IAI Actuarial Core Principles · Economic Modelling · Simple models for credit risk
A risky zero-coupon bond pays ₹100 at time 2 if no default occurs and nothing otherwise (zero recovery). The risk-free continuously compounded rate is 5% and the risk-neutral hazard rate is constant at 2%. Which is the price of the bond closest to?
With zero recovery, the price equals 100 discounted at the risk-free rate plus the hazard rate: 100×exp(-0.07×2) = about ₹86.94, so the nearest option is ₹86.99. The default-adjusted rate is 7%, not 5%.
- A₹90.48
- B₹86.99
- C₹93.99
- D₹82.70Correct
- ₹100.00
Explanation
Price = 100 × exp(-(r+λ)T) = 100 × exp(-0.07×2) = 100 × exp(-0.14) = 86.94, which is close to 86.99... check: exp(-0.14)=0.8694, so price 86.94. Nearest option is ₹86.99.
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