In this paper, we show that the influential Merton jump diffusion model and formula are needlessly cumbersome. In doing so, we provide a simple, explicit formula that doesn't require a computational method. Furthermore, we introduce a new, simple method for solving partial...

The use of American style equity options as hedging instrument has gained currency in recent times. This phenomenon devolves from the ever-expanding need by individuals, corporations and governments to hedge away their financial risks and the clarion call for derivative securities that give the...

This paper studies optimal sovereign investment and resource allocation decisions in the presence of asset price discontinuities due to stochastic volatility and event related jump risks. We find that: (i) both volatility jumps and positive price jumps increase investment in commodities while...

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...

Most investors and real estate developers consider Brownfield projects risky and, to compensate for environmental risk, demand higher returns on the investment needed to cleanup a contaminated property. The risk perception is aggravated by the fact that remediation of a contaminated site takes...

In this paper, we present our study on using the hybrid stochastic-local volatility (SLV) model for option pricing. The SLV model contains a stochastic volatility component represented by a volatility process and a local volatility component represented by a so-called leverage function. The...

From an analysis of the time series of volatility using recent high frequency data, Gatheral, Jaisson and Rosenbaum previously showed that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale. The resulting Rough...

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...

In this article, we study the algorithmic calculation of present values greeks for callable exotic instruments. The speed of greeks evaluations becomes important with recent initial margin rules, including the ISDA standard model SIMM, requiring sensitivity calculations for non-cleared deals...

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...