Why Normal Rate Assumptions Can Simplify CMS Spread Option Pricing

Summary

The document raises a pricing question about a constant-maturity-swap (CMS) spread option under a normal model. If the two underlying CMS rates are jointly normal, their difference is also normally distributed, which can make an option on that spread amenable to an analytic price formula.

It does not provide the formula, a derivation, citations, or market evidence; it asks readers to identify a publication. The key modeling caveat is that normal marginals alone do not specify the spread distribution: the rates’ dependence, including their correlation, is needed to determine its variance. The post contrasts this search problem with the more readily found literature on lognormal models, but does not compare model fit or establish when the normal assumption is appropriate.

Key ideas

• Under a joint normal model, the difference between two CMS rates is normally distributed.
• An option on that spread may therefore have an analytic pricing formula.
• The spread variance depends on the rates’ covariance as well as their individual variances.
• The document asks for a reference and supplies no formula, derivation, or empirical validation.

Tags

# Searching for a paper on CMS Spread Option normal model price formula


# Searching for a paper on CMS Spread Option normal model price formula












Apparently if we assume that each underlying CMS rate is normally distributed then a formula for the CMS Spread Option price can be evaluated analytically in the absence of any contingency due to the fact that the difference in two normally-distributed random variables is also normally distributed. However, wherever I search I only find information on lognormal models. Please, can anyone point me to a paper or publication on this subject?

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