Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we propose a general account for finding the optimal tilting...

The probabilities considered in value-at-risk (VaR) are typically of moderate deviations. However, the variance reduction techniques developed in the literature for VaR computation are based on large deviations methods. Modeling heavy-tailed risk factors using multivariate $t$ distributions, we...

We derive a pricing model for employee stock options (ESO) that expands on Ingersoll (2006) by including default risk and that additionally considers the effects of employee over-confidence. We find that illiquidity reduces subjective value and alters incentive effects and value sensitivities....

We provide methodologies to price discretely monitored exotic options when the underlying evolves according to a double exponential jump diffusion process. We show that discrete barrier or lookback options can be approximately priced by their continuous counterparts’ pricing formulae with a...

We provide closed-form solutions for a continuous time, Markov-modulated jump diffusion model in a general equilibrium framework for options prices under a variety of jump diffusion specifications. We further demonstrate that the two-state model provides the leptokurtic return features,...