Unlike vanilla variance swaps, generalized variance swaps such as gamma, corridor variance and conditional variance swaps are expected to be not free from interest rates because of their weight processes. To examine the impact of stochastic interest rates on the generalized variance swaps, this paper considers discrete sampling times and the Heston stochastic volatility model incorporated by stochastic interest rates driven by the Cox–Ingersoll–Ross process. Based on the explicit calculation of the discounted characteristic function of Duffie et al. (2000), we obtain exact solutions for the fair strike prices of the generalized variance swaps for an affine version of the hybrid model. The solutions are given in closed form expression for the vanilla variance and gamma swaps and in Fourier integral expression for the corridor and conditional variance swaps. We apply the projection techniques of Grzelak and Oosterlee (2011) to the original non-affine model with a generalized correlation structure and obtain affine approximate solutions. We show the effects of stochastic interest rates on the strike prices of the generalized variance swaps.
Bibliographical noteFunding Information:
We thank the anonymous reviewers for their comments which helped to considerably improve the quality of the manuscript. The author J.-H. Kim was supported by the National Research Foundation of KoreaNRF-2017R1A2B4003226.
We thank the anonymous reviewers for their comments which helped to considerably improve the quality of the manuscript. The author J.-H. Kim was supported by the National Research Foundation of Korea NRF-2017R1A2B4003226 .
© 2019 International Association for Mathematics and Computers in Simulation (IMACS)
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)
- Numerical Analysis
- Modelling and Simulation
- Applied Mathematics