An analytical approach for variance swaps with an Ornstein-Uhlenbeck process
Keywords:variance swaps, Ornsteinâ€“Uhlenbeck process, closed-form solution, stochastic volatility.
AbstractPricing variance swaps have become a popular subject recently, and most research of this type come under Hestonâ€™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 (Ornsteinâ€“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
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