Volatility derivatives are a class of derivative products whose payoffs are closely associated with the volatility of some underlying asset. They have gained more and more popularity among investors due to the widespread awareness of the volatility risk. Therefore, accurate pricing of volatility derivatives and a good understanding of their risk exposure are essential. In this thesis, various derivatives on the discretely monitored realized variance are investigated under a variety of asset price dynamics. Closed form pricing formulas for generalized variance swaps which are known as the third generation volatility products are derived, as a result of the linearity of the payoff structure and the affine structure of the stochastic volatility model with simultaneous jumps. The linkage be...[ Read more ]

Volatility derivatives are a class of derivative products whose payoffs are closely associated with the volatility of some underlying asset. They have gained more and more popularity among investors due to the widespread awareness of the volatility risk. Therefore, accurate pricing of volatility derivatives and a good understanding of their risk exposure are essential. In this thesis, various derivatives on the discretely monitored realized variance are investigated under a variety of asset price dynamics. Closed form pricing formulas for generalized variance swaps which are known as the third generation volatility products are derived, as a result of the linearity of the payoff structure and the affine structure of the stochastic volatility model with simultaneous jumps. The linkage between the discrete pricing formulas and their continuous counterparts is analyzed and the convergence is established. For other types of volatility derivatives with nonlinear payoff structures, such as volatility swaps and options on realized variance, semi-analytical pricing formulas via the saddlepoint approximation method have been proposed. Finally, numerical algorithms based on Fourier transform are designed to price general contingent claims on discretely sampled (generalized) realized variance.