IAI Actuarial Core Principles · Economic Modelling · Simple models for credit risk
A one-year zero-coupon bond from an Indian corporate has face value Rs 100. The risk-free one-year rate is 6% p.a. effective. The probability of default is 4%, and on default the recovery is 50% of face value. Assuming risk-neutral valuation and that the stated default probability is risk-neutral, what is the price of the bond?
The price is the expected payoff discounted at the risk-free rate: 0.96×100 plus 0.04×50 gives 98, divided by 1.06 gives Rs 92.45.
- ARs 88.68
- BRs 90.57Correct
- CRs 92.45
- DRs 94.34
- Rs 96.23
Explanation
Expected payoff = 0.96×100 + 0.04×50 = 96 + 2 = 98. Discounting at 6%: 98/1.06 = 92.45. Check: the option labelled Rs 92.45 is therefore correct, so the key must be index 2.
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