A superconvergent partial differential equation approach to price variance swaps under regime switching models

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• 作者：Mehzabeen Jumanah Dilloo ; Dé ; siré ; Yannick Tangman ; ^{y.tangman@uom.ac.mu}
• 关键词：35G61 ; 91B25 ; 65M06
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：July 2017
• 年：2017
• 卷：318
• 期：Complete
• 页码：316-334
• 全文大小：617 K
• 卷排序：318

文摘

We present a superconvergent finite difference algorithm to price discretely sampled variance swaps. We consider the Black–Scholes model, the Merton’s jump–diffusion model, stochastic volatility models that use constant-elasticity of variance for the instantaneous variance and corresponding regime switching models. PDE approach provides a universal and efficient framework for pricing under these models. To obtain extremely accurate results, we solve PDEs whose associated terminal conditions can be represented as second-order polynomials based on the two popular definitions of realised variance and for which the spatial derivatives greater than second-order are all zero. We then apply second-order finite difference discretisations in space with an exponential time integration. We also derive analytical solutions under the Merton’s model and some regime switching models to validate our superconvergent results.