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N(d1) and N(d2) in Merton Model

Could some one explain to me how the N(d1) and N(d2) is computed in this question below?

Let firm value (V) equal $1 billion with face value of debt (F) equal to $800 million. The debt is zero-coupon and matures in four years (T = 4.0). The riskless rate is 5.0%. The estimate of the volatility of the firm, sigma(V), is 20% per annum. The firm’s assets are expected to grow at 10% per annum. What does the Merton model return for the value of the firm’s equity?

This is the question 4 in study note of Reading 43 of Bionic Turtle FRM Part 2 Market Risk, The answer just give some d1 and d2 but I have difficulty understanding where they come from?


Well-Known Member
d1 and d2 are derived from the BSM model which is applied in the Merton model for the valuation of Equity and Debt.
https://www.bionicturtle.com/forum/threads/merton-model-a-summary-of-the-issues.5646/. David covers in great detail how to calculate the value under the Merton model
https://www.bionicturtle.com/forum/threads/p2-t6-303-malz-on-merton-model.6794/, the last post has an Excel sheet that derives the d1 and d2 based on the BSM model. If you just plug in the numbers to the BSM valuation model, you get the Merton model value of Equity of the firm