Risk Management of credit

Management of risk is done by figuring out the Value at Risk(var), the tail probability, the diffusion models, the jump models and insurance.

I leave out the diffusion model because the mathematics is involved, complicated and is controversial.

VAR corresponds to value that can be lost in a portfolio of debt issued. Take for instance a debt priced today at 108. If it is supposed to be at default and on so 50% is recoverable then,

100=1/108((Px100)+(1-P)50) from which P can be calculated( single equation one variable) and say it is equal to 0.96 which is called the Survival probability or rate. So off the 100% debt the issuer can hope to get back on 96%. The remaining 0.04 is called the default rate or default probability which is derived by,

-Ln P = - Ln 0.96=0.04.

Then 4% of the debt is called the VAR.

Jump models assume Poisson jumps. Here,

Default probability λ = e^{∫λ x t. dt}

Diffusion process which I don’t explain make use of affine processes and is based on Black and Scholes derivation and Cox, Irwine, Rubenstien stochastic processes. It involves variables like drift, reversion time, mean return paths, 2^nd order Brownian motion of survival time and default time which if not taken carefully can have abnormal results which is controversial so avoided.

Insurance consists of finding out the premium which if we call μ then,

μ=Π x d, where Π is the probability of default and d is the damage.

So for a debt rated cc+ the spread can be compared to an AA+ bond whose yield is ‘a’ is (a + Π). For credit default swap it is (price + loss rate) the value of the premium paid each period. It is the controversial insurance that killed many Investment Banks like Shearson and insurance companies like AIG along with subrpime mortgages.

Risk free rates are not used as the base case from which spread of other rated debt is calculated because of the inverse correlation of t-bill rates with other bond rates.

The tail probability is the default probability which is also called the default boundary when the interest rates hits this we say the default level is reached or there is highly likely default possibility.

I have to accept the fact that this is only a birds of eye view of credit risk management and those who are interested can go further from here.