The recent turbulence in financial markets, of which a famous casualty is the collapse of the Long Term Capital Management hedge fund, has made market liquidity an issue of high concern to investors and risk managers. The latter group in particular realised that financial models, based on the assumption of perfectly liquid markets where investors can trade large amounts of assets without affecting their prices, may fail miserably under the circumstance where market liquidity vanishes. Understanding the robustness and reliability of models used for trading and risk management purposes is therefore crucially important in the risk analysis. Part I of this thesis studies liquidity risk and its measurement via mean reversion jump diffusion processes. An efficient Monte Carlo method is suggested to find approximate VaR and CVaR for all percentiles with one set of samples from the loss distribution, which applies to portfolios of securities as well as single security. Part II investigates the computational efficiency and flexibility of application of the FFT-based option pricing methodologies. First, an empirical testing of alternative twofactor stochastic volatility affine jump-diffusion models is conducted against an extensive S&P 500 index options data set, using a nonlinear ordinary least squares estimation framework. It is then shown how the two-dimensional FFT may be applied for the pricing of spread options, which have payoff functions and exercise regions that are nonlinear in the underlying log-asset prices. Furthermore, a non-affine four-factor stochastic volatility diffusion model is considered and an approximate CCF specification derived.