An analyst is using a two state continuous time model to study the credit risk of zero coupon bonds issued by different companies The risk neutral transition intensity function is (s) 0 0148 for Company A, and A (s) 0 01s for Company B where s measures time in years from now The analyst observes that the credit spread on a 3 year zero coupon bond just issued by Company B is twice that on a 3 year zero coupon bond just issued by Company A (1) Given that the risk free force of interest is 5 pa, and that the average recovery rate in the event of default, 8, where 0 8 1, is the same for both companies, calculate 8 7 Explain how the two state model for credit risk can be generalised to give the Jarrow Lando Turnbull model 3 Total 10 The credit worthiness of debt issued by companies is assessed at the end of each year by a credit rating agency The ratings are A (the most credit worthy), B and D (debt defaulted) Historical evidence supports the view that the credit rating of a debt can be modelled as a Markov chain with the following matrix of one year transition probabilities (1) (0 92 0 05 0 03) X 0 05 0 85 0 1 001 Determine the probability that a company rated A will never be rated B in the future 2 (ii) (a) Calculate the second order transition probabilities of the Markov chain (b) Hence calculate the expected number of defaults within the next two years from a group of 100 companies, all initially rated A 2 The manager of a portfolio investing in company debt follows a downgrade trigger strategy Under this strategy, any debt in a company whose rating has fallen to B at the end of a year is sold and replaced with debt in an A rated company (iii) Calculate the expected number of defaults for this investment manager over the next two years, given that the portfolio initially consists of 100 A rated bonds 2 (iv) Comment on the suggestion that the downgrade trigger strategy will improve the return on the portfolio 2 Total 8

Question: An analyst is using a two-state continuous-time model to study the credit risk of zero- coupon bonds issued by different companies. The risk-neutral transition

An analyst is using a two-state continuous-time model to study the credit risk of zero- coupon bonds issued by different companies. The risk-neutral transition intensity function is: (s) = 0.0148 for Company A, and A (s) = 0.01s for Company B where s measures time in years from now. The analyst observes that the credit spread on a 3-year zero-coupon bond just issued by Company B is twice that on a 3-year zero-coupon bond just issued by Company A. (1) Given that the risk-free force of interest is 5% pa, and that the average recovery rate in the event of default, 8, where 0

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