Michel Crouhy

A comparative analysis of current credit risk models

The new BIS 1998 capital requirements for market risks allows banks to use internal models to assess regulatory capital related to both general market risk and credit risk for their trading book. This paper reviews the current proposed industry sponsored Credit Value-at-Risk methodologies. First, the credit migration approach, as proposed by JP Morgan with CreditMetrics, is based on the probability of moving from one credit quality to another, including default, within a given time horizon. Second, the option pricing, or structural approach, as initiated by KMV and which is based on the asset value model originally proposed by Merton (Merton, R., 1974. Journal of Finance 28, 449‐470). In this model the default process is endogenous, and relates to the capital structure of the firm. Default occurs when the value of the firm’s assets falls below some critical level. Third, the actuarial approach as proposed by Credit Suisse Financial Products (CSFP) with CreditRisk+ and which only focuses on default. Default for individual bonds or loans is assumed to follow an exogenous Poisson process. Finally, McKinsey proposes CreditPortfolioView which is a discrete time multi-period model where default probabilities are conditional on the macro-variables like unemployment, the level of interest rates, the growth rate in the economy, ... which to a large extent drive the credit cycle in the economy. ” 2000 Elsevier Science B.V. All rights reserved.

Prototype risk rating system

Abstract This paper explores the traditional and prevalent approach to credit risk assessment – the rating system. We first describe the rating systems of the two main credit rating agencies, Standard & Poors and Moodys. Then we show how an internal rating system in a bank can be organized in order to rate creditors systematically. We suggest adopting a two-tier rating system. First, an obligor rating that can be easily mapped to a default probability bucket. Second, a facility rating that determines the loss parameters in case of default, such as (i) “loss given default” (LGD), which depends on the seniority of the facility and the quality of the gurantees, and (ii) “usage given default” (UGD) for loan commitments, which depends on the nature of the commitment and the rating history of the borrower.

The Subprime Credit Crisis of 07

The current U.S. financial crisis began in 1997 when the market lost confidence in the creditworthiness of subprime mortgages and the structured financial products tied to them. In attempting to unravel the origins of the current problems, it has become clear that many factors and many market participants have played a role. In this article, the authors dissect the subprime mortgage crisis and clarify its many facets and offer a number of recommendations for changes to the system that could greatly reduce the probability of similar crises in the future.

Optimal hedging in a futures market with background noise and basis risk

Abstract This paper examines hedging behavior in an incomplete market in which there exists an unhedgeable and uninsurable independent background risk. In the case of a basis risk that satisfies the regressibility property, the background risk might be partly endogenous. Background risk generally has an ambiguous effect on the optimal hedge ratio. However, if preferences exhibit standard risk aversion and the background risk is fully exogenous, the qualitative effect of the added background risk is determinate and depends on the direction of any bias in the futures market. In all cases, the speculative component of the hedge ratio is reduced in the presence of background risk. When the background risk is a basis risk and futures prices exhibit normal backwardation, this qualitative effect need not hold and it depends in part on the direction of regressability for spot and futures prices.

The pricing of forward-starting asian options

Abstract Asian options are path-dependent options whose payoff is based on an average. In some cases, the underlying asset of the option is an average; in others, the strike price itself is computed as an average of the underlying asset recent prices. Asian currency options, as an example, allow corporate users to cover seasonal and so-called strategic foreign exchange positions. Averages are also found in some recent warrant issues, where they are mostly used as poison pills to preclude hostile takeovers. This paper derives a closed-form solution for the valuation of European asian options whose strike price is an average. Both “plain vanilla” average options—i.e. those for which the time interval taken into account for the strike average calculation is the life of the option—and forward-starting average options are considered. The valuation formula is obtained by relying upon a slight linear approximation. Although some previous contributions in the literature already use approximation techniques, our approach contrary to others allows the derivation of a formal upper bound to the approximation error. The numerical values given by this formula are then compared to those generated by an antithetic variate Monte-Carlo method. Based on this comparison and the computation of an upper bound to the approximation error, it is shown that the closed-form solution performs quite well and is obviously computationally efficient.

