An Exact Bond Option Formula

Abstract

This paper derives a closed-form solution for European options on pure discount bonds, assuming a mean-reverting Gaussian interest rate model as in Vasicek [8]. The formula is extended to European options on discount bond portfolios.

A model of discontinuous interest rate behavior, yield curves, and volatility

“…In this manner, one could price bonds and other interest rate contingent claims without knowing the true volatility of interest rates. This contrasts with the bond option models of Cox et al (1985) and Jamshidian (1989) that require the true volatility of interest rates.…”

Change of numeraire in the two-marginals martingale transport problem

“…The technique of change of numeraire was first introduced by Jamshidian [12] in the context of interest rate models and turned out to be a very powerful tool in derivatives pricing (see Geman et al [ We consider a two-period financial market with one riskless asset, whose price is identically equal to one, and one risky asset whose discounted price evolution is modelled by the process (M t ) 2 t=0 = (1, X, Y ). The random variables X and Y , modelling respectively the prices at time t = 1 and t = 2, are defined on the canonical measurable space ( , F), where = 1 × 2 with 1 = 2 = R ++ and F = B( ).…”

Interest rate options valuation under incomplete information

“…They differ only by their boundary conditions. Instead of solving a PDE for each kind of option, which requires tedious calculus, in the following section, an alternative method is used, pioneered by Jamshidian (1989), to obtain preferencefree pricing formulas for the interest-rate-sensitive options. We make use of the forwardneutral probability measure equivalent to the risk-neutral measure.…”