Numerical methods for Cox-Ingersoll Ross process

The Heston model is widely used in the financial industry for pricing of financial instruments. There is a huge financial and economical importance to find precise and fast solutions to two dimentional system of stochastic differential equations for volatility and price processes. During the summer project different discretisation schemes for volatility process were studied. Volatility process by itself also known as Cox-Ingersoll-Ross process. The studied schemes included Quadratic Exponential with martingale correction method of Andersen, Full Truncation method of Lord et al., and Direct Inversion method of Wiese and Malham. All three methods were implemented and speeded up using Python computer language. The novelty of the project was to use Chebyshev polynomial approximation to function representing volatility process. All three methods were applied to Andersen's three cases of foreign exchange options, interest rate options and equity option markets.