Closed Form Spread Option Valuation
23 Pages Posted: 13 Jun 2008
Date Written: December 1, 2006
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: Suggested Citation