Calculating credit risk in unlisted assets is challenging, even more so when it comes to infrastructure. Estimating the Probability of Default (PD) and Loss Given Default (LGD) of infrastructure debts presents unique obstacles, partly because - historically - the senior debt of these kinds of issuers is very rarely officially declared to be in default.

Senior lenders usually have tight control of the assets and operations, so that when an infrastructure project is struggling to service its debt and make payments, they have access to a range of options to "rescue" their investment other than bankrupt or liquidation.

How can we see when an issuer might be in trouble? One sign is when the debt service cover ratio (DSCR) decreases quickly and approaches 1 - the threshold of default. The DSCR is simply the ratio of the firms free cash flow available for debt service or CFADS, to the current debt service.

But there are relatively few examples of this unique feature of defaulted cases available for analysis. However, this also implies that there were many triggered credit events 'hidden' behind the lenders' interventions.These hidden or 'soft' credit events are the consequence of senior debt instruments' embedded optionality, step-in rights that determine contemporary decisions based on the expected value. This optionality leads us to use a structural model to estimate potential credit events and risks.

We measure credit risk by estimating the best fit for the volatility of the firm's free cash flow given its market value and book value and use this implied volatility measure to compute a series of credit risk metrics. Indeed, the free cash flow determines the entire value of the firm and, though the cash flow waterfall, that of debt and equity.

Thus,

- given a value for CFADS volatility \sigma, we can compute the expected value of debt and the expected value of equity, as is done in standard option pricing, using the equity risk premia derived from our asset pricing methodology.
- in the same process, we also produce a number of scenarii of the CFADS which include an number of default and restructuring scenarios
- given these scenarios, we can compute credit metrics: the probability of default, loss given default and expected loss
- we pick the value of \sigma that best fits the fundamental relationship between book and market value by solving FirmValue(\sigma) = TotalAssetValue
- This process can be re-interated to compute the credit risk metrics of each firm on each valuation (quarter end) date.

The inputs used include

- the observed book value of the firm
- the estimated equity risk premia and relevant interest rate curves
- expected (forecast) CFADS at the time of estimation
- future aggregate senior debt service at the time of estimation

Given the best fit for \sigma, we compute debt and equity equity values in each cash flow scenarii, including when debt cannot be repaid and needs to be restructured (which impacts future dividends and the value of equity).