Suppose that the price of a zero-coupon bond maturing at time T follows the process 

and the price of a derivative dependent on the bond follows the process 

Assume only one source of uncertainty and that f provides no income. 

(a) What is the forward price, F, of f for a contract maturing at time T? 

(b) What is the process followed by F in a world defined by numeraire P(t, T)? 

(c)  What is the process followed by F in the traditional risk-neutral world? 

(d) What is the process followed by f in a world defined by a numeraire equal to a bond maturing at time T^* where T^* ≠ T? Assume that σ^*_P is the volatility of this bond 

Transcribed Image Text:

dP(t,T) = µ,P(t,T)dt + o,P(t,T) dz %3D df = µ; f dt + o,f dz