Exact probability density functions were derived for the discretely and continuously monitored arithmetic average prices when asset returns follow a normal distribution. They were calculated by a one-step time convolution to maturity, normalized by Esscher transform. They are of an...

Numerous studies find S-shaped pricing kernels, which is conflicting with standard theory. In contrast to that, based on a novel GARCH model with structural breaks, I show that the pricing kernel is consistently U-shaped. The results are robust to variations in the methodology and hold for...

The Accardi-Boukas quantum Black-Scholes framework, provides a means by which one can apply the Hudson-Parthasarathy quantum stochastic calculus to problems in finance. Solutions to these equations can be modelled using nonlocal diffusion processes, via a Kramers-Moyal expansion, and this...

In this paper, we propose a general framework for the valuation of options in stochas-tic local volatility (SLV) models with a general correlation structure, which includes the Stochastic Alpha Beta Rho (SABR) model and the quadratic SLV model as special cases. Standard stochastic volatility...

We generalize the Kou (2002) double exponential jump-diffusion model in two directions. First, we independently displace the two tails of the jump size distribution away from the origin. Second, we allow for each of the displaced tails to follow a gamma distribution with an integer-valued shape...