Pricing Variance Swaps for Stochastic Volatilities with Delay and Jumps

[摘要] We study the valuation of the variance swaps under stochastic volatility with delayand jumps. In our model, the volatility of the underlying stock price process not onlyincorporates jumps, which are found to be active empirically, but also exhibits past dependence: the behavior of a stock price right after a given timetdepends not only onthe situation attbut also on the whole past (history) of the processS(t)up to timetas well. The jump part in our model is finally represented by a general version of compoundPoisson processes. We provide some analytical closed forms for the expectation of therealized variance for the stochastic volatility with delay and jumps. We also present alower bound for delay as a measure of risk. As applications of our analytical solutions,a numerical example usingS&P60 Canada Index (1998–2002) is then provided to pricevariance swaps.

[学科分类] 应用数学