There has been an on-going debate about choices of the most suitable model amongst avariety of model specifications and parameterizations. The first dissertation essay investigateswhether asymmetric leptokurtic return distributions such as Hansen’s (1994) skewed tdistributioncombined with...

There has been an on-going debate about choices of the most suitable model amongst a variety of model specifications and parameterizations. The first dissertation essay investigates whether asymmetric leptokurtic return distributions such as Hansen's (1994) skewed tdistribution combined with...

In this paper we investigate dependence properties and comparison results for multidimensional Lévy processes. In particular we address the questions, whether or not dependence properties and orderings of the copulas of the distributions of a Lévy process can be characterized by corresponding...

In this paper we investigate dependence properties and comparison results for multidimensional Lévy processes. In particular we address the questions, whether or not dependence properties and orderings of the copulas of the distributions of a Lévy process can be characterized by corresponding...

In this paper we propose new option pricing models based on class of models with jump contain in the Lévy-type based models (NIG-Lévy, Merton-jump (Merton 1976) and Duan based model (Duan 2007)). By combining these different class of models with several volatility dynamics of the GARCH type,...

We calculate the leading term of asymptotics of the prices of barrier options and first-touch digitals near the barrier for wide classes of Lévy processes with exponential jump densities, including the Variance Gamma model, the KoBoL (a.k.a. CGMY) model and Normal Inverse Gaussian processes. In...

A fast and accurate method for pricing early exercise and certain exotic options in computational finance is presented. The method is based on a quadrature technique and relies heavily on Fourier transformations. The main idea is to reformulate the well-known risk-neutral valuation formula by...

We present a fast and accurate FFT-based method of computing the prices and sensitivities of barrier options and first-touch digital options on stocks whose log-price follows a Lévy process. The numerical results obtained via our approach are demonstrated to be in good agreement with the...

This paper examines how well alternate time-changed Lévy processes capture stochastic volatility and the substantial outliers observed in U.S. stock market returns over the past 85 years. The autocorrelation of daily stock market returns varies substantially over time, necessitating an...