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Pricing of Commodity Derivatives on Processes with Memory

Author

Listed:
  • Fred Espen Benth

    (Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway
    These authors contributed equally to this work.)

  • Asma Khedher

    (Korteweg-de Vries Institute for Mathematics, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands
    These authors contributed equally to this work.)

  • Michèle Vanmaele

    (Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Krijgslaan 281 S9, B-9000 Gent, Belgium
    These authors contributed equally to this work.)

Abstract

Spot option prices, forwards and options on forwards relevant for the commodity markets are computed when the underlying process S is modelled as an exponential of a process ξ with memory as, e.g., a Volterra equation driven by a Lévy process. Moreover, the interest rate and a risk premium ρ representing storage costs, illiquidity, convenience yield or insurance costs, are assumed to be stochastic. When the interest rate is deterministic and the risk premium is explicitly modelled as an Ornstein-Uhlenbeck type of dynamics with a mean level that depends on the same memory term as the commodity, the process ( ξ ; ρ ) has an affine structure under the pricing measure Q and an explicit expression for the option price is derived in terms of the Fourier transform of the payoff function.

Suggested Citation

  • Fred Espen Benth & Asma Khedher & Michèle Vanmaele, 2020. "Pricing of Commodity Derivatives on Processes with Memory," Risks, MDPI, vol. 8(1), pages 1-32, January.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:1:p:8-:d:311524
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    References listed on IDEAS

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