Our first aim in this paper is to introduce a futures-based model able of capturing the main features displayed by Crude Oil futures and options contracts, such as the Samuelson volatility effect and the volatility smile. We calculate the joint characteristic function of two futures contracts in...

This paper deals with the problem of modelling the volatility of futures prices in agricultural markets. We develop a multi-factor model in which the stochastic volatility dynamics incorporate a seasonal component. In addition, a maturity dependent damping term accounts for the Samuelson effect....

The aim of this paper is to obtain the risk-neutral density of an underlying asset price as a function of its option implied volatility smile. We derive a known closed form non-parametric expression for the density and decompose it into a sum of lognormal and adjustment terms. By analyzing this...