We describe a model for evolving commodity forward prices that incorporates three important dynamics which appear in many commodity markets: mean reversion in spot prices  , decorrelation of moves in different points on the forward curve, and implied volatility skew and smile. This model is a "forward curve model" - it describes the stochastic evolution of forward prices - rather than a "spot model" that models the evolution of the spot commodity price (and possibly the convenience yield) . Two Brownian motions drive moves across the forward curve, with a third Heston-like stochastic volatility process scaling instantaneous volatilities of all forward prices. In addition to an efficient numerical scheme for calculating European vanilla and early-exercise option prices, we describe an algorithm for Monte Carlo-based pricing of more generic derivative prices which involves an efficient approximation for the risk neutral drift that avoids having to simulate drifts for every forward settlement date required for pricing.
We describe a model for evolving commodity forward prices that incorporates three important dynamics which appear in many commodity markets: mean reversion in spot prices and the resulting Samuelson effect on volatility term structure , decorrelation of moves in different points on the forward curve, and implied volatility skew and smile. This model is a "forward curve model" - it describes the stochastic evolution of forward prices - rather than a "spot model" that models the evolution of the spot commodity price . Two Brownian motions drive moves across the forward curve, with a third Heston-like stochastic volatility process scaling instantaneous volatilities of all forward prices. In addition to an efficient numerical scheme for calculating European vanilla and early-exercise option prices, we describe an algorithm for Monte Carlo-based pricing of more generic derivative payoffs which involves an efficient approximation for the risk neutral drift that avoids having to simulate drifts for every forward settlement date required for pricing.
A
and the resulting Samuelson effect on volatility term structure
D
(and possibly the convenience yield)
R
prices
payoffs