# FRM Level 2 Formulas – Credit Risk Measurement and Management

## Introduction

We present the formulas for the Credit Risk Measurement and Management segment.

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## Firm Value

[ Firm Value *  N ( d1 ) ]  –  [ Debt * e –rT  * N ( d2 ) ]

## Netting Factor

Netting Factor = ( ( n + n*(n – 1)r )½  /  n

## Expected Loss

Expected Loss = KN ( –e2 ) – At * e u ( T – t ) * N ( -e1 )

## Debt Value

Value of Debt  =  Value of Risk Free Debt – Value of Put Option

St  =  Vt N * ( k + sv ( T – t ) ½ ) – K e –r(T – t)  * N ( k )

F’ ( t ) = l * e lt

F(u) =  1 – exp ( – hu )

Where:

h = ( Spread ) / ( 1 – Recovery )

Credit Spread =  yD ( t,T ) – y P*( t,T ) =  lG

## Conditional Prepayment Rate (CPR)

Conditional Prepayment Rate  =  1 – ( 1 –  Single Month Mortality Rate )12

CPR =  1 – ( 1 –  SMM )12

CVA   =  Loss Given Default  *  Exposure at Default  *  Default Probability

CVA  =  LGD * EAD * DP

CVA  =   ( 1 – Recovery Rate ) * S  [  ( Discount Factor ) * ( Exposure ) * ( Probability of Default ) ]

## Average Life

Average Life  = S [ ( t * Principal time t ) / ( 12 * Total Principal ) ]

CPR = 1 – ( 1 – SMM )12

## Probability of Default

Default Probability = 1 – e lt

NB:

l  = Spread / ( 1 – Recovery Rate )

## Default Correction

rab    = [ pab  –  (  pa  *  pb ) ]  /  [ pa * ( 1 –  pa ) ] ½  *  [ pb * ( 1 –  pb ) ] ½

EAD = Amount Drawn + ( Amount Limit – Amount Drawn ) * Loan Equivalent Ratio

## Summary

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