The development of an e¤ective mechanism for pricing options has inspired a large volume of academic research and has ultimately changed the landscape of the �nancial markets. Since the publication of Black and Scholes�(1973) seminal paper on option pricing, the �nance literature has explored and at least partially resolved many of the limitations associated with the original model. The reality of stochastic volatility contradicts a key assumption of the Black-Scholes model and addressing this has motivated the development of more appropriate volatility models. The improved speci�cation and forecasting of asset price volatility has been influenced by the demands of risk management and portfolio functions. The increased use of quantitative methods in portfolio management is due, in part at least, to successful academic research into asset volatility. Existing research is extended in this thesis by �rst examining the forecasting power of implied volatilities from traded UK equity options. Composite implied volatilities are created using weighting techniques that efficiently capture the predictive information in traded options. These implied volatilities are benchmarked against subsequently realized stock price volatility estimated from high-frequency stock price data. The predictive information provided by the options market is compared against that available from sophisticated statistical models such as the generalized autoregressive conditional heteroskedastic (GARCH) model and the exponential-GARCH (E-GARCH) model. Comparison of implied and statistical forecasts is carried out over a number of forecasting horizons using regression analysis as well as robust pairwise tests. The second part of this thesis uses semi-parametric techniques to examine the long-run dynamics of UK equity volatility. The nature of volatility persistence found in both the implied and realized volatility series of a number of companies is carefully examined. Testing the time-domain properties of the volatility series identities the extent to which structural breaks in volatility contribute to observed levels of persistence in our sample of companies. The nature of the long-run relationship between implied and realized volatility is also examined. The relevance of these empirically observed volatility characteristics is examined in the final part of this thesis. Using dynamic programming techniques together with Monte Carlo simulation, optimal portfolio weights are determined for a derivative strategy implemented in discrete time. The derivative strategy is activated across a six-month investment horizon and rebalancing occurs at the beginning of each month. The creation of a series of variance grid points at each time step makes the dynamic programming approach computationally feasible. Progressing backwards from the end of the investment horizon, optimal portfolio weights are found for each of the variance grid points. The optimisation procedure assumes that volatility is driven by a short-memory affine process. The economic cost associated with omitting long-memory effects is isolated by simulating a fractionally integrated process across the same investment horizon and applying the previously assigned weights at each time step. The relevance of omitting possible regime shifts in the volatility process are evaluated in the same manner. Portfolio outcomes are derived for the optimal case, that is, when actual volatility follows a short memory process. Outcomes are also derived for the alternative conditions, that is, a 'true' long memory, fractionally integrated process as well as the 'spurious' long memory or regime-switching case. The impact of volatility mis-specification is captured in the characteristics of the portfolio's terminal wealth distribution.