A New Computational Scheme for Computing Greeks by the Asymptotic Expansion Approach
- 59 Downloads
We developed a new scheme for computing “Greeks” of derivatives by an asymptotic expansion approach. In particular, we derived analytical approximation formulae for Deltas and Vegas of plain vanilla and average European call options under general Markovian processes of underlying asset prices. Moreover, we introduced a new variance reduction method of Monte Carlo simulations based on the asymptotic expansion scheme. Finally, several numerical examples under CEV processes confirmed the validity of our method.
Keywordsasymptotic expansion approach option pricing Greeks CEV process Monte Carlo simulation variance reduction method
Unable to display preview. Download preview PDF.
- Ikeda, N. and Watanabe, S. (1989) Stochastic Differential Equations and Diffusion Processes, Second Edition, North-Holland/Kodansya, Tokyo.Google Scholar
- Imamura, S, Takahashi, A. and Uchida, Y. (2004) On risk sensitivity analysis of options based on malliavin calculus, IMES Discussion Paper Series 2004-J-24, Bank of Japan (in Japanese).Google Scholar
- Kunitomo, N. and Takahashi, A. (2003a) On Validity of the Asymptotic Expansion Approach in Contingent Claim Analysis, Annals of Applied Probability 13 (3), Aug. 2003.Google Scholar
- Kunitomo, N. and Takahashi, A. (2003b) Foundation of Mathematical Finance-Application of Malliavin Calculus and Asymptotic Expansion Method-, Toyo-Keizai (in Japanese).Google Scholar
- Kunitomo, N. and Takahashi, A. (2004) Applications of the Asymptotic Expansion Approach based on Malliavin-Watanabe Calculus in Financial Problems, Stochastic Processes and Applications to Mathematical Finance, World Scientific, 195–232.Google Scholar
- Takahashi, A. (1995) Essays on the valuation problems of contingent claims, Ph.D. dissertation, Univ. California, Berkeley.Google Scholar
- Takahashi, A. and Matsushima, S. (2004) Monte Carlo Simulation with an Asymptotic Expansion in HJM framework, FSA Research Review 2004, Financial Services Agency (in Japanese), 82–103.Google Scholar
- Takahashi, A. and Saito, T. (2003) An Asymptotic Expansion Approach to Pricing American Options, Monetary and Economic Studies, Bank of Japan (in Japanese) 22, 35–87.Google Scholar
- Takahashi, A. and Uchida, Y. (2006) New Acceleration Schemes with the Asymptotic Expansion in Monte Carlo Simulation, Advances in Mathematical Economics 8, 411–431.Google Scholar
- Takahashi, A. and Yoshida, N. (2005) Monte Carlo Simulation with Asymptotic Method, The Journal of Japan Statistical Society 35, 171–203.Google Scholar