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A Barndorff-Nielsen and Shephard model with leverage in Hilbert space for commodity forward markets

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  • Fred Espen Benth

    (Oslo University)

  • Carlo Sgarra

    (Università di Bari)

Abstract

We propose an extension of the model introduced by Barndorff-Nielsen and Shephard, based on stochastic processes of Ornstein–Uhlenbeck type taking values in Hilbert spaces and including the leverage effect. We compute explicitly the characteristic function of the log-return and the volatility processes. By introducing a measure change of Esscher type, we provide a relation between the dynamics described with respect to the historical and the risk-neutral measures. We discuss in detail the application of the proposed model to describe the commodity forward curve dynamics in a Heath–Jarrow–Morton framework, including the modelling of forwards with delivery period occurring in energy markets and the pricing of options. For the latter, we show that a Fourier approach can be applied in this infinite-dimensional setting, relying on the attractive property of conditional Gaussianity of our stochastic volatility model. In our analysis, we study both arithmetic and geometric models of forward prices and provide appropriate martingale conditions in order to ensure arbitrage-free dynamics.

Suggested Citation

  • Fred Espen Benth & Carlo Sgarra, 2024. "A Barndorff-Nielsen and Shephard model with leverage in Hilbert space for commodity forward markets," Finance and Stochastics, Springer, vol. 28(4), pages 1035-1076, October.
    • Handle: RePEc:spr:finsto:v:28:y:2024:i:4:d:10.1007_s00780-024-00546-0
    DOI: 10.1007/s00780-024-00546-0
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    References listed on IDEAS

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    Cited by:

    1. Martin Friesen & Sven Karbach, 2024. "Stationary covariance regime for affine stochastic covariance models in Hilbert spaces," Finance and Stochastics, Springer, vol. 28(4), pages 1077-1116, October.
    2. Fred Espen Benth & Heidar Eyjolfsson, 2024. "Robustness of Hilbert space-valued stochastic volatility models," Finance and Stochastics, Springer, vol. 28(4), pages 1117-1146, October.

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    More about this item

    Keywords

    Forward prices; Stochastic volatility; Leverage; Ornstein–Uhlenbeck; Processes in Hilbert space; Positive definite operators; Fourier transform; Lévy processes;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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