Copyright © 2011 Anatoliy Swishchuk and Li Xu. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study the valuation of the variance swaps under stochastic volatility with delay
and jumps. In our model, the volatility of the underlying stock price process not only
incorporates jumps, which are found to be active empirically, but also exhibits past dependence: the behavior of a stock price right after a given time depends not only on
the situation at but also on the whole past (history) of the process up to time as well.
The jump part in our model is finally represented by a general version of compound
Poisson processes. We provide some analytical closed forms for the expectation of the
realized variance for the stochastic volatility with delay and jumps. We also present a
lower bound for delay as a measure of risk. As applications of our analytical solutions,
a numerical example using S&P60 Canada Index (1998–2002) is then provided to price