The Valuation of Corporate Liabilities as Compound Options
01 Nov 1977-Journal of Financial and Quantitative Analysis (Cambridge University Press)-Vol. 12, Iss: 4, pp 541-552
TL;DR: In this article, the authors applied the technique for valuing compound options to the risky coupon, bond problem and derived