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 consider two competing financial state space models and investigate whether additional information in the form of option price data is helpful to the estimation of either the unobservable state variable (volatility) or the unknown parameters in the model. The complete discussion of the...

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...