Unexpected Loss Computation

Keywords: default mode, expected default frequency, uniform deviates, asset correlation, obligor mapping, migration, equity buffer, events. netting rules, loss given default, stochastic recovery.

Risksvr™  simulates credit default events in three different ways:

  • Through a Markov chain, which assumes events are independent.
  • Through correlated events, which assumes default events are dependant. 
  • Through Time to Default, which can be seen as a bridge between the two.

However, it always ends up computing the Loss Given Default probability density function.

Once a default event has been observed, Risksvr™ computes the value of the account:

The Value of the Account during the state of default can follow different  assumptions. 
This means you can choose which type of approach you want your loss given default calculation to follow.
This flexibility is very important since there are many schools of thought and approaches that can be followed to compute Loss-Given Default.:

  • The value can be computed from full revaluation.
    In this case, the value can be defined from:
    • The exact value of the instrument at the time of default or
    • From the Mean Average value up to the simulation horizon when the party defaulted.

    This option is available to users who believe the true value might underestimate the loss when they occur 
    near the end of the simulation horizons.  

  • The value can be computed from a series of user defined Add-On Rules and Factors. These factors can take into account 
    Time Bucket of Exposure, Credit Rating, Market Value, Mean, Volatility, Skew, Kurtosis, Correlation, Yield of Instrument, Counterparty and account terms and conditions.

Then for each account, all receivable and payable amounts are summed by rating category.

If the cumulated account position value is positive and the account 
can be netted then the portfolio is given a value of zero.
 
If the Account cannot be netted, the value of all receivable transactions are set to zero. 
the loss is then computed as the value of the portfolio if it is positive and can be netted or the cumulated receivables if it cannot be be netted.

If Recovery Rates are active, ( either static or stochastic), the loss will be net of recovery i.e.(1-Recovery Rate) 
Which will always  be less conservative than if no recovery is applied. 
This is due to the fact that recovering an amount on the lost capital which we are seeking to compute will 
be reduced by the recovery amount (if static recoveries are selected) or the mean +/- the mean volatility times the random draw
(if stochastic recoveries are selected ) .

 
 
  		Recovery rates are NOT active by default. 
Since Recovery values diminish the amount due, they reduce the overall Credit Risk and are therefore less Conservative.

If collateral has been activated, the collateral will serve to absorb the outstanding portion of the loss.
if country risk and Home office risk is active, then the values will be then absorbed by each party in the chain of guarantors.


Once all these computations have been performed, the simulation engine aggregates position values and accumulates
the four key statistics (mean, variance, skew and kurtosis), computes any dependant factor, buckets the distribution of returns into  quantiles (or only the tail if requested)  and then proceeds to the next node in time. 

 with asset Value VH at horizon H

 

 

Required Capital can then calculated 

either as the Present Value or Forward Value (i.e. the Discount Factor becomes 1) of the Losses Given Default or the Loss  found in the left hand tail of the Portfolio's Losses Given Default Probability distribution. 
 
  		Risksvr assumes Forward Values are used by default since a Present Value will diminish the Loss and thus reduce Credit Risk and is therefore less Conservative.

 

 

Equity buffer capital can also be complemented with Operation Risk, Market, Liquidity Risk and Country Risk either through Copula or Sum of Variance approaches.

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