This question is on stochastic interest rates a. Suppose the spot interest rate r, which is a function of time t, satisfies the stochastic differential equation dr= dWt. Using this model for the spot rate, by hedging one bond V(r,t;T) of maturity T, with another of a different maturity, derive the bond pricing equation tV+21r22VrVrV=0 where =(r,t) is an arbitrary function. b. By considering an unhedged bond and the risk free return, explain how and why arises in (5.1). This question is on stochastic interest rates a. Suppose the spot interest rate r, which is a function of time t, satisfies the stochastic differential equation dr= dWt. Using this model for the spot rate, by hedging one bond V(r,t;T) of maturity T, with another of a different maturity, derive the bond pricing equation tV+21r22VrVrV=0 where =(r,t) is an arbitrary function. b. By considering an unhedged bond and the risk free return, explain how and why arises in (5.1)