A contingent claim analysis of a regulated depository institution

Abstract A model of financial intermediation to determine the market value of bank equity, deposits and deposit insurance is developed. The implicit equilibrium interest rate on deposits is derived and analyzed. Three types of risks are considered in the model: interest-rate risk, financial risk and default risk. The effect of different regulatory measures, such as capital adequacy, reserve and liquidity requirements, deposit insurance and interest rate ceilings is analyzed and their impact on the bank behavior is also assessed. Moreover, we investigate the interactions among these measures to determine which are dominant under alternative circumstances, and which are redundant.

The interaction between the financial and investment decisions of the firm: the case of issuing warrants in a levered firm

Abstract In this paper we analyze the value of warrants and stock in a firm that has both equity and debt in its capital structure, and assume that the proceeds from exercising the warrants are reinvested in the firm. The effect of potential future scale investment on the firms stock, debt and warrants are investigated. The warrants in our analysis are European. In this framework there are two sources for the nonstationarity of the rate of return on any kind of financial claim; the first stems from changes in the firms capital structure, and the second is due to the potential scale increase in the value of the firm should the warrants be exercised. The effect of a potential transfer of wealth from equity-holders to debt-holders at time of exercise is analyzed. When warrants are exercised and the proceeds are reinvested in a scale expansion project, the probability of default may decrease. It follows, therefore, that ceteris paribus debt is likely to appreciate in value at the expense of equity. The method of pricing by arbitrage, as proposed by Harrison and Kreps is used to derive values for claims on the firm. Problems associated with measuring the volatility of equity are discussed.

An economic assessment of capital requirements in the banking industry

Abstract The paper uses a two-period model to evaluate the capital requirements imposed on banks. In particular, the interaction between capital requirements and other regulatory measures is analyzed. It is shown that, in a competitive set-up, there is a tradeoff between the capital ratio and the liquidity of assets.

Stochastic equity volatility related to the leverage effect II: valuation of European equity options and warrants

We propose a general framework to assess the value of the financial claims issued by the firm, European equity options and warrantsin terms of the stock price. In our framework, the firms asset is assumed to follow a standard stationary lognormal process with constant volatility. However, it is not the case for equity volatility. The stochastic nature of equity volatility is endogenous, and comes from the impact of a change in the value of the firms assets on the financial leverage. In a previous paper we studied the stochastic process for equity volatility, and proposed analytic approximations for different capital structures. In this companion paper we derive analytic approximations for the value of European equity options and warrants for a firm financed by equity, debt and warrants. We first present the basic model, which is an extension of the Black-Scholes model, to value corporate securities either as a function of the stock price, or as a function of the firms total assets. Since stock prices are observable, then for practical purposes, traders prefer to use the stock as the underlying instrument, we concentrate on valuation models in terms of the stock price. Second, we derive an exact solution for the valuation in terms of the stock price of (i) a European call option on the stock of a levered firm, i.e. a European compound call option on the total assets of the firm, (ii) an equity warrant for an all-equity firm, and (iii) an equity warrant for a firm financed by equity and debt. Unfortunately, to compute these solutions we need to specify the function of the stock price in terms of the firms assets value. In general we are unable to specify this expression, but we propose tight bounds for the value of these options which can be easily computed as a function of the stock price. Our results provide useful extensions of the Black-Scholes model.

Stochastic equity volatility and the capital structure of the firm

This paper develops a general model for equity volatility when the firm is financed by equity, debt and any other financial instruments like warrants and convertible bonds. The stochastic nature of equity volatility is endogenous and comes from the impact of a change in the value of the firm’s assets on the financial leverage. We first present the basic model to value corporate securities, which is an extension of the Black-Scholes model. Then, we are able to propose an analytic approximation for equity volatility, which is shown to be extremely precise. Finally, we study the behaviour of equity volatility when the firm is financed by equity and debt.