In this note we provide an alternative proof that the Heston asset price process converges to the Normal Inverse Gaussian (NIG) distribution in the large-time limit in a certain sense. Our proof, which is based on the convergence of conditional time-integrated variance to the Inverse Gaussian...

We introduce a new stochastic volatility model that includes, as special instances, the Heston (1993) and the 3/2 model of Heston (1997) and Platen (1997). Our model exhibits important features: first, instantaneous volatility can be uniformly bounded away from zero, and second, our model is...

This thesis presents our study on using the hybrid stochastic-local volatility model for option pricing. Many researchers have demonstrated that stochastic volatility models cannot capture the whole volatility surface accurately, although the model parameters have been calibrated to replicate...

Phase-type distribution has been one of the most important probabilistic tools in the analysis of complex stochastic system evolution. However, in their empirical study, Frydman (2005) and Frydman and Schuermann (2008) found that the inclusion of available credit rating information helps improve...

We establish an explicit pricing formula for a class of non-gaussian models (the Lévy-stable, or Log-Lévy model with finite moments) allowing a straightforward evaluation of an European option, without numerical simulations and with as much accuracy as one wishes. The formula can be used by...

We revisit the question whether commodities should be included in investors' portfolios. We employ for the first time a stochastic dominance efficiency (SDE) approach to construct optimal portfolios with and without commodities and we evaluate their comparative performance. SDE circumvents the...

The purpose of this research is the realistic forecast of volatility in frame of a risk parity class of strategies. The custom rescaling of volatility – naïve risk parity - doesn't consider market inefficiencies which correspond to cyclical patterns like crisis and the following recovery. The...

In this paper we examine the Heston model in the limit of infinitely fast mean-reversion for the stochastic volatility process (CIR). We show that, under an appropriate scaling of the model parameters, the two-factor stochastic volatility Heston model can be exactly mapped to a one-factor...

This paper presents a new formalism to price European options in all asset classes that fits the market data remarkably well. We use a model-independent representation of European Option prices as path integrals over all of the underlying asset price from inception to maturity. The no arbitrage...

The proliferation of algorithmic high-frequency trading in financial markets has also led to an increase in new types of fraudulent activity. Since the flash-crash of 2010 first brought it to popular prominence, layering or spoofing fraud has become a major concern for financial regulators...