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

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

for constants κ and σ and g(·) is chosen to fit the current yield curve.

(a) Calculate the forward rates fs(u) using the Vasicek bond pricing formula.

(b) Calculate αs(u) and σs(u)such that, as s changes, dfs(u) = αs(u)ds+ σs(u)dB∗

s .

(c) Prove that

αs(u) = σs(u)

u s

σs(t)dt .