Therefore, we will suspend disbelief for a while and derive the Black-Scholes-Merton formula in a world where interest rates are deterministic, and then turn around and apply these to interest rate options!

Before we get there, however, a bit of probability review is in order.

A random variable (r.v.) *X* is said to have a *Normal* distribution with mean *µ* and standard deviation *σ* , if the probability that it lies in some region [*x, x* + *dx*] is approximately

We will use the shorthand *X* ~ *N*(*µ, σ* ^{2} ). More precisely, the *cumulative distribution function* (CDF) of an *N*(*µ, σ* ^{2} ) random variable *X* is

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