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20180627 Yue Kuen Kwok：Saddle point approximation methods for pricing VIX and variance options

时间：2018-06-11

时间：2018年6月27日 下午2:00-4:00

地点：明德主楼1016会议室

题目：Saddle point approximation methods for pricing VIX and variance options

摘要: The saddle-point approximation is an effective analytic approximation approach for approximating a density in the tails of the distribution from its associated moment generating function or cumulant generating function. Pricing of a financial option requires valuation of the discounted expectation under a pricing measure of the tail distribution of the terminal price of a risky asset. We consider the saddle-point approximation methods for pricing financial options whose payoffs depend on the discrete realized variance of the underlying asset price process. Under the Levy models and stochastic volatility models with jumps, we manage to obtain the saddle-point approximation formulas for pricing VIX products and volatility derivatives using the small time asymptotic approximation of the Laplace transform of the discrete realized variance. We examine numerical accuracy and reliability of various types of the saddle-point approximation techniques when applied to pricing derivatives on discrete realized variance under different types of asset price processes. The limitations of the saddle-point approximation methods in pricing variance products and volatility derivatives are also discussed.

简介：Yue Kuen Kwok (郭宇权) is a Professor in the Department of Mathematics, the Hong Kong University of Science and Technology (HKUST). He is the founding director of MSc degree in Financial Mathematics and the current director of BSc degree in Mathematics and Economics at HKUST. Professor Kwok’s research interests concentrate on pricing and risk management of financial derivatives. He has published more than 100 research articles in major research journals in financial mathematics and mathematical sciences. In addition, he is the author of two books on quantitative finance: “Mathematical Models of Financial Derivatives”, second edition, (2008), and “Saddle-point Approximation Methods in Financial Engineering” (2018), both published by Springer Verlag. He has provided consulting services to a number of financial institutions on various aspects of derivative trading and credit risk management. He has served in the editorial boards of *Journal of Economic and Dynamics Control*, *Asian-Pacific Financial Markets *and *International Journal of Financial Engineering*. He received his PhD degree in Applied Mathematics from Brown University in 1985.