Term Structure Derivatives

Vasicek bond option pricing

If the term structure model is Vasicek's model there is a solution for the price of an option on a zero coupon bond, due to Jamshidan (1989).

Under Vacisek's model the process for the short rate is assumed to follow.

where , and are constants. We have seen earlier how to calculate the discount factor in this case. We now want to consider an European Call option in this setting.

Let be the time price of a zero coupon bond with a payment of $1
at time (the discount factor). The price at time of a European call
option maturing at time on on a discount bond maturing at time is( See
Jamshidan (1989) and Hull (1993))

where

In the case of ,

2003-10-22