A note on closed-form spread option valuation under log-normal models

TL;DR

This paper introduces a new closed-form formula for spread call option valuation under log-normal models, generalizing previous formulas and demonstrating improved accuracy in certain parameter ranges.

Contribution

It provides an alternative, more flexible closed-form formula for spread option pricing that encompasses previous models as special cases.

Findings

The new formula generalizes existing models.

Numerical tests show improved accuracy in specific parameter ranges.

The formula simplifies to previous models under certain parameters.

Abstract

In the papers Carmona and Durrleman [7] and Bjerksund and Stensland [1], closed form approximations for spread call option prices were studied under the log normal models. In this paper, we give an alternative closed form formula for the price of spread call options under the log-normal models also. Our formula can be seen as a generalization of the closed-form formula presented in Bjerksund and Stensland [1] as their formula can be obtained by selecting special parameter values to our formula. Numerical tests show that our formula performs better for certain range of model parameters than the closed-form formula presented in Bjerksund and Stensland [1].