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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
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
Credit Valuation Adjustment (CVA)
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
Exposure at Default (EAD)
EAD = Amount Drawn + ( Amount Limit – Amount Drawn ) * Loan Equivalent Ratio
Summary
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