Kindly assist in getting the solutions for the following. Thanks

Company X has just issued some 5-year zero-coupon bonds, A continuous-time two-state model is to be used to model the status of the company and to calculate the fair price of the bonds. It is believed that the risk-neutral transition rate for failure of the company is 1 () = 0.0021, where r is the time in years since the issue of the bonds. The 5-year risk-free spot yield is 5.25% expressed as an annual effective rate. (i) Calculate the risk neutral probability that the company will have failed by the end of 5 years. [2] (ii) In the event of failure of the company, the bonds will make a reduced payment at the maturity date. The recovery rate for a payment due at time f is: 8 (1) = 1-0.05t Calculate the fair price to pay for f100 nominal of a Company X bond, taking into account the possibility of company failure. [3] (mii) An analyst is concerned that the estimate of 2 () may be too simplistic. Explain the possible reasons for his concern and how the model could be developed to deal with this. [3] [Total 8]In a particular two-state intensity-based model with constant transition intensities, the integrated generator matrix M = A(w)du has the form M = where S b a =0.2(f-s) and b=0.1(1 -s). (i) Show that, in this case. M-=-(a+b)M . (ii) Hence deduce an explicit formula for e in terms of a and b. (Hii) IIence deduce a set of formulae for the transition probabilities p;(s,()