Description
Credit Portfolio Risk Modeling Using MKMV Approach
Credit Portfolio Risk Modeling using MKMV Approach
Introduction
• When does the firm default? • MKMV approach - Value of assets - Asset risk - Leverage (BV of liabilities relative to MV of assets) • Estimating Default Point and net worth • Distance-to-default (net worth/asset risk)
Estimation of Asset Value and volatility BSM Model
Asset Returns
Asset value and a drunken man
Applying Ito’s Lemma and equating to variance, we get
Adjustments to BSM model
• Different types of liabilities such as long-term, short-term, convertibles, preferred equity and common equity. • Default at any time • Modeling equity as a perpetual option
Distance-to-Default
• Do the firms have only two types of liabilities? • DD is anything but normal
Estimating PD
• • • • PD = N(-DD) Is DD really normal? Do the dividends have any impact on DD? DD-to-PD mapping – History tells a different story.
Other Data
• • • • • Reference rates Zero-PD rates Interest-rate parity adjusted forward FX rates Obligor data (Country and Industry, R-sq) Exposure data (Commitment and exposure, UGD, LGD, other terms and fees in indenture)
Zero-PD rates
Estimating firm’s correlation with market
• Country and industry indices • Custom index based on firm’s exposure to country and industry • Regress asset returns over custom returns • Correlation = sqrt(R-squared)
Loss Given Default
• How do you know how much you will recover when firm defaults?
Beta distribution
LGD…continued
How do you determine mean LGD and k?
Non-normality of credit returns
Incorporating higher order effects
• Analytical approximation calibrated to empirical distribution • Monte Carlo Simulation • Accelerated Monte Carlo
Valuation – Analytical methods
• Book value approach • Risk-Comparable Valuation • Lattice Valuation
RCV valuation
V0RCV ? ?1 ? LGD ? ? RFV 0 ? LGD ? RYV 0RCV
Risk-free and risky value
RFV 0 ? ? C t ? DFt
t ?0 M Rf
RYV
RCV 0
? ? ?1 ? PDt ? ? Ct ? DFt
t ?0
M
Rf
• Two-state model – Default or no-default • Factors in uncertainty over certain cash flows, but not the conditional cash flows
Lattice valuation
• Grids as different states • Each vertical line represents the time at which cash flow is due • Horizontal line represents a probability of transitioning to a state at the time.
Ratings transition matrix
Valuation at horizon
• Expected value given default • Expected value given no-default
Valuation at horizon
• EV|Default = (1-LGD) * RFV at horizon • EV|no-default = cash flow between today and horizon + RFV at horizon + Risky value at horizon
Spread and losses
Unexpected Loss
Aggregating at portfolio level
Correlation
Decomposing risk
Applying factors
Tricky question
Thank you
doc_141079838.pptx
Credit Portfolio Risk Modeling Using MKMV Approach
Credit Portfolio Risk Modeling using MKMV Approach
Introduction
• When does the firm default? • MKMV approach - Value of assets - Asset risk - Leverage (BV of liabilities relative to MV of assets) • Estimating Default Point and net worth • Distance-to-default (net worth/asset risk)
Estimation of Asset Value and volatility BSM Model
Asset Returns
Asset value and a drunken man
Applying Ito’s Lemma and equating to variance, we get
Adjustments to BSM model
• Different types of liabilities such as long-term, short-term, convertibles, preferred equity and common equity. • Default at any time • Modeling equity as a perpetual option
Distance-to-Default
• Do the firms have only two types of liabilities? • DD is anything but normal
Estimating PD
• • • • PD = N(-DD) Is DD really normal? Do the dividends have any impact on DD? DD-to-PD mapping – History tells a different story.
Other Data
• • • • • Reference rates Zero-PD rates Interest-rate parity adjusted forward FX rates Obligor data (Country and Industry, R-sq) Exposure data (Commitment and exposure, UGD, LGD, other terms and fees in indenture)
Zero-PD rates
Estimating firm’s correlation with market
• Country and industry indices • Custom index based on firm’s exposure to country and industry • Regress asset returns over custom returns • Correlation = sqrt(R-squared)
Loss Given Default
• How do you know how much you will recover when firm defaults?
Beta distribution
LGD…continued
How do you determine mean LGD and k?
Non-normality of credit returns
Incorporating higher order effects
• Analytical approximation calibrated to empirical distribution • Monte Carlo Simulation • Accelerated Monte Carlo
Valuation – Analytical methods
• Book value approach • Risk-Comparable Valuation • Lattice Valuation
RCV valuation
V0RCV ? ?1 ? LGD ? ? RFV 0 ? LGD ? RYV 0RCV
Risk-free and risky value
RFV 0 ? ? C t ? DFt
t ?0 M Rf
RYV
RCV 0
? ? ?1 ? PDt ? ? Ct ? DFt
t ?0
M
Rf
• Two-state model – Default or no-default • Factors in uncertainty over certain cash flows, but not the conditional cash flows
Lattice valuation
• Grids as different states • Each vertical line represents the time at which cash flow is due • Horizontal line represents a probability of transitioning to a state at the time.
Ratings transition matrix
Valuation at horizon
• Expected value given default • Expected value given no-default
Valuation at horizon
• EV|Default = (1-LGD) * RFV at horizon • EV|no-default = cash flow between today and horizon + RFV at horizon + Risky value at horizon
Spread and losses
Unexpected Loss
Aggregating at portfolio level
Correlation
Decomposing risk
Applying factors
Tricky question
Thank you
doc_141079838.pptx