**主 题：**Pricing Discrete Timer Options under Stochastic Volatility Models

**主讲人：**Yue Kuen Kwok (郭宇权) 香港科技大学教授

**主持人：**经济数学学院 马敬堂教授

**时 间：**2016年1月15日（星期五）上午10:00

**地 点：**柳林校区通博楼B412

**主办单位：**经济数学学院 科研处

**主讲人简介：**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 currently the Program Director of MSc degree in Financial Mathematics as well as MSc degree in Mathematics and Economics at HKUST. Professor Kwok’s research interests concentrate on pricing and risk management of equity and fixed income derivatives. He has published more than 100 research articles in major research journals in financial mathematics and mathematical sciences, like *Mathematical Finance, SIAM Journals, Quantitative Finance*, *Journal of Economic and Dynamics Control*. In addition, he is the author of the book titled “Mathematical Models of Financial Derivatives”, second edition, (2008) published by Springer. 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 board of *Journal of Economic and Dynamics Control* and *Asian-Pacific Financial Markets*. Yue Kuen Kwok received his PhD degree in Applied Mathematics from Brown University in 1985.

**内容提要: **Timer options are barrier style options in the volatility space. A typical timer option is similar to its European vanilla counterpart, except with uncertain expiration date. The finite-maturity timer option expires either when the accumulated realized variance of the underlying asset has reached a pre-specified level or on the mandated expiration date, whichever comes earlier. The challenge in the pricing procedure is the incorporation of the barrier feature in terms of the accumulated realized variance instead of the usual knock-out feature of hitting a barrier by the underlying asset price. We construct the fast Hilbert transform algorithms for pricing finite-maturity discrete timer options under different types of stochastic volatility processes. The stochastic volatility processes nest some popular stochastic volatility models, like the Heston model and 3/2 stochastic volatility model. The barrier feature associated with the accumulated realized variance can be incorporated effectively into the fast Hilbert transform procedure with the computational convenience of avoiding the nuisance of recovering the option values in the real domain at each monitoring time instant in order to check for the expiry condition. Our numerical tests demonstrate high level of accuracy of the fast Hilbert transform algorithms. We also explore the pricing properties of the timer options with respect to various parameters, like the volatility of variance, correlation coefficient between the asset price process and instantaneous variance process, sampling frequency, and variance budget.