Abstract
In this dissertation, the Heston model is introduced, implemented and calibrated.
A foundation of necessary concepts is built and an introduction to stochastic
volatility models is given. The fast Fourier transform method is used to calibrate
model parameters to market data by using the closed-form option pricing
formula under the Heston model. Thereafter, discretisation methods such as the
Euler, Milstein and Kahl-Jackel schemes are used in Monte Carlo simulation to
price exotic options. The effect of different models and discretisation methods on
the prices of exotic options is studied as a brief introduction to model risk.