Pricing variance swaps under stochastic volatility and stochastic interest rate. (English) Zbl 1410.91438
Summary: 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 T. Little and V. Pant [“A finite-difference method for the valuation of variance swaps”, J. Comput. Finance 5, No. 1, 81–103 (2001; doi:10.21314/jcf.2001.057)] 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.
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |
| 91G70 | Statistical methods; risk measures |
| 91G30 | Interest rates, asset pricing, etc. (stochastic models) |
Keywords:
generalized Fourier transform; Heston-CIR hybrid model; realized variance; stochastic interest rate; stochastic volatility; variance swapReferences:
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