Mixed Monte Carlo in the foreign exchange market - Baker, Christopher (Division of Actuarial Science, 2017)
The stochastic differential equation (SDE) describing the spot FX rate is of central importance to modelling FX derivatives. A Monte Carlo estimate of the discounted individual payoffs of FX derivatives is taken to arrive at the price, provided there does not exist a closed form solution for the price. One propagates the FX spot rate through time under risk-neutral dynamics to realise the before-mentioned payoffs. A drawback to Monte Carlo becomes evident when the model dynamics become more complicated, such as when more dimensions are added to the dynamics of the model. These additional dimensions can be stochastic volatility and/or stochastic domestic and foreign short rates. This dissertation describes the calibration of such a model using mixed Monte Carlo, as described in Cozma and Reisinger (2015), to both model-generated and market data. Profit and loss analysis of hedging FX derivatives using the mixed Monte Carlo method is conducted when hedging against both model-generated and market data .