  In this chapter, we consider volatility swap, variance swap and VIX future
pricing under different stochastic volatility models and jump diffusion models
which are commonly used in financial market. We use convexity correction
approximation technique and Laplace transform method to evaluate volatility
strikes and estimate VIX future prices. In empirical study, we use Markov chain
Monte Carlo algorithm for model calibration based on S&P 500 historical data,
evaluate the effect of adding jumps into asset price processes on volatility
derivatives pricing, and compare the performance of different pricing
approaches.
