Suppose that the survival probabilities up to time T for a defaultable asset and the price...

   

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Suppose that the survival probabilities up to time T for a defaultable asset and the price of the default-free ZCB are given in the following table: T 1-F(T) 0.25 0.95 0.5 0.92 0.75 0.88 1 0.7 1.5 0.65 (a) Calculate and comment on the hazard rates of defaults. (b) Estimate the price of the corresponding defaultable ZCB for all the maturities above, assuming zero recovery rate. (c) Do the same estimations when the expected recovery rate is 30%, 50% and 70% (assuming partition times 0.25, 0.5, 0.75, 1 and 1.5). (d) What is the implied recovery rate R if the defaultable bond price BR (0,1) is 0.88? b(0,T) 0.98 0.97 0.94 0.93 0.90 HW1-2. Assume that the current continuous-time hazard rate is given by h(0, t) = t, for all 0 t T, for some constants > 0, a 0. The free-risk interest rate is constant at r > 0. (a) Calculate the probability of default up to time T = 0.5. (b) Derive the formulas for b(0, t), F(t), B(0, t), Br(0, t). (c) Is the probability of default up to time t an increasing or decreasing function of a? Suppose that the survival probabilities up to time T for a defaultable asset and the price of the default-free ZCB are given in the following table: T 1-F(T) 0.25 0.95 0.5 0.92 0.75 0.88 1 0.7 1.5 0.65 (a) Calculate and comment on the hazard rates of defaults. (b) Estimate the price of the corresponding defaultable ZCB for all the maturities above, assuming zero recovery rate. (c) Do the same estimations when the expected recovery rate is 30%, 50% and 70% (assuming partition times 0.25, 0.5, 0.75, 1 and 1.5). (d) What is the implied recovery rate R if the defaultable bond price BR (0,1) is 0.88? b(0,T) 0.98 0.97 0.94 0.93 0.90 HW1-2. Assume that the current continuous-time hazard rate is given by h(0, t) = t, for all 0 t T, for some constants > 0, a 0. The free-risk interest rate is constant at r > 0. (a) Calculate the probability of default up to time T = 0.5. (b) Derive the formulas for b(0, t), F(t), B(0, t), Br(0, t). (c) Is the probability of default up to time t an increasing or decreasing function of a?