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IAI Actuarial Core Principles · Economic Modelling · Simple models for credit risk

A one-year zero-coupon bond of face Rs 1,000 is issued by a firm. The risk-free annual effective rate is 5%. Under the Jarrow-Lando-Turnbull style simple model, default probability in the year is 4% and recovery is 50% of face value, paid at the end of the year in default. What is the price of the bond, to the nearest rupee, using risk-neutral probabilities equal to the real-world ones?

The price is about Rs 933. Expected payoff is 0.96 times 1,000 plus 0.04 times 500, equal to Rs 980, and discounting one year at 5% gives Rs 933.

  1. ARs 933Correct
  2. BRs 952
  3. CRs 962
  4. DRs 971
  5. Rs 914

Explanation

Expected payoff = 0.96×1000 + 0.04×500 = 960 + 20 = 980. Discount at 5%: 980/1.05 = 933.33, so Rs 933. Rs 952 is the price with no default; Rs 914 would use 0 recovery... check: 960/1.05 = 914.3, so Rs 914 omits recovery.

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