Hedge fund industry has grown to be a key player in the financial markets. Just as large investment banks, the failure of this industry will greatly destroy the liquidity and stability of the whole system. However, contrast to regulated mutual funds, hedge funds are private and lightly regulated...

Longer horizon returns are modeled by two approaches, which have different impact on skewness and excess kurtosis. The Levy approach, which considers the random variable at longer horizon as the cumulants of i.i.d random variables from shorter horizons, tends to decrease skewness and excess...

Dependence modeling plays a critical role in pricing and hedging multi-asset derivatives and managing risks with a portfolio of assets. With the emerge of structured products, it has attracted considerable interest in using multivariate Levy processes to model the joint dynamics of multiple...

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...

We entertain the hypothesis that leverage considerations are relevant in describing the evolution of asset returns both statistically and risk neutrally. Adopting a constant elasticity of variance formulation in the context of a general Levy process as the driving uncertainty we show that the...