In a recent study, we present a tree methodology to evaluate the expected generalized realized variance in a general stochastic volatility model. This provides an efficient way of calculating the fair value of the strike for variance swaps. In this article, we expand the methodology to price...

A new valuation and calibration method for VIX futures and VIX options is proposed. The method is based on a closed-form Hermite series expansion for a stochastic volatility model with the stochastic variance process driven by an affine drift term. We implement the methodology for the Heston and...

In this paper, we propose an approach to modeling the jump component of a jump-diffusion model using a log mixture of normals distribution. We define explicitly theproperties of the distribution and use it to create an analytic formula for Europeanoption price. Numerous examples of applications...

"This book falls broadly in the area of financial mathematics. It presents a multitude of topics that are relevant to the quantitative finance community. Experts in teaching and active in research, the authors aim to discuss theory in the context of applications to specific practical problems....

In this paper, we develop a Markov chain-based approximation method to price arithmetic Asian options for short maturities under the case of geometric Brownian motion. It has the advantage of being a closed-form approximation involving only matrices. It is an accurate, efficient, and stable...

Attempted dynamic replication based valuation of equity options is analyzed using the Optimal Hedge Monte-Carlo (OHMC) method. Detailed here are (1) the option hedging strategy and its costs; (2) irreducible hedging errors associated with realistically fat-tailed & asymmetric return...