Analytical Pricing of Asian Options with Jump Risk
Ning Cai, Assistant Professor
Department of Industrial Engineering and Logistics Management
The Hong Kong University of Science and Technology
2010年12月30日（周四）下午2:00-3:00
北京大学光华管理学院新楼217教室
Asian options (or average options) are among the most popular exotic options traded actively in the financial markets and have a wide application in equity, currency, commodity, etc. In this paper we obtain a closed-form solution for the double-Laplace transform of the Asian option price under the hyper-exponential jump diffusion model (HEM). Similar results are available in the literature only in the special case of the Black-Scholes model (BSM). Even in the case of the BSM, our approach is simpler as we essentially use only the Ito`s formula and do not need more advanced techniques such as Bessel processes and Lamperti`s representation. Furthermore, our approach is more general as it applies to the HEM. As a by-product we also show that a well-known recursion relating to Asian options has a unique solution in a probabilistic sense. The double-Laplace transforms can be inverted numerically via a two-sided Euler inversion algorithm. Numerical results indicate that our pricing method is fast, stable, and accurate.
This is joint work with Steven Kou from Columbia University.
Ning Cai is currently an Assistant Professor in financial engineering in the Department of Industrial Engineering and Logistics Management at the Hong Kong University of Science and Technology. He received his B.S. and M.S. in probability and statistics in the School of Mathematical Sciences at Peking University in 2000 and 2003 respectively, and his Ph.D. in operations research in the Department of Industrial Engineering and Operations Research at Columbia University in 2008.