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

A one-year zero-coupon corporate bond with face value Rs 100 trades at a continuously compounded yield of 8% p.a. The risk-free continuously compounded rate is 5% p.a. Assuming zero recovery and a risk-neutral default intensity constant over the year, what is the implied annual risk-neutral default intensity (approximately, using the credit spread)?

With zero recovery, the credit spread equals the risk-neutral default intensity under continuous compounding. The spread is 8% minus 5%, so the intensity is 3% per annum.

  1. A1% p.a.
  2. B2% p.a.
  3. C3% p.a.Correct
  4. D5% p.a.
  5. 8% p.a.

Explanation

With zero recovery, price = 100·e^{-(r+λ)}, so the yield spread equals the default intensity: λ = 8% − 5% = 3%. Using 8% alone ignores the risk-free component, and 5% is the risk-free rate itself.

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