Assume the short rate is rt = rt +g(t), where dr = rdt + dB and

Assume the short rate is rt = ˆrt +g(t), where drˆ = −κrˆdt + σ dB∗

and g(·) is chosen to fit the current yield curve.

(a) Consider a forward contract maturing at T on a discount bond maturing at u > T. Let Ft denote the forward price for t ≤ T. What is the volatility of dFt/Ft?

(b) What is the average volatility between 0 and T of dFt/Ft in the sense of (17.9)?

(c) Consider a call option maturing at T on a discount bond that matures at u > T. Derive a formula for the value of the call option at date 0.