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.
