This objective of this paper is to develop a generic, yet practical framework for construction of Markov models for commodity derivatives. We aim for sufficient richness to permit applications to a broad variety of commodity markets, including those that are characterized by seasonality and by...

This paper considers the pricing of European options on assets that follow a stochastic differential equation with a quadratic volatility term. We correct errors in the existing literature, extend the pricing formulas to arbitrary root configurations, and list alternative representations of...

Stochastic volatility models are increasingly important in practical derivatives pricing applications, yet relatively little work has been undertaken in the development of practical Monte Carlo simulation methods for this class of models. This paper considers several new algorithms for...

Polynomial splines are popular in the estimation of discount bond term structures, but suffer from well-documented problems with spurious inflection points, excessive convexity, and lack of locality in the effects of input price perturbations. In this paper, we address these issues through the...

In this paper, we demonstrate that many stochastic volatility models have the undesirable property that moments of order higher than one can become infinite in finite time. As arbitrage-free price computation for a number of important fixed income products involves forming expectations of...

While convertible bond models recently have come to rest on solid theoretical foundation, issues in model calibration and numerical implementation still remain. This paper highlights and quantifies a number of such issues, demonstrating, among other things, that naiuml;ve calibration approaches...

This paper introduces stochastic volatility to the Libor market model of interest rate dynamics. As in Andersen and Andreasen (2000a) we allow for non-parametric volatility structures with freely specifiable level dependence (such as, but not limited to, the CEV formulation), but now also...

This paper presents a number of new theoretical results for replication of barrier options through a static portfolio of European put and call options. Our results are valid for options with completely general knock-out/knock-in sets, and allow for time- and state-dependent volatility as well as...

This paper investigates the effect of interest rate correlation in the pricing of Bermudan swaptions. Investigating both Gaussian Markov models and Libor Market models, we find that Bermudan swaption prices depend only weakly on the number of factors in the underlying interest rate model....

The standard approach (e.g. Dupire (1994) and Rubinstein (1994)) to fitting stock processes to observed option prices models the underlying stock price as a one-factor diffusion process with state- and time-dependent volatility. While this approach is attractive in the sense that market...