Efficiently pricing continuously monitored barrier options under stochastic volatility model with jumps

Stochastic volatility model with jumps fits almost perfectly the empirical implied volatility surface. Under this model, this paper considers continuously monitored barrier options pricing by Monte Carlo simulation. Based on quadratic exponential scheme, this paper develops an algorithm for pricing barrier options and provides convergence of the algorithm by moment-matching techniques. Variance reduction technique based on control variates further improves the efficiency of the algorithm. The algorithm is also extended to stochastic volatility model with contemporaneous jumps in variance and stock price. Simulations show that the proposed algorithm is efficient and easy to implement. Compared to contemporaneous jumps in variance and stock price, only jumps in stock price produce more profound impact on barrier options prices.