Multi-asset spread option pricing and hedging

Abstract

We provide two new closed-form approximation methods for pricing spread options on a basket of risky assets: the extended Kirk approximation and the second-order boundary approximation. The latter method generalizes the results in Li et al. [J. Deriv., 2008, 15, 58–80] to spread options on an arbitrary number of assets. Numerical analysis shows that while the latter method is more accurate than the former, both methods are extremely fast and accurate. Closed-form approximations for important Greeks are also derived. Our approximation methods enable the accurate pricing of a bulk volume of spread options on a large number of assets in real time, which offers traders a potential edge in a dynamic market environment.

Keywords:

• Multi-asset spread options
• Second-order boundary approximation
• Closed-form approximation

Acknowledgements

The authors thank participants at the 2008 FMA Meeting, the 2008 EFA Meeting, and seminars at GaTech and the Chinese University of Hong Kong, especially Malcolm Wardlaw at the University of Texas at Austin, and Cai Li at the University of Massachusetts, for useful discussions. Feedback from Stephen Figlewski at NYU, Neil Pearson at UIUC, and Rene Carmona at Princeton, Krzysztof Wolyniec at Sampra Commodities, Sundeep Jain at UBS, and Gary Kennedy at Calypso, are greatly appreciated. We also thank Daniel Toro at the University of Manchester, John van der Hoek at the University of South Australia, Roberto Modafferi at the Banca Fideuram SpA, and Simon Benninga at Tel-Aviv University for their interest in our paper and for the questions they have raised that often led us to think further. Dr Kyuseok Lee's help in proof-reading the manuscript is also gratefully acknowledged. All remaining errors are ours.