Risk Management Models: Construction, Testing, Usage Robert A. Jarrow  y March 15, 2011 Abstract Financial risk management models are alleged to have helped cause the 2007 credit crisis. There is some truth to these concerns. Risk manage- ment models were used wrongly prior the crisis and they are still being misused today. The purpose of this paper is to critically analyze risk management models - construction, testing, and usage. In the process we show that there are two common misuses of these models associated with calibration and hedging "the greeks." In particular we show that: (i) vega hedging with a calibrated Black-Scholes option pricing model is a nonsensical procedure, (ii) using the implied default probabilities from a structural credit risk model to price credit default swaps is erroneous, and (iii) using the default correlations obtained from credit risk copula models for computing value-at-risk measures leads to misspecied estimates. We provide alternatives to these misuses and a roadmap for the proper usage of risk managment models. 1 Introduction The 2007 credit crisis was a wake-up call with respect to model usage. It has been alleged that the misuse of risk management models helped to generate the crisis. For example, "The turmoil at AIG is likely to fan skepticism about the complicated, computer-driven modeling systems that many nancial giants rely on to minimize risk." 1 Even the nancial wizard himself, Warren Bu/et, is skeptical about models "All I can say is, beware of geeks...bearing formulas." 2  Johnson Graduate School of Management, Cornell University, Ithaca, New York 14853. email: raj15@cornell.edu and Kamakura Corporation. y Helpful comments form Arkadev Chatterjea, Steve Figlewski, and a referee are gratefully acknowledged. 1 Wall Street Journal, Monday Nov 3, 2008, Behind AIGs Fall, Risk Models Failed to Pass Real-World Test. 2 Wall Street Journal, Monday Nov 3, 2008, Behind AIGs Fall, Risk Models Failed to Pass Real-World Test. 1