Optimization of option pricing : - Variance reduction and low-discrepancy techniques

Sammanfattning: In recent years, the importance and the interest in financial instrument especially derivatives have increased. The Nobel Prize in Economics 1997 was dedicated to Black & Scholes for their work with finding a new method that estimates option prices for Plain Vanilla Options. Since the dynamics of the underlying assets can be very complex it is preferable to use numerical methods such as Monte Carlo simulations, to get rid of the assumptions in the Black & Scholes models. Monte Carlo simulations is a preferable pricing method and is often the only method available for pricing options with complex trajectories dependencies. Simulations can moreover give further insights into how the options actually works. A huge advantage is that the convergence rate is independent of the dimension of the simulated problem. Meanwhile the backside of the method is the slow convergence, the need of significant computational power and that the simulations are time consuming. Hence the aim with this research is to find an optimized pricing method for both Plain Vanilla options and Exotic options. In order to optimize option pricing different variance reduction- and low-discrepancy methods are examined and com- pared based on following criteria. Convergence to the option price, execution time and the uncertainty in the estimated price. The findings of this research are that there are both strengths and weaknesses with each of the described methods. Depending on if one wants to optimize only the convergence/uncertainty or execution time. In conclusion there exists a silver bullet in option pricing, which has performed on each criterion, this method is named Importance Sampling.