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

Jianpeng Cao, Yan-Bing Fang


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.



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


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