Suppose the forward rate volatility under the one-factor HJM model takes the form 

show that the Jamshidian decomposition technique (Jamshidian, 1989) cannot be used to price an option on a coupon bearing bond with coupon payment date T_i,i = 1, 2, ··· ,n. Find an approximation price formula to the European call option on a coupon bearing bond whose weight w_i(r, t) is defined by (8.2.12).

The short rate process under the given volatility structure is non-Markovian. The stochastic duration is the solution D(t) to the following equation

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OF(t, T) = 01 +0₂[1 - e-α(T-1)],