We present an application of importance sampling in a Monte Carlo simulation for multi-asset options and in a Multi-Level Monte Carlo simulation. We demonstrate that applying importance sampling only on the first level of the Multi-Level Monte Carlo significantly improves its effective...

This paper provides a strategy for portfolio risk management by inferring extreme movements in financial markets. The core of the provided strategy is a statistical model for the joint tail distribution that attempts to capture accurately the data generating process through an extremal modelling...

Using the joint characteristic function of equity price and state variables, we can price contingent claims on both equity and VIX consistently. Based on linear approximation of jump size, we show that one factor models implies all VIX future contract of different maturities are perfectly...

We introduce a stochastic volatility model with self-exciting jump intensity to capture the change in pricing dynamic triggered by big negative stock returns. The stochastic variance and jump intensity, and their risk premium are estimated jointly from daily stock returns and option data over...