C.01.Hull 23

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C.01.Hull 23
2012-05-09 16:21:06
Credit Risk

Credit Risk
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  1. Default probabilities
    • unconditional prob of def = prob that exist at 0 will default
    • def intensity / hazard rate = prob def given no default at t
    • prod def by t =
  2. Recovery rate
    • % pmt recovered in case of default
    • negatively correlated w default rates
  3. Estimating def prob from bd price
    • assumption: only reason why P > risk-free P is default
    • approximation:
    • exp loss from def = P - risk-free P
    • set PV(exp loss) = PV(rf value) - PV(recovery)
    • more realistic: def more often, constant intensity, diff Q patterns
  4. Estimating def prob from equity price (Merton's Model)
    • and
    • p(default) = N(-d2)
  5. Credit risk mitigation
    • netting: default on all or nothing
    • collateralization: revalue contract and ask for more collateral if exceeds threshold (-) if fin trouble won't post
    • downgrade triggers: if cr rating falls below threshold, close contract (-) protects small jumps only (-) only works well if counterparty has few outstanding contracts with that clause
  6. Gaussian Copula model for time to default
    • cpies in same region affected by similar econ events
    • def from one cpy may cause other def
    • assumption: all cpies will eventually default
    • xi=N-1[Qi(ti)] -> f(x1,x2) bivariate normal
  7. Credit Metrics
    • cr VaR of Y at x% conf lvl = x% conf that cr loss < Y
    • Cr Metrics: program that derives prob dist of cr loss
    • (+) accounts for impact of downgrage
    • (+) can incorporate cr mitigation clauses
    • (-) computationally time intensive

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