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Credit Risk Measurement In and Out of the Financial Crisis: New Approaches to Value at Risk and Other Paradigms, Third Edition by Linda Allen, Anthony Saunders

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CHAPTER 5
Reduced Form Models: Kamakura’s Risk Manager

INTRODUCTION

The structural models described in Chapter 4 use the information embedded in equity prices in order to solve for default probabilities. Reduced form models use debt and other security prices to accomplish the same goal.1 However, whereas structural models posit an economic process driving default (i.e., the point at which asset values fall below the repayment value of debt), reduced form models offer no economic model of default causality. In reduced form models, the default process itself is exogenous and observable in a default risk premium included in debt prices and yields. In a world free of arbitrage opportunities, expected returns on a risky asset must equal the return on a risk-free asset (the risk-free rate). More specifically, the observed yield on risky debt can be decomposed into a risk-free rate plus a risk premium. Reduced form models utilize this decomposition in order to solve for default probabilities, recovery rates, and risky debt prices.
The use of risk-neutral probabilities to value risky assets has been in the finance literature at least as far back as Arrow (1953) and has been subsequently developed by Harrison and Kreps (1979), Harrison and Pliska (1981), and Kreps (1982). In finance, it has been traditional to value risky assets by discounting cash flows on an asset by a risk-adjusted discount rate. To do this, one needs to know a probability distribution for cash flows and the risk-return ...

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