Question 3 Consider the following SDE for the short rate of interest - drt = (...

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Question 3 Consider the following SDE for the short rate of interest - drt = ( r ) d t + d t where , and are known positive constants and , is a standard Wiener process under probability measure Q. a) i) For 0 t t 0, is given by where P (t, r) = e^(t,T)-C(t,T) r 1-e-a (T-t) C(t, T) A(t, T) = [C(t, T') - (T - t)] (T-1)] ( - 02 (C(t, T)) 2 a 4 a i) By writing down the SDE governing PT (t, r+) or otherwise, identify the diffusion parame- ter for a bond that matures at time T and comment on its sign. ii) What happens to bond price volatility as maturity approaches? Is this expected? Question 3 Consider the following SDE for the short rate of interest - drt = ( r ) d t + d t where , and are known positive constants and , is a standard Wiener process under probability measure Q. a) i) For 0 t t 0, is given by where P (t, r) = e^(t,T)-C(t,T) r 1-e-a (T-t) C(t, T) A(t, T) = [C(t, T') - (T - t)] (T-1)] ( - 02 (C(t, T)) 2 a 4 a i) By writing down the SDE governing PT (t, r+) or otherwise, identify the diffusion parame- ter for a bond that matures at time T and comment on its sign. ii) What happens to bond price volatility as maturity approaches? Is this expected?