Suppose the bond price B(t, T) satisfies the following PDE:

?rtB + Bt + Br(? ? ??B) + ?Brr?2 = 0

B(T, T) = 1.

Define the variable V(u) us

(a) Let B(t, T) be the bond price, Calculate the d(BV).

(b) Use the PDE in (93) to get an expression for dB(t, T).

(c) Integrate this expression from t to T and take expectations with respect to martingale equality to obtain the bond pricing formula:

Where the expectation is conditional on the current rt which is assumed to be known.

Transcribed Image Text:

V(u) = e-r.ds e"lalr,.s)dW,-}a(r,sf'as)