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

In a Merton model, the risk-free rate is 5% per year continuously compounded, debt has face value Rs 100 crore due in 2 years, and the firm's assets are worth Rs 150 crore. Use the replication idea: the debt equals a risk-free bond less a put option on the assets. If the put (strike Rs 100 crore, expiry 2 years) is worth Rs 4 crore, what is the value of the debt, to the nearest Rs 0.1 crore? (e^-0.1 = 0.904837)

The debt is worth about Rs 86.5 crore. Discounting Rs 100 crore at 5% for two years gives Rs 90.48 crore, and subtracting the Rs 4 crore put, which represents the shareholders' default option, gives Rs 86.48 crore.

  1. ARs 86.5 croreCorrect
  2. BRs 90.5 crore
  3. CRs 94.5 crore
  4. DRs 94.5 crore plus the put, Rs 98.5 crore
  5. Rs 146.0 crore

Explanation

Risk-free bond = 100 x 0.904837 = 90.4837. Risky debt = 90.4837 - 4 = 86.4837, about Rs 86.5 crore. Rs 90.5 crore ignores the put (the default risk). Adding the put wrongly (94.5) uses the wrong sign.

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