Merton Model of Asset Value and Its Volatility Using Equity Market Valuation Merton Model of…

FNAN 491 Computational Finance Using Excel and Mathematica
© Problem Set 4: Merton Model of Asset Value and Its Volatility Using Equity Market Valuation
Merton Model of Asset, Debt and Equity Valuation
In this problem, worth 20 points, the Merton model of Asset, Debt and Equity Valuation will be employed to estimate a firm’s:
1. market asset values (as opposed to book asset values),
2. the market implied volatility of asset returns,
3. risk premium on its debt,
4. solvency ratio,
5. distance to default (as defined by KMV), and
6. probability of insolvency computed assuming V is a lognormal variable.
Data that is needed will come from the firm’s balance sheet and includes:
1. The book value of assets as of the last annual report to start the estimation,
2. The sum of debt of the company separated into secured debt and subordinated debt,
3. The risk free interest rates for 1, 2 and 3 years’
4. The market capitalization of the firm near the lasts annual report, and
5. An estimate of the volatility over 1 year of the firm’s stock returns (implied volatility can be used for a 1 year call option).
Choose two firms: one that seems to be near bankruptcy and another that is not.
Computational Requirements
Use Mathematica to perform your calculations. Two approaches will be used:
1. The Mathematica function of FindRoot or Nsolve using the two equations in the Merton Model as shown below, and
2. Newtons’s iterative method as shown in the Matlab and Mathematica coding added to BlackBoard.





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