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Pricing of Commodity Derivatives on Processes with Memory

Authors
  • benth, fred espen
  • khedher, asma
  • vanmaele, michèle
Publication Date
Jan 21, 2020
Identifiers
DOI: 10.3390/risks8010008
OAI: oai:mdpi.com:/2227-9091/8/1/8/
Source
MDPI
Keywords
Language
English
License
Green
External links

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 &xi / with memory as, e.g., a Volterra equation driven by a L&eacute / vy process. Moreover, the interest rate and a risk premium &rho / 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 ( &xi / / &rho / ) 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.

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