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Pricing Asian Options with Stochastic Convenience Yield and Jumps

27 Pages Posted: 13 Jun 2017  

Christian-Oliver Ewald

University of Glasgow; Center for Dynamic Macroeconomic Analysis, University of St. Andrews - School of Economics and Finance

Yuexiang Wu

University of Glasgow - Adam Smith Business School

Aihua Zhang

University of Leicester - Department of Mathematics

Date Written: June 12, 2017

Abstract

We price Asian options on commodity futures contracts in the presence of stochastic convenience yield and interest rates as well as jumps in the commodity spot price. We obtain a closed-form solution for the geometric average case without the presence of jumps. This analytic result enables us to apply suitable control variates to price an arithmetic average Asian option via Monte Carlo simulation. We observe a significant reduction in the size of confidence intervals. Varying the parameters of the model, we obtain a good understanding as to how option prices change accordingly. We then consider a variation of the model through adding 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 leads to 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, Commodities, Stochastic Convenience Yield

JEL Classification: G11

Suggested Citation

Ewald, Christian-Oliver and Wu, Yuexiang and Zhang, Aihua, Pricing Asian Options with Stochastic Convenience Yield and Jumps (June 12, 2017). Available at SSRN: https://ssrn.com/abstract=2984865

Christian-Oliver Ewald (Contact Author)

University of Glasgow ( email )

Adam Smith Building
Glasgow, Scotland G12 8RT
United Kingdom

Center for Dynamic Macroeconomic Analysis, University of St. Andrews - School of Economics and Finance ( email )

Castlecliffe
The Scores
St. Andrews, Fife KY16 9AL
United Kingdom
+44(0)1334 462435 (Phone)

HOME PAGE: http://www.maths.usyd.edu.au/u/ewald/

Yuexiang Wu

University of Glasgow - Adam Smith Business School ( email )

Glasgow, Scotland
United Kingdom

Aihua Zhang

University of Leicester - Department of Mathematics ( email )

University Road
Leicester, LE1 7RG
United Kingdom

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