Hi All,
I'm having problems determining the value of the firm's assets and the asset's volatility with the merton's model. I understand that to solve for the asset value and volatility, we have to go through iterations of the Newton rhapson method, coupled with the complexity of merton's model and ito's lemma would be extremely exhausting to work on by hand. I was wondering if there is a software or a programme for those calculations.
I have several questions regarding the merton model as well
1) Debt value - I was looking at balance sheets of financial institution for their debt value, specifically their total liabilities. Am i looking at the right place?
2) The r in the merton's model, sometimes it refers to expected return and sometimes it is refered to as risk-free interest rate. What is the rationale for that and which one is more approproate if i'm determining PD for banks.
3) Ito's lemma, has a component, volatility of equity returns. I determine that value by taking the standard deviation of the percentage difference of daily stock prices.
Eg:
Date, Stock price, Percent Change,
1st Jan 2007, 22.2
2nd Jan 2007, 22.3, 0.45%
3rd Jan 2007, 22.1, -0.90%
The PX change is calculated by taking the ln of the current day divided by the previous day. Therefore 0.45% on 3/1/2007 is calculated by taking ln(22.3/22.2). It is calculated in this fashion all the way towards the end of the year.
Sigma A is actually the volatility of the stock value. It is calculated by taking the standard deviation of all the PX change from 1/1/2007 to 31/12/2007 then multiplying by the square root of 365. I think its the wrong way but I don't know the right way
I apologise if my questions sound like I never took any banking modules at school. Truth is I never did and this research paper is what i was assigned. I'm at my wits end and I would appreciate any help i can get here.
Alex
