Contents
- Index
Application of Merton's Model: Example 1
©2009 OS Financial Trading System
Suppose the underlying asset value of firm =$50M and the face amount of the outstanding debt is $80M. That is, the firm is insolvent and it's debt is in the "junk bond" range.
Can this stock trade at a positive price?
The answer is yes because the stock has option value. Although the underlying asset value is $50 M the asset value process has volatility associated with it which implies that it can fluctuate both in a positive and or negative manner. If a positive bounce is experienced then the firm becomes solvent once again and the stock has value. That is, we can view the stock as an option that is currently "out of the money" but given volatility has a positive probability of going "into the money."
Option pricing has six inputs into the valuation model:
Underlying asset value V = $50 million and suppose the annualized volatility of the total assets is 30%.
Strike price: in this case it is the face value of debt-holders who are paid off prior to the stockholders. So the strike price is K = $80 million
Life of the option (suppose weighted average time to maturity of the debt equals the projected life until default) then the life is T = 10-years
Finally, suppose the risk free rate = 5%
We can now enter these inputs into the Black Scholes option pricing model to estimate the value of the stock:
You can launch the Option Calculator directly from the FTS Real Time client by selecting FTS Modules and then
The input variables can now be entered into the option as follows:
The value of the option is 24.03994 million and this implies that the value of the debt is $50M - $24.03994 = $25.96 M.