Project focuses on replicated quasi Monte Carlo methods for path dependent option pricing and hedging (focusing on arithmetic and geometric Asian call options for experiments) in the Black-Scholes world. It is divided into 3 component:
1) Convergence and time complexity analysis of quasi Monte Carlo methods and dimension reduction techniques (Spectral/PCA, Brownian bridge) for geometric Asian option pricing (which is available in closed form as underlying truth).
2) Variance reduction via antithetic and geometric Asian control variates for arithmetic Asian option pricing.
3) Dynamic Delta-hedging simulations for Asian arithmetic and geometric options.
4) Application to real world historical market data using rolling volatilities.