Analytic pricing of discretely sampled generalized variance swaps and options

  Analytic pricing of discretely sampled generalized variance swaps and options Zheng Wendong, The Hong Kong University of Science & Technology, Hong Kong Date: 29 Jan 2014 Time: 4.30pm – 5.30pm Venue: S17-05-11 (This seminar is organized jointly with the Applied and Computational Mathematics (ACM))

About the Speaker

Wendong Zheng is a Postdoctoral Fellow in the Department of Mathematics at the Hong Kong University of Science and Technology where he has been a staff member since 2012. Wendong completed his M.Phil. and Ph.D. at the Hong Kong University of Science and Technology and his undergraduate studies at Zhejiang University. His research interests lie in the area of mathematical finance, ranging from financial derivative pricing, quantitative risk management, and quantitative trading models. With expertise in both analytic methods and numerical algorithms, he has been actively contributing to the literature on pricing and hedging volatility derivatives.

Abstract

Variance derivative is a financial instrument that provides pure volatility exposure. Most of the existing literature on pricing variance derivatives assumes continuous sampling of the realized variance, though in reality a discrete sampling mechanism is used. In an attempt to circumvent the drawbacks of the traditional quadratic variation approximation and replication approach, we propose a parametric approach for pricing discretely sampled generalized (weighted) variance swaps in closed form under the general stochastic volatility framework that can accommodate a variety of instantaneous variance dynamics and jump specifications. In addition, we present an effective PEB approximation method for pricing options on realized variance which has strong path dependency. We manage to obtain an explicitly computable lower bound for the option price and some accurate approximations of the residual term based on the asymptotic properties of the discrete realized variance.