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

In a simple model, a one-year zero-coupon bond has a risk-neutral default probability of q and a recovery rate of R fraction of face value. Under risk-neutral pricing, which expression gives the approximate continuously compounded credit spread for small q?

The approximate spread is q(1 - R), the default probability times the loss given default. The price is the risk-free discounted expected payoff, and for small q the log of 1 - q(1 - R) is about minus q(1 - R).

  1. Aq
  2. Bq(1 - R)Correct
  3. Cq/(1 - R)
  4. DqR
  5. (1 - q)R

Explanation

Price = e^-r [1 - q(1 - R)] and the risky yield satisfies e^-y = that price, so spread = -ln[1 - q(1 - R)], which is about q(1 - R) for small q. Spread q ignores recovery, and qR uses the recovered amount instead of the loss.

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