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

CHAPTER 4

Loans as Options: The Moody’s KMV Model

INTRODUCTION

The idea of applying option pricing theory to the valuation of risky loans and bonds has been in the literature at least as far back as a 1974 article by R. C. Merton. In recent years, Merton’s ideas have been extended in many directions. One example is the generation of structural default prediction models (e.g., Moody’s KMV model) that produce and update default predictions for all major companies and banks that have their equity publicly traded.¹ In this chapter, we first look at the link between loans and options and subsequently investigate how this link can be used to derive a default prediction model.

THE LINK BETWEEN LOANS AND OPTIONS

Figure 4.1 shows the payoff function to a bank lender of a simple loan. Assume that this is a one-year loan and the amount, B, is borrowed on a discount basis. Technically, option formulas (discussed later) model loans as zero-coupon bonds with fixed maturities. Over the year, a borrowing firm will invest the funds in various projects or assets. Assume that at the end of the year the market value of the borrowing firm’s assets is A₂. The owners of the firm then have an incentive to repay the loan (B) and keep the residual (A₂—B) as profit or return on investment. Indeed, for any value of the firm’s assets exceeding B, the owners of the firm will have an incentive to repay the loan. However, if the market value of the firm’s assets is less than B (e.g., A₁ in Figure 4.1