Banking: KMV model

Résumé du document

Risk management is a very important issue in financial markets. Moody's KMV Model is a structural model inspired from Merton's model. It is equivalent to an option model that evaluates the implied volatility of the company's assets. It relies on Black & Scholes valuation model (1973). This document discusses various facets of the model in the field of risk management.

Extraits

[...] The valuation of risky cash flows consists of the valuation of the default-free component and the valuation of the component exposed to credit risk: PV = Present Value of the cash flow FV = Future Value (the obligation) LGD = Loss Given Default, in percent 1 LGD = recovery rate i = the 1-year risk-free rate Q = probability that the issuer defaults in 1 year, which is derived from EDF II Intermediate conclusion Variations in the stock price, the leverage ratio, and the asset volatility can all change the firm's EDF. Higher volatility of asset return implies that the market has more uncertainty on the fim's business value. To calculate the CreditVaR, KMV defines the portfolio loss as the difference between risk less value of the portfolio and its market value. As we have exposed, KMV's methodology relies almost exclusively on equity market information. [...]

[...] We can expect that because of the current subprime crisis, mathematical finance researchers will go through this type of models. As for other valuation models, it is still very difficult to take extreme events into account, and many theoretical assumptions may be violated in practice. BELLALAH M., (2005) : Gestion des risques de taux d'intérêt et de change De Boeck BOURBONNAIS R., TERRAZA M., (2007) : Analyse des séries temporelles Dunod, 2ème édition COLMANT B. (2004) : Les obligations Cahiers Financiers GUJARATI D., (2001) : Econométrie De Boeck HULL J., (2005) : Options, Futures, Produits Dérivés Pearson Education, 5ème édition. [...]

[...] EDF provides a cardinal rather than ordinal ranking of credit quality. Accurate and timely information from the equity market provides a continuous credit monitoring process that is difficult and expensive to duplicate using traditional credit analysis. Annual reviews and other traditional credit processes cannot maintain the same degree of vigilance that EDFs calculated on a monthly or a daily basis can provide. IV Weaknesses of KMV Model It requires some subjective estimation of the input parameters. It is difficult to construct theoretical EDF's without the assumption of normality of asset returns. [...]

[...] Moody's bought the KMV Model. KMV Model is a structural model inspired from Merton's model. It is equivalent to an option model that evaluates the implied volatility of the company's assets. It relies on Black & Scholes valuation model (1973). I Description of KMV Model KMV is a trademark of KMV Corporation that was founded in 1989. The KMV model calculates the Expected Default Frequency (EDF) based on the firm's capital structure, the volatility of the assets returns and the current asset value. [...]

[...] LGD = loss given default (assumed to be 40% here) Q = risk neutral probability that the issuer defaults in one year from now (assumed to be 20% here) The expectation is calculated using the risk neutral probabilities but not the actual probabilities as they can be observed in the market from historical data or EDFs. Conclusion Today, Moody's-KMV model is the most famous model all over the world. But other type of models were developed such as CréditMetrics(1996: JPMorgan) and CreditRisk+ (1997: Credit Suisse First Boston). They rely on the same assumptions and only a few differences can be noticed. [...]