Closed Form Spread Option Valuation

23 Pages Posted: 13 Jun 2008

See all articles by Petter Bjerksund

Petter Bjerksund

Norwegian School of Economics (NHH) - Department of Business and Management Science

Gunnar Stensland

Norwegian School of Economics (NHH) - Department of Business and Management Science

Date Written: December 1, 2006

Abstract

This paper considers the valuation of a spread call when asset prices are lognormal. The implicit strategy of the Kirk formula is to exercise if the price of the long asset exceeds a given power function of the price of the short asset. We derive a formula for the spread call value, conditional on following this feasible but non-optimal exercise strategy. Numerical investigations indicate that the lower bound produced by our formula is extremely accurate. The precision is much higher than the Kirk formula. Moreover, optimizing with respect to the strategy parameters (which corresponds to the Carmona-Durrleman procedure) yields only a marginal improvement of accuracy (if any).

Keywords: Spread option, closed form, valuation formula, lognormal asset prices

JEL Classification: G12, G13, D81, C63

Suggested Citation

Bjerksund, Petter and Stensland, Gunnar, Closed Form Spread Option Valuation (December 1, 2006). NHH Dept. of Finance & Management Science Discussion Paper No. 2006/20. Available at SSRN: https://ssrn.com/abstract=1145206 or http://dx.doi.org/10.2139/ssrn.1145206

Petter Bjerksund (Contact Author)

Norwegian School of Economics (NHH) - Department of Business and Management Science ( email )

Helleveien 30
Bergen, NO-5045
Norway

Gunnar Stensland

Norwegian School of Economics (NHH) - Department of Business and Management Science ( email )

Helleveien 30
Bergen, NO-5045
Norway

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