An analyst is using a two-state continuous-time model to study the credit risk of zero- coupon...

 

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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) = 0.01s² 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] 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) = 0.01s² 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]

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The images contain two separate questions concerning risk analysis and transition probabilities Lets address each question individually Starting with the first question about the credit risk of zeroco... View the full answer