Pricing of Commodity Derivatives on Processes with Memory

Fred Espen Benth, Asma Khedher and Michèle Vanmaele
Additional contact information
Fred Espen Benth: Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway
Asma Khedher: Korteweg-de Vries Institute for Mathematics, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands
Michèle Vanmaele: Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Krijgslaan 281 S9, B-9000 Gent, Belgium

Risks, 2020, vol. 8, issue 1, 1-32

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.

Keywords: equivalent measures; derivatives pricing; commodity markets; Langevin equation; affine processes; Fourier transform (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2020
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