Subordinated affine structure models for commodity future prices

Abstract

To date the existence of jumps in different sectors of the financial market is certain and the commodity market is no exception. While there are various models in literature on how to capture these jumps, we restrict ourselves to using subordinated Brownian motion by an α-stable process, α ∈ (0,1), as the source of randomness in the spot price model to determine commodity future prices, a concept which is not new either. However, the key feature in our pricing approach is the new simple technique derived from our novel theory for subordinated affine structure models. Different from existing filtering methods for models with latent variables, we show that the commodity future price under a one factor model with a subordinated random source driver, can be expressed in terms of the subordinator which can then be reduced to the latent regression models commonly used in population dynamics with their parameters easily estimated using the expectation maximisation method. In our case, the underlying joint probability distribution is a combination of the Gaussian and stable densities.

Keywords

• stable distributions
• affine structure models
• latent regression models