There is ample historical data to suggest that log returns of stocks and indices are not independent and identically distributed Normally, as is commonly assumed. Instead, the returns of financial assets are skewed and have higher kurtosis. To account for skewness and excess kurtosis, it is...

The VIX index measures the one-month risk-neutral forward volatility of the S&P500 (SPX) index. While Lévy processes such as the CGMY process can price options on the underlying stock or index, they implicitly assume a constant forward volatility. This makes them unsuitable for pricing options...

In this paper, we introduce DSPMD, discretely sampled process with pre-specified marginals and pre-specified dependence, and SRLMD, series representation for Levy process with pre-specified marginals and pre-specified dependence. In the DSPMD for Levy processes, some regular copula can be...