| As a pure tool hedging the exposure of volatility risk, variance swap has played an important role in the volatility risk management. According to the data of American risk magazine, variance trading has roughly doubled every year for the past few years.In recent years, due to the Asian financial crisis, and the US subprime crisis in2007, the global economy has experienced unpredictable increase and slump, which makes it more and more necessary to incorporate jump diffusion and stochastic volatility in the variance swap pricing model. Moreover, since the cash-flow exchanges in the variance swaps is not continuous in practical life, pricing variance swaps in the context of discrete sampling will draw growing interest.This article discusses the valuation of discretely sampled variance swaps within the frame of Heston’s two-factor stochastic volatility under jump-diffusion model. The joining of the continuous dividend rate and the jump-diffusion model in the dynamics of the underlying asset price is a great characteristic of this paper compared with the work done by Song-Ping Zhu and Guang-Hua Lian. As a main contribution of this paper, we prove the independence of a Brownian motion and a compound Poisson process(depicting jumps in the price of underlying asset) so that the realized variance can be decomposed into two parts. Furthermore, we introduce two different jump-diffusion models and find a closed-form solution in both circumstances. In the end, we prove that the value of our discrete model asymptotically approach the value of the continuous approximation model when the sampling frequency increases to infinity. And the effect of jumps in the fair variance strike is also analyzed. |
