Local Volatility Models for Commodity Forwards

Lavagnini Silvia, BI Norwegian Business School
Detering Nils , Universität Düsseldorf

We present a class of Hilbert-space valued local-volatility models designed specifically for forward curves in commodity markets. These models are governed by a stochastic partial differential equation, and we establish the existence and uniqueness of solutions within our framework. In addition, martingality and positivity conditions are derived. Our approach encompasses a wide range of specifications, including an Hilbert-space valued constant elasticity of variance (CEV)-type model. However, we find that the CEV model lacks the flexibility required to reproduce the smile-shaped implied volatility observed in electricity markets, among others. Motivated by empirical findings, we propose a local volatility specification for forwards curves that offers the necessary flexibility to capture the volatility surface. We then introduce a machine learning approach for pricing and model calibration. This methodology enables us to overcome some of the inherent numerical complexities associated with this class of models.

Area: CS58 - Recent advances in Heath-Jarrow-Morton modelling in finance (Claudio Fontana and Alessandro Gnoatto)

Keywords: HJM, commodity markets, local-volatility

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