The KMV credit correlation model is a multi-factor statistical model for estimating the correlation of credit risk between borrowers, developed by KMV Corporation from the late 1980s onwards and marketed after 2002 by Moody's Analytics under the name GCorr (Global Correlation Model). Its distinguishing feature is that it infers correlations between firms' asset values — which are not directly observable — from equity market data, by inverting a structural model of the firm in the tradition of Robert Merton. The model addressed a problem that had made portfolio credit risk measurement largely intractable: default events are rare, so the joint default behaviour of any particular pair of borrowers is almost never observed directly. By recasting the question as one about correlated asset returns, and by extracting those returns from liquid equity markets, KMV made it possible to assign a correlation to any pair of firms, including pairs that had never defaulted. The framework became the basis of KMV's Portfolio Manager software and, subsequently, of Moody's Analytics RiskFrontier and PortfolioStudio. Its theoretical core — Oldrich Vasicek's asymptotic single risk factor model — was adopted by the Basel Committee on Banking Supervision as the engine of the Basel II internal ratings-based approach to bank capital, giving the model a direct influence on global financial regulation.
History KMV Corporation was founded in San Francisco in 1989 by Stephen Kealhofer, John "Mac" McQuown and Oldrich Vasicek, the firm taking its name from their initials. Some accounts date the founding to 1991; the founders' own recollections place the origin of the venture in the late 1980s, following earlier collaboration on a loan-pooling business dating to 1986. The company's insight, according to Kealhofer, was that credit portfolios behave differently from equity portfolios with respect to diversification. Individual equity risks fall within a relatively narrow band of volatilities, so an approximately equally weighted stock portfolio is naturally well diversified; credit exposures, by contrast, exhibit wide divergences in the level of risk attached to individual names, making diversification a first-order concern rather than an automatic consequence of holding many positions. KMV's principal products were Credit Monitor, which produced Expected Default Frequency (EDF) estimates for individual firms, and Portfolio Manager, which applied the correlation model at portfolio level. The correlation model itself was first released commercially in 1996. Moody's Corporation acquired KMV in an all-cash transaction for $210 million, agreed on 10 February 2002 and completed on 12 April 2002. The business was combined with Moody's Risk Management Services to form Moody's KMV, later folded into Moody's Analytics. The founders had previously declined approaches from Standard & Poor's, Barra and MSCI, and by their own account were divided over whether to accept the Moody's offer.
Theoretical foundations
The Merton framework The model descends from Merton's 1974 observation that the equity of a levered firm can be treated as a call option on the firm's assets, struck at the face value of its debt. If the asset value A T {\displaystyle A_{T}} at debt maturity exceeds the liability D {\displaystyle D} , shareholders repay and retain the surplus; otherwise they surrender the firm. Equity value therefore satisfies the Black–Scholes formula
E = A N ( d 1 ) − D e − r T N ( d 2 ) , d 1 = ln ( A / D ) + ( r + 1 2 σ A 2 ) T σ A T {\displaystyle E=A\,N(d_{1})-De^{-rT}N(d_{2}),\qquad d_{1}={\frac {\ln(A/D)+(r+{\tfrac {1}{2}}\sigma _{A}^{2})T}{\sigma _{A}{\sqrt {T}}}}}
with d 2 = d 1 − σ A T {\displaystyle d_{2}=d_{1}-\sigma _{A}{\sqrt {T}}} . Because E {\displaystyle E} and its volatility σ E {\displaystyle \sigma _{E}} are observable while A {\displaystyle A} and σ A {\displaystyle \sigma _{A}} are not, the relation can be inverted: two equations — the pricing identity above and σ E = A E N ( d 1 ) σ A {\displaystyle \sigma _{E}={\tfrac {A}{E}}N(d_{1})\sigma _{A}} — in two unknowns.
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