” Ph.D. dissertation, School of Mathematics and Applied Statistics University of Wollongong, http://ro.uow.edu.au/theses/4234, 2014.
S.-P. Zhu and J. Zhang, “Using Laplace transform to price American puts,” Dynamics of Continuous, Discrete and Impulsive Systems-B: Applications and Algorithms, vol. 19, no. 4, pp. 447–469, 2012.
