Evaluating Risk using the Merton Model

s mentioned previously, for my AMP466 Assignment, I'll be using the Merton Model to evaluate credit risk of corporate debt i.e. calculate the probability of default for a given company.

You can learn more about the Merton Model here.

Basically, the model uses a single debt and equity issue to represent the financing. The assets of the company is the total market capitalization and the debt is the market capitalization multiplied by the debt/equity ratio. Adding the two numbers gives the total value of the company. The model is used to calculate numbers for one year.

It is mostly an academic tool, since there are problems with its application in real world scenarios, a few short comings are:

• the model can be used only for companies who have stock
• governments cannot be evaluated

To compensate for these limitations a company, KMV, was created to commercialize Merton's work, it was later bought by Moodys.

I choose to evaluate First Solar (FSLR):

First you need to calculate the historical volatility of the stock, here and here is some more info on that. First Solar has been public since Nov 17th, 2006, so I used all of the available daily data.

logarithmic return: is the stock value on day i

sample variance: , is the mean of daily returns.

annualized volatility: multiply by 252 trading days since I use daily data

I calculated the historical volatility to be 70

Whenever necessary, I used the LIBOR risk free interest rate of 2.52%, it changes so look it up.

Credit Spread
S = Market Cap = 21,864.65 million
B = Current Debt = S * Debt/Equity = 21864.65e6 * 0.0986 = 2155.85 million
V = B + S = 2155.85e6 + 21864.65e6 = 24020.5 million

Finding Future Debt
K = 0.0986 * 2155.85e6 * e0.0252 = 2210.87 million this is the value of the debt discounted to one year into the future.

Using the Black-Scholes formula I find the volatility of the assets. John Hull has a B-S calculator on his website, I recommend using it or another of the B-S calculators floating around.
Treat the Future Debt as the strike price, and the Total Assets as the value of the equity. Use the historical volatility that was calculated previously.

Updating the volatility on each iteration, using the result is σv = 71.52% Asset Volatility

ln(K/B) = ln(2210.87/2155.85) = 0.0252  yield
2.52% - (risk free rate = 2.52%) = 0%  Credit Spread

Annual Risk Neutral Probability of Default

to be con't

Expected Credit Loss

to be con't


All the beautiful equations that you see are care of LATEX for blogger.

Ready, Set, Run

I'll try to use this blog to keep me honest in my pursuit of knowledge in Finance. I am a Computer Engineer, in my last month of M.Eng. My budding interest in finance as a area of study and profession has set me on a course to read many books, explore new computer systems and build some cool tools...

I plan to:

• C++ : finish reading Primer, I need a better grasp
• Read books on Finance
• Paul Wilmott
• John Hull
• more...
• Read books on Math
• Stochastic Calculus
• Optimization
• more...
  
• Learn Erlang
• Read some books on Trading systems
• Learn VBA: seems to be required
• Python: this one is a maybe
• Put together a nice trading system, allow for easy expansion through ready made components...
• MAKE SOME MONEY :)
  

But first, need to finish my assignment on Credit Risk analysis (APM466) :)