Let the dynamics of the short rate r(t) be governed by the extended Vasicek model 

Show that the value of the European call option with strike price X maturity at T on a T’-maturity discount bond is given by

where B(t,T ) is the discount bond price, 

Also, show that the put-call parity relation between the prices of the European put and call options on the same underlying discount bond is given by 

Transcribed Image Text:

dr (t) = [p(t) - ar(t)] dt+ or dZ(t).