This paper analyses the volatility structure of commodity derivatives markets. The model encompasses hump-shaped, unspanned stochastic volatility, which entails a finite-dimensional affine model for the commodity futures curve and quasi-analytical prices for options on commodity futures. Using...

By employing a continuous time stochastic volatility model, we analyse the dynamic relation between price returns and volatility changes in the commodity futures markets. We use an extensive daily database of gold and crude oil futures and futures options to estimate the model that is well...

This paper analyzes the volatility structure of commodity derivatives markets. The model encompasses stochastic volatility that may be unspanned by futures contracts. A generalized hump-shaped volatility specification is assumed that entails a finite-dimensional affine model for the commodity...

Research on the Heath-Jarrow-Morton (1992) term structure models so far has focused on the class having time-deterministic instantaneous forward rate volatility. In this case the forward rate is Markovian, even if the spot rate process is not. However, this Markovian feature can only be used...

This paper considers the dynamics for interest rate processes within the Heath, Jarrow and Morton (1992) specification. It is well known that one of the difficulties in using this specification for estimation is the non-Markovian nature of the dynamics. The paper focuses on a fairly broad family...

We propose a generalization of the Shirakawa (1991) model to capture the jump component in fixed income markets. The model is formulated under the Heath, Jarrow and Morton (1992) framework, and allows the presence of a Wiener noise and a finite number of Poisson noises, each associated with a...

Here I consider the dynamics of interest rate processes in the multi-factor model specified in Heath, Jarrow and Morton (1992). Despite its flexibility and theoretical advances, the number of empirical studies using the HJM model remains inadequate, principally because of the difficulty...

The following sections are included:The Model

The following sections are included:IntroductionProblem Statement — The Heston ModelFinding the Density Function using Integral TransformsSolution for the American Call OptionNumerical Scheme for the Free SurfaceConclusionAppendixProof of Proposition 5.8 — The European Option PriceEvaluation...

In this chapter we shall drop the stochastic volatility component from the dynamics by assuming that the variance is constant and merely discuss how to handle the jump term in the transform approach. Option pricing under jump-diffusion dynamics was originally investigated by Merton (1976) for...