Donald R. van Deventer

The Pricing of Risky Debt When Interest Rates are Stochastic

We derive a closed form solution for the valuation of risky discount debt when interest rates are stochastic. We extend Mertons [1974] approach to risky discount debt valuation under constant interest rates to the stochastic interest rate environment of Vasicek [1977]. Business risk is modelled as a geometric Brownian motion that is correlated with interest rates. We derive and explore the relationship between the credit premium and the term premium of corporate debt. In a banking environment, the results can also be applied to analyze (a) the allocation of capital to banking activities of varying credit risk and interest rate risk, (b) the measurement of relative capital adequacy when compared to peer banks, and (c) the interest rate risk-minimizing funding strategy.

The arbitrage-free valuation and hedging of demand deposits and credit card loans

Abstract Using a market segmentation argument, this paper uses the interest rate derivatives arbitrage-free methodology to value both demand deposit liabilities and credit card loan balances in markets where deposits/loan rates may be determined under imperfect competition. In this context, these financial instruments are shown to be equivalent to a particular interest rate swap, where the principal depends on the past history of market rates. Solutions are obtained which are independent of any particular model for the evolution of the term structure of interest rates.

A robust test of Merton's structural model for credit risk

This paper presents a robust test of Mertons structural model for credit risk that does not depend on either estimated parameters for the firms value or estimated default probabilities. We derive a test for the consistency of the changes in observed debt and equity prices (positive or negative changes) with the Merton model. For all firms selected and for all debt issues examined, the evidence strongly rejects Mertons structural model. employed to manage credit risk in banks and bond portfolios. Mertons model invokes the arbitrage free pricing methodology in friction- less and competitive markets. The key characteristic of Mertons model is that the underlying state variable that determines a firms default is the value of its assets. Default free interest rates are assumed to be constant. Given a specific balance sheet for the firm (a fixed and static structure), at the maturity date of its short-term debt (a discount bond), if the firms value falls below the face value of the short-term debt, then default occurs. In the event of default, the payoffs to the firms liabilities follow absolute priority (written into the debts covenants). Under this structure, the firms equity is analogous to a call option on the firms assets. As is well known, Mertons model has four empirical difficulties that make its implementation problematic:

Synthetic CDO Equity: Short or Long Correlation Risk?

This article clarifies and contests the common market belief that synthetic CDO equity is long correlation risk, i.e. as correlation increases equity spreads decline. In fact, the impact of correlation on CDO equity spreads is indeterminate apriori and model specific. We argue that, for realistic models, CDO equity will be short correlation risk, contrary to common belief.

A Simple, Transparent, and Accurate MortgageValuation Yield Curve

This article presents a simple method for generating a primary mortgage loan yield curve using the relation, derived herein, between a coupon-bearing mortgage loan’s value and a portfolio of equal risk mortgage zero-coupon bonds. This new methodology is transparent because it is based on readily available government data. We provide an example to illustrate the computations involved.

Asset and Liability Management from an Enterprise-Wide Risk Management Perspective

Publisher Summary This chapter briefly discusses the barriers that have historically promoted silo risk management contrary to the best interests of shareholders and regulators of national financial institutions. It introduces the concept of the Jarrow–Merton put option as the best single measure of total risk. The chapter highlights the contribution of asset and liability management to total risk, which is included in the value of this put option. Furthermore, it provides a review of outstanding options for Citigroup—a concrete market signal of the total risk of major financial services companies. The chapter also outlines an approach that allows going far beyond Black–Scholes using the Merton reduced form model of an option on the common stock of a company that can default. It uses this model to extract the term structure of default risk and business risk (that is, implied volatility) for Citigroup over a three-year horizon. It compares this term structure of default probabilities to a properly benchmarked reduced form model and confirms the finding of many others that the options market implied default.