KRM-cr Innovations
KRM-cr has been constructed to incorporate a very substantial
unpublished extension of Professor Robert Jarrow’s credit models. The
full 165 page technical document containing the mathematical formulation
for the model is fully disclosed to Kamakura clients. There are no black
boxes at Kamakura Corporation.
Kamakura Corporation has been the leader in risk management research
in general and credit risk research in particular for more than a
decade. For a complete list of working papers and research in the public
domain please see Kamakura’s research publications. In KRM-cr, the most
important papers in the public domain which are helpful in understanding
Kamakura’s approach to credit risk are these papers by Robert Jarrow and
Don van Deventer of Kamakura: Robert Jarrow,
“Default Parameter
Estimation Using Market Prices,” Financial Analysts Journal
(September/October 2001). This paper provides an introduction to the
Jarrow reduced form credit model which has been popular with clients of
the Kamakura credit module KRM-cr. Robert Jarrow and Yildiray Yildirim,
“A Simple Model for Valuing Default Swaps When Both Market Risk and
Credit Risk are Correlated,” forthcoming, Journal of Fixed Income.
Jarrow and Yildirum show the power of reduced form models to model
market risk and credit risk on a fully integrated basis using the
example of default swaps Robert Jarrow and Don van Deventer,
“Integrating Interest Rate Risk and Credit Risk in Asset and Liability
Management,” Asset and Liability Management: The Synthesis of New
Methodologies, Risk Publications (1998). Jarrow and van Deventer show
that the hedging performance of reduced form models produces
significantly less hedging error than hedging with the Merton model of
risky debt. Robert Jarrow and Don van Deventer,
“Practical Use of
Credit Risk Models in Loan Portfolio and Counterparty Exposure
Management,” Credit Risk: Models and Management, Risk Publications
(1999). This Jarrow and van Deventer paper gives the default
probability formulas for the Merton model of risky debt and shows that
the original Merton credit model must be combined with a general
equilibrium model of asset pricing to derive the default probabilities
Jarrow and van Deventer show that two unobservable parameters are
necessary to make this derivation and that they are the critical
determinants of the default probabilities derived from the Merton model.
David Shimko, Naohiko Tejima and Don van Deventer,
“The Pricing of
Risky Debt when Interest Rates are Stochastic,” Journal of Fixed Income,
September 1993. Shimko, Tejima and van Deventer show that it is
unnecessary to assume constant interest rates, the most common
assumption in the commercial applications of the Merton model of risky
debt. The authors derive a random interest rates version of the model,
allowing integrated market risk and credit risk management. The KRM-cr
module has these key extensions of Kamakura’s industry-leading
analytics:
1. KRM-cr implements Robert Jarrow’s reduced form model of credit
risk with a time dependent default intensity 2. KRM-cr can use
observable debt prices to imply both default intensity and market
liquidity’s impact on observable credit spreads for sovereigns,
corporations and other issuers of debt. Counterparties who are not
themselves issuers of debt are modeled using another credit as a
benchmark for their credit risk. Their default may or may not be
correlated with the benchmark.
3. KRM-cr recognizes that the liquidity of the debt markets and the
equity markets impact market prices and that this impact should not be
mistaken for a change in default probabilities
4. KRM-cr introduces a seventh KRM yield curve smoothing method,
maximum smoothness credit spread smoothing. Maximum smoothness credit
spread smoothing, along with the Jarrow liquidity adjustment, reveals
expected losses implied by debt prices with great clarity 5. KRM-cr
models credit-adjusted value at risk with the true “two humped”
probability distribution that results when issuers of debt are truly in
distress. |
