Quote Originally Posted by Snoopy View Post
Grunter, if I read the paper correctly, the authors are studying corporate bonds, the vast majority investment grade. In particular the study looks at the market interest rate of those bonds as it varies in time with a one month sampling frequency for the data. Attempts are then made to see if this data can be used to correlate with the default risk of the assiciated individual company for each bond considered.

A default is a default after it has happened. But there is a long standing practical problem of determining the mathematical boundaries for when a default happens - the covenant that triggers the default can vary between companies in practice. This paper attempts to get around this problem by defining default as a "two-factor square-root diffusion model."

A "two-factor square-root diffusion model", from what I can figure, is in general terms, modelling (equations 3a and 3b) a kind of 'decay behaviour' (By this I mean you start with a constant value and subtract a time series function around variable 's'). The 'initial state' dissipates in proportion to the function of 's' entities decaying, plus a variable term related to the square root of 's' multipled by the standard deviation from some central condition. In mathematical terms the form is:

Change = [Constant - Decay Function] + [Standard Deviation] x [Square Root of Decay Function] x [Another Constant]

This equation form is entirely selected by the authors, and already includes a 'variability term'. Thus far from 'proving' that variability and its triigger of volatility is related to company default, the paper appears to set up this prospect by 'definition' at the outset.

Then, in a 'huge surprise' ;-), this 'defintion of default' is best actuated by another function, the bouncing up and down of bond interest rates which introduces a 'volatility' that satisfies the variability trigger of the model! I may have interpreted all this incorrectly. But it looks to me Grunter, like a circular argument you are running. Define a 'default' as a 'function of variabilty', then introduce a 'volatility' that triggers the 'variabilit'y that 'proves' your case.

I am struck by the following comment in the introduction to the reference paper

"Much of the literature follows Merton (1974) by explicitly linking the risk of a firm’s de-fault to the variability in the firm’s asset value. Although this line of research has proven very useful in addressing the qualitatively important aspects of pricing credit risks, it has been less successful in practical applications."

Have you considered that the reason many of these studies have 'failed to work in practice' (for individual companies) is that the underlying premise of the model being studied is wrong?

Are you able to articulate, without referencing an academic paper, exactly why you feel 'volatility' is related to the 'risk of bankruptcy' for any particular investment?

SNOOPY
Snoopy,

Most banks are listed, and also have debt issuances. In sophisticated markets, most also have Credit Default Swaps on these bonds. This is the best way to price the risk of default in the bank.

You seem to think that Banks are an entirely different beast - they are not.

You also seem to not know what parts of the paper to read - you don't read what the paper is proposing - just read the theory parts. I'm not trying to propose ways of measuring risk - I post the papers so they explain the theoretical underpinnings of the argument to make clearer to you.

Essentially volatility is related to the risk of bankruptcy as the risk of bankruptcy is defined as when the value of the bank's assets fall to a defined amount (zero/below solvency requirements whatever). As the value of the assets fluctuates through time, this means that the value of the assets is volatile. Therefore it is easy to see that low volatility means that it is less likely the bank's assets will drop below the bankruptcy benchmark, and more volatility means that it is more likely the benchmark will be reached.

I fail to see how you haven't grasped this concept?