The Talk of Mathematical Finance Series

Title: Analytic Pricing of Discrete Exotic Variance Swaps and Timer Options

Time: 4:00pm - 5:00pm , October 31/2014

Location: Zhiyuan Building 107

Presenter: Professor Yue Kuen KWOK

Department of Mathematics,

Hong Kong University of Science and Technology, Hong Kong

This is a joint work with Wendong ZHENG

Abstract:

We consider pricing of exotic variance swaps and timer option written on the discretely sampled realized variance of an underlying asset under stochastic volatility models. 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. Thanks to the analytical tractability of the joint moment generating functions of the affine models, we manage to derive closed form analytic formulas for variance swap products with corridor features. Interestingly, the closed form pricing formulas of the continuously sampled counterparts can be deduced from those of the discretely sampled variance swaps, while direct derivation of pricing formulas of the corridor type variance swaps based on continuously sampling may appear to be insurmountable. We also propose an effective analytic approach for pricing finite-maturity discrete timer options under 3/2-model by decomposing into a portfolio of timelets. 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.

演讲人介绍:Professor Yue Kuen KWOK (郭宇权教授)是世界著名的金融数学家. 发表了100左右的学术论文和专著. 他目前研究的方向在 Financial mathematics, Derivatives pricing theory, and Credit risk theory.

Analytic Pricing of Discrete Variance Swaps and Timer Options