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.