Pricing Asian Options with Stochastic Convenience Yield and Jumps

32 Pages Posted: 30 Jan 2020 Last revised: 30 Jul 2020

See all articles by Christian-Oliver Ewald

Christian-Oliver Ewald

University of Glasgow; Høgskole i Innlandet

Yuexiang Wu

University of Glasgow

Aihua Zhang

University of Leicester - Department of Mathematics

Date Written: July 29, 2020

Abstract

We price Asian options on commodity futures contracts in the presence of stochastic convenience yield, stochastic interest rates and jumps in the commodity spot price. We obtain a closed-form solution for the case of a geometric average option without the presence of jumps, both for continuous and discrete averaging. This analytic result enables us to employ the geometric average option as suitable control variate for pricing the corresponding arithmetic average Asian option via Monte Carlo simulation. We observe a significant reduction in the size of confidence intervals in relation to plain Monte Carlo. Varying the parameters of the model, we obtain a good understanding as to how Asian option prices change accordingly in relation to a stochastic convenience yield. We then consider a variation of the model by adding stochastic jumps to the commodity spot price dynamics. By conditioning on the jump times first and then averaging over the sequences of jump times, we show that our control variate still provides a significant variance reduction, even though a closed-form solution for a geometric average Asian option in the presence of jumps is unavailable.

Keywords: Asian Options, Stochastic Convenience Yield, Jump Diffusion, Derivatives

JEL Classification: G13, G11, D52, C63

Suggested Citation

Ewald, Christian-Oliver and Wu, Yuexiang and Zhang, Aihua, Pricing Asian Options with Stochastic Convenience Yield and Jumps (July 29, 2020). Available at SSRN: https://ssrn.com/abstract=3516694 or http://dx.doi.org/10.2139/ssrn.3516694

Christian-Oliver Ewald

University of Glasgow ( email )

Adam Smith Building
Glasgow, Scotland G12 8RT
United Kingdom

Høgskole i Innlandet ( email )

Lillehammer, 2624
Norway

Yuexiang Wu (Contact Author)

University of Glasgow ( email )

Adam Smith Business School
Glasgow, Scotland G12 8LE
United Kingdom

Aihua Zhang

University of Leicester - Department of Mathematics ( email )

University Road
Leicester, LE1 7RG
United Kingdom

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