Exact Pricing with Stochastic Volatility and Jumps

Abstract

A stochastic volatility jump-diffusion model for pricing derivatives with jumps in both spot returns and volatility dynamics is presented. This model admits, in the spirit of Heston, a closed-form solution for European-style options. The structure of the model is also suitable to obtain the fair delivery price of variance swaps. To evaluate derivatives whose value does not admit a closed-form expression, a methodology based on an "exact algorithm'', in the sense that no discretization of equations is required, is developed and applied to barrier options. Goodness of pricing algorithm is tested using DJ Euro Stoxx 50 market data for European options. Finally, the algorithm is applied to compute prices and Greeks of barrier options.

Keywords: Monte Carlo simulation, derivative valuation, stochastic volatility jump-diffusion model