Moments of brightness!


In the darkest of the darkest moments,
One may think that the future is dark,
And the world around you is ending soon…
Give it some time,
And you shall soon realise,
That it was an eclipse that was about to end,
Or a dark cloud that was about to rain…
Wait for the bright sun,
Or the cool shower,
Your day has arrived…
Give it some time…


Are you inclined towards quantitative modelling, but have no funds?


Continuing my efforts towards a utilitarian policy, here are some links to some sites, which provide free Add-ins, and packages. You may use them, by agreeing to the License Agreements specified in each.

I’ve used many, and they are worth a try, if you don’t have enough funds to buy those rocket-scientist’s quant packages.

PopTools [Good for Matrices and Simulations]:

FreeStatistics [Decide what you want before opening this link caz you will be amazed by the choice provided]:

ASAP Utilities [Are you deep into Excel-based Modelling, you will need this, for cleaning and maintaining data sheets]:

Go ahead, start number crunching in a better way…

But, if you have some doubts on Statistics, go to,

Key Parameters for Capital Models, under IRB Approach

Basel II, Credit Risk, Quant

First thing first….how do you find a Default (or what all can be treated as a default)?

Default event arises from non-payment of principal or interest, for more than a particular period of time [say, 90 days].

Incase of an exposure, where in the interest is due for more than 90 days, bank should stop accruing interest on this exposure, and transfer it to non-accrual/non-performing category, and consider it as a default. Sufficient importance should be given to capture these non-performing exposures for reporting purposes, internally, and externally. All concerned processes should align with Bank’s policy of identifying default. If any of the exposures of a particular customer to any of the lenders turn to default, then it should be considered as a default, by all lenders, even with a zero LGD.

How do you compute Expected Loss?

In an advanced approach, the three main parameters to be calculated are:

Probability of Default [PD/Expected Default Frequency]: This is the default probability for a borrower over a certain time period, say one-year. This is often mapped to Risk Grading/Rating of the borrower. Bank should have a sound Rating methodology for PD calculation, which can be a point-in-time (PIT, depends on current market indicators) or a through-the-cycle [TTC, a long-term view followed by Rating Agencies]. Basel prefers a TTC model over PIT, as it indicates the use of long term historical data. To verify the consistency of rating models, banks should do a Rating Migration Study on the historical data. Migration studies can be done over different pools, like organizations, locations, or type of borrowers. Banks should plot ‘Cumulative Accuracy Profile’ [CAP] for finding out the differentiating capacity of the models they developed. CAP is plotted for each category, with Defaults vs. All Ratings.

The clue for an accurate model is, the closer the graph is towards the northwest, the more accurate the models are.

Loss given Default [LGD/Loss Severity]: This is the expected amount of loss on a facility provided to a borrower given a default event. It can be treated as another way of representing Recovery Rate.i.e.1-Recovery Rate = LGD. For an efficient calculation of LGD, three main parameters should be identified correctly, and they are,
(i) identify the defaulted exposure,
(ii) exposures outstanding at the time of default, and
(iii) amount and timing of repayments ultimately received after the default.

All qualitative parameters, structure and Claim of Bank over the exposure [Senior, Sub etc.] are to be captured along with the quantitative parameters for accurate profiling. Other items to be captured along with the above mentioned are, Definition of LGD, Exposure measurement, determination of what constitutes resolution, calculation methodology and collateral segmentation. Other details to be collected include Charge-offs, Recoveries, Timings for the recoveries, Cost-of-collection, and other administrative costs. While, for market traded bonds, the market value of bonds immediately [say, 3 weeks to 1 month] represent the LGD value, for non market traded instruments, LGD is calculated by discounting the net cash flows, after default event. All past due interest, if any, should also be added to the final value. When the aggregation is done on an exposure level, this should include all exposures/facilities against the customer. Any further lending/extension of loan, after the default event [for enhancing the repayment ability] should also be included in the cash flows. Sometimes, cash flows happen over a very long time period, like 5-6 yrs, particularly in Corporate Loans. Discretion should be made for this time period, that, the bank should limit its data collection to a time period of 2-3 years. Once all the cash flows are reconstructed, these should be discounted at an appropriate discount rate. This discount rate should resemble a rate, which is the rate at which a buyer will be ready to pay for these distressed assets. Adequate provisions should be made in the bank system to trigger covenants/collaterals in case of a single default or when the credit quality deterioration from the customer, even if other facilities are not at default. During LGD calculation, sufficient importance should be made to capture the information on collaterals/covenants. Banks should maintain two LGD figures – one, at the time of disbursement of loan which is the average experienced rate, and second, in the event of default.

Exposure at Default [EAD/Usage given Default]: This is the amount of exposure at the time of default. In normal circumstances, this is the face amount of exposure at the time of default, but for committed credit lines, even if there is an unused/undrawn portion, this also should be included in the exposure. A Loan Equivalent [LEQ] factor can also be included, which denotes the probability of drawing the unused portion also, at the time of default. The average utilization rate [while not at default] should not be taken as a proxy of this, but should be calculated on a historical basis according to characteristics. The LEQ is usually represented as percentage of unused commitment. Thus EAD is the sum of current utilization percentage of total commitment and LEQ rate applied unutilized commitment. i.e. EAD = Util + LEQ(100% – Util). While calculating LEQ, all revolving exposures against a particular customer should be treated as a single exposure, as customer may arbitrarily choose to withdraw from any facility. It is good practice to floor LEQ at slightly above 0%, even if the customer pays back some amount prior to default thus resulting in a negative LEQ. Another best practice to be followed is to cap utilization at 100%, even if there may be instances of customer drawing more than what is allowed, due to operational errors, or a revised rating immediately before default event. Banks should decide whether they want to create a new exposure replacing an old exposure, or continue the same exposure, when facilities have revolving nature. It is important to note that longer the period of commitment, higher is the probability of drawing down unused commitment before default because the chances of a credit deterioration is high in longer commitment periods. An important point to note down is the change in LEQ with respect to the change in credit qualities, as better credit rated exposures have few covenants and thus risky in an event of default, while lower categories are more closely watched, and will have tight covenants. A best practice to be followed here is to determine an equation/relation [regression methods] with respect to LEQ, Rating and tenor, T, for a period I, during the tenor T. Thus a weighted average LEQ should be calculated by considering LEQ for individual periods, and applying the probabilities for individual periods. For Basel compliance, these individual LEQs, which are f (Rating, T), should be validated at various time points.

And finally, we’ve arrived at the Expected Loss [EL] formula: EL is the product of PD, LGD and EAD, with a maturity adjustment.