An analytical approach for variance swaps with an Ornstein-Uhlenbeck process

Jianpeng Cao, Yan-Bing Fang

Abstract


Pricing variance swaps have become a popular subject recently, and most research of this type come under Heston’s two-factor model. This paper is an extension of some recent research which used the dimension-reduction technique based on the Heston model. A new closed-form pricing formula focusing on a log-return variance swap is presented here, under the assumption that the underlying asset prices can be described by a mean-reverting Gaussian volatility model (Ornstein–Uhlenbeck process). Numerical tests in two respects using the Monte Carlo (MC) simulation are included. Moreover, we discuss a procedure of solving a quadratic differential equation with one variable. Our method can avoid the previously encountered limitations, but requires more time for calculation than other recent analytical discrete models.

doi:10.1017/S1446181117000268

Keywords


variance swaps, Ornstein–Uhlenbeck process, closed-form solution, stochastic volatility.



DOI: http://dx.doi.org/10.21914/anziamj.v59i0.11489



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.