# How to estimate market based PD and LGD for small enterprises?

I am estimating CVA/DVA for derivatives...

How to estimate PD and LGD (or RR) based on market data for the small enterprises, if there is no external rating for them and they don't have bonds or equities on exchange market? Note that these are companies from small open economy, so there are also no external ratings other than for the whole country.

I am asking for literature, methods or any tips and tricks...

• Do you have CDS data? If so, you can use it to estimate PDs and LGDs – FunnyBuzer Feb 13 at 12:12
• Here is a post about computing PDs using CDS spreads, RRs and time points as input variables quant.stackexchange.com/questions/15986/… – FunnyBuzer Feb 13 at 12:20
• No, I don't have CDS data... that's the point of my problem. – Vesnič Feb 13 at 12:31
• Then you need a PD and LGD model based for instance on IFRS9 or CECL standards. LGD is often based on expert judgement (especially for retail portfolios), whereas PD is normally estimated via a scorecard model. However, since you don't have an external rating, you can calibrate it on your dataset, provided you have a sufficient amount of defaults. Note that you also need several statistical tests (AUROC, Gini, etc.) in order to select the market variables that are deemed discriminatory in your scorecard model. – FunnyBuzer Feb 13 at 12:50
• As an alternative to all this, you can make a research on the industry-based proxies for the LGDs and a proxy CDS spread curve and then you are only left with the estimation of the EAD, which is non-trivial. – FunnyBuzer Feb 13 at 12:55

In '74 Merton proposed a Credit Risk Model based on modelling the equity of a company as a call on its assets. Its very straight forward. You can calibrate on a single point or over a time series of the variables below.

You only need the book value of a firm's equity, E, total assets, A, total liabilities, L and the volatility of them.

$$PD=1−N(DD)$$

where DD,

$$DD= (ln(A)+(μ_A−σ^2_A/2)T−ln(L))/(σ_A\sqrt{T})$$

https://www.mathworks.com/help/risk/default-probability-using-the-merton-model-for-structural-credit-risk.html

Unless there are reference instruments you can back out the implied PD or implied LGD you cannot find market-based pds and lgds for small companies. To my knowledge the only way to calculate the PD and LGDs for these smaller corporates / enterprises is to build models based on balance sheet information, or other characteristics you have for the counterparties.

You might work in a bank or similar - ask your credit risk modelling team to provide you with the point in time PDs and stressed LGDs for your list of companies.

I need to follow IFRS13 so I cannot use PDs and LGDs calculated for IFRS9...

As above noted I will use balance sheet data, but there are more than one options to do it:

• using Merton-like default models
• using regression analysis that use financial indicators as independent variable.
• What would be your dependent variable for the regression? – FunnyBuzer Feb 21 at 10:02
• The event of bankruptcy, compulsory settlement or compulsory liquidation – Vesnič Feb 21 at 10:17
• Yes, if you have enough data, that would serve your purpose. I'd recommend the Merton model only in case you don't have enough data. Otherwise better to fit a logit, which is usually quite robust. – FunnyBuzer Feb 21 at 10:30