Particle Markov Chain Monte Carlo methods for Calibration and Estimation of Multi Factor s.d.e. Commodity Models

Sandwich Seminar

I will review models proposed in the literature based on multi factor s.d.e. frameworks for commodity modeling, including the basic economic justification for such factors in the models and the different structures proposed. Then based on a recent general class of multi factor s.d.e. models proposed in the literature, we will formulate a special case of such a model for which closed from expressions for futures prices and vanilla options prices may be obtained. This extends the multi-factor long-short model in Schwartz and Smith (Manag Sci 893–911, 2000) and Yan (Review of Derivatives Research 5(3):251–271, 2002) in two important aspects: firstly we allow for both the long and short term dynamic factors to be mean reverting incorporating stochastic volatility factors and secondly we develop an additive structural seasonality model.

In developing this non-linear continuous time stochastic model we maintain desirable model properties such as being arbitrage free and exponentially affine, thereby allowing us to derive closed form futures prices. In addition the models provide an improved capability to capture dynamics of the futures curve calibration in different commodities market conditions such as backwardation and contango.

A Milstein scheme is used to provide an accurate discretized representation of the s.d.e. model. This results in a challenging non-linear non-Gaussian state-space model. To carry out inference, we develop an adaptive particle Markov chain Monte Carlo method. This methodology allows us to jointly calibrate and filter the latent processes for the long-short and volatility dynamics. This methodology is general and can be applied to the estimation and calibration of many of the other multi-factor stochastic commodity models proposed in the literature. We demonstrate the performance of our model and algorithm on both synthetic data and real data for futures contracts on crude oil.


Gareth Peters (UCL)

Monday, November 5, 2012 - 12:30
to 13:30