Monte Carlo methods and variance reduction
Monte Carlo methods (or Monte Carlo experiments) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. Their essential idea is using randomness to solve problems or compute mathematical quantities that might be deterministic in principle. (wikipedia)
Exercise : use monte carlo method to price a call option and implement variance reduction to improve convergence and simulation time.
- Classic monte carlo for option pricing
- Variance reduction for better performance and less computation time : Antitethic Variable, Control Variable, Importance function.
Implementation with c++ (C++ 11 and STL)