# How to interpret negative asset volatility numerical results in Merton model?

I am currently working on my thesis where I discuss the Merton default probability model. I have a huge sample of US firms for the period 1990-2010. I use both numerical and complex iterative approach to estimate asset volatility and asset value.

I have a problem with the numerical approach because when I estimate asset value and asset volatility (in statistical software R with this code) for some firms in the sample I get a negative annual asset volatility. This does not make sense as something which is result of square root can't be negative, but it could be due estimation in numerical approach.

Has anyone come across something like this or what are your thoughts regarding this phenomenon.

• I think it would be more helpful if you were to post your code and link to the data. Without knowing what calculations you did, help is limited. – rocinante May 15 '14 at 8:55
• here is the link R code – user3618375 May 15 '14 at 8:57

• You may also want to check to make sure you are expressing data in the right terms. Balance sheet data is usually in M$, CDS Spreads are in bps Notional, CDS Upfront quotes are in pct Notional etc. – CodeJockey May 15 '14 at 15:09 The estimation method you use places no restriction on the parameters. One solution would be to use the$\log\$ of the volatility and backtranform in the estimation function.
Alternatively, you can use the R package I have made. See the function BS_fit. All methods guarantee a positive volatility. A caveat is that I do not implement the numerical methods as it is unstable.