Pricing variance swaps under stochastic volatility and stochastic interest rate

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• 作者：Jiling Cao^a ; ^{jiling.cao@aut.ac.nz" class="auth_mail" title="E-mail the corresponding author} ; Guanghua Lian ; ^b ; ^c ; ^{guanghua.lian@unisa.edu.au" class="auth_mail" title="E-mail the corresponding author} ; ^{ligu151@163.com" class="auth_mail" title="E-mail the corresponding author} ; Teh Raihana Nazirah Roslan^a ; ^d ; ^{raihana.roslan@aut.ac.nz" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Generalized Fourier transform ; Heston&ndash ; CIR hybrid model ; Realized variance ; Stochastic interest rate ; Stochastic volatility ; Variance swap
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：20 March 2016
• 年：2016
• 卷：277
• 期：Complete
• 页码：72-81
• 全文大小：418 K

文摘

In this paper, we investigate the effects of imposing stochastic interest rate driven by the Cox–Ingersoll–Ross process along with the Heston stochastic volatility model for pricing variance swaps with discrete sampling times. A dimension reduction mechanism based on the framework of Little and Pant (2001) is applied which later reduces to solving two three-dimensional partial differential equations. A semi-closed form solution to the fair delivery price of a variance swap is obtained via the derivation of characteristic functions. Practical implementation of this hybrid model is demonstrated through numerical simulations.