Closed form spread option valuation

This paper considers the valuation of a spread call when asset prices are log-normal. 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 greater 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).