Local Volatility Model With Stochastic Interest Rate

Many different models exist to describe the behaviour of asset prices and are used to value options on such an underlying asset. This report investigates the local volatility model in a stochastic interest rates framework. First, we derive the local volatility function for this model, which allows the local volatility surface to be exacted from the prices of traded call options. Next, we present numerical approaches to construct a local volatility surface based on finite difference approximation, Monte Carlo simulation and Lipschitz interpolation. Then, Monte Carlo simulation is applied to value options using the local volatility surface. Finally, a numerical implementation of the model and its results are reported and compared with real market data.