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Risks 2018, 6(3), 77; https://doi.org/10.3390/risks6030077

Calendar Spread Exchange Options Pricing with Gaussian Random Fields

Institute of Statistics, Biostatistics and Actuarial Sciences, University Catholique de Louvain, Voie du Roman Pays 20, 1348 Louvain-la-Neuve, Belgium
Received: 6 July 2018 / Revised: 31 July 2018 / Accepted: 2 August 2018 / Published: 8 August 2018
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Abstract

Most of the models leading to an analytical expression for option prices are based on the assumption that underlying asset returns evolve according to a Brownian motion with drift. For some asset classes like commodities, a Brownian model does not fit empirical covariance and autocorrelation structures. This failure to replicate the covariance introduces a bias in the valuation of calendar spread exchange options. As the payoff of these options depends on two asset values at different times, particular care must be taken for the modeling of covariance and autocorrelation. This article proposes a simple alternative model for asset prices with sub-exponential, exponential and hyper-exponential autocovariance structures. In the proposed approach, price processes are seen as conditional Gaussian fields indexed by the time. In general, this process is not a semi-martingale, and therefore, we cannot rely on stochastic differential calculus to evaluate options. However, option prices are still calculable by the technique of the change of numeraire. A numerical illustration confirms the important influence of the covariance structure in the valuation of calendar spread exchange options for Brent against WTI crude oil and for gold against silver. View Full-Text
Keywords: Gaussian fields; Exchange options; Calendar options Gaussian fields; Exchange options; Calendar options
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Hainaut, D. Calendar Spread Exchange Options Pricing with Gaussian Random Fields. Risks 2018, 6, 77.

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