This thesis makes a number of contributions in the derivative pricing and risk management literature and to the growing literature that exploits information embedded in option prices. First, it develops an effective numerical scheme for importance sampling scheme of Fouque and Tullie (2002) based on a 2-dimensional lookup table of stock price and time to maturity that dramatically improves the speed of this importance sampling scheme. Second, the thesis presents an application of this importance sampling scheme in a Multi-Level Monte Carlo simulation. Such combination yields greater variance reduction compared to Multi-Level Monte Carlo or importance sampling alone. Third, it demonstrates how the Greeks can be computed using the Likelihood Ratio Method based on characteristic function, and how combining it with importance sampling leads to a significant variance reduction for the Greeks. Finally, it documents the positive relationship between the risk-neutral skewness (RNS) and future realized stock returns that is driven by the underperformance of highly negative RNS portfolio. The results provide strong evidence that the underperformance of stocks with the lowest RNS is driven by those stocks that are associated with a higher hedging demand, relative overvaluation and are also too costly or too risky to sell short. Moreover, by decomposing RNS into its systematic and idiosyncratic components, this thesis shows that the latter drives the positive relationship with future realized stock returns.