The main result of the paper is a formula for zero time-to-maturity limit of implied volatilities of European options under a broad class of stochastic volatility models. Based on this formula, we propose a closed-form approximation of the implied volatility smile. Numerical examples suggest...

In the complete market model of geometric Brownian motion, all kinds of exotic options can be priced and hedged perfectly using a delta hedging strategy which duplicates the option's payoff. If trading takes place in a frictionless market, this delta hedging strategy is said to eliminate the...

This paper discusses a new approach to contingent claim valuation in general incomplete market models. We determine the neutral derivative price which occurs if investors maximize their local utility and if derivative demand and supply are balanced. We also introduce the sensitivity process of a...

This paper uses a probabilistic change-of-numeraire technique to compute closed-form prices of European options to exchange one asset against another when the relative price of the underlying assets follows a diffusion process with natural boundaries and a quadratic diffusion coefficient. The...

In this paper we address the pricing of double barrier options. To derive the density function of the first-hit times of the barriers, we analytically invert the Laplace transform by contour integration. With these barrier densities, we derive pricing formulÖfor new types of barrier options:...

We consider the pricing of derivatives written on the discretely sampled realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limit, the quadratic variation of the underlying log-price. Here, we characterize the...

The valuation of options and many other derivative instruments requires an estimation of exante or forward looking volatility. This paper adopts a Bayesian approach to estimate stock price volatility. We find evidence that overall Bayesian volatility estimates more closely approximate the...

The valuation of options and many other derivative instruments requires an estimation of exante or forward looking volatility. This paper adopts a Bayesian approach to estimate stock price volatility. We find evidence that overall Bayesian volatility estimates more closely approximate the...