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FRM Part II · FRM Exam Part II · Estimating Default Probabilities

A risk analyst uses the Merton model to estimate asset volatility from observable equity data. Which relationship does she use to link equity volatility to asset volatility?

The link is sigma_E = sigma_V times N(d1) times V0 divided by E0. Equity behaves like a call on assets, so its volatility is asset volatility scaled by the call delta and leverage; this is solved jointly with the equity pricing equation.

  1. Asigma_E = sigma_V * N(d1) * V0 / E0Correct
  2. Bsigma_E = sigma_V * N(d2) * E0 / V0
  3. Csigma_E = sigma_V * N(-d1) * D / E0
  4. Dsigma_E = sigma_V * V0 / D

Explanation

Equity is a call on assets, so its volatility equals the asset volatility scaled by the option delta N(d1) and the leverage ratio V0/E0. Using N(d2) or the E0/V0 ratio inverts or misstates the sensitivity, and the equation is solved together with the equity value equation.

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