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Stevens Institute of Technology, USA ,Zhenyu Cui, Probability Density, Implied Volatility and Timer Options in Stochastic Volatility Models

(发布于:2016-05-30 )

主 题:Probability Density, Implied Volatility and Timer Options in Stochastic Volatility Models

主讲人:Stevens Institute of Technology, USA ,Zhenyu Cui

主持人:经济数学学院 马敬堂教授

时 间:2016年5月31日(星期二)下午4:00

地 点:柳林校区通博楼B412

主办单位:经济数学学院  科研处


 Dr. Zhenyu Cui is an Assistant Professor in Financial Engineering at the School of Systems and Enterprises at Stevens Institute of Technology. His research interests are in financial econometrics, stochastic processes and applied probability, and stochastic simulation. His research has appeared in Mathematical Finance, Finance and Stochastics, and Journal of Economic Theory. He has been funded twice through the Individual Grant Competitions of the Society of Actuaries. He holds a Ph.D. in Statistics, a Master in Quantitative Finance from the University of Waterloo, and a Bachelor of Science in Actuarial Science from the University of Hong Kong.


In this talk, we describe a generic probabilistic method to derive explicit exact probability density functions for stochastic volatility models. Our method is based on a novel application of the exponential measure change in Palmowski and Rolski (2002). With this generic method, we first derive explicit exact probability densities in terms of model parameters for five popular stochastic volatility models with non-zero correlation, namely the Heston, Hull-White, 3/2, 4/2 and alpha-hypergeometric stochastic volatility models. Next, we combine the probability densities, the mixing approach of Romano and Touzi (1996), and a representation of the implied volatility surface to obtain explicit exact formulae for European call options and the corresponding implied volatilities for these five models in terms of model parameters. Finally, we apply our generic probabilistic method to develop explicit exact formulae for prices of timer options in Heston, 3/2 and alpha-hypergeometric models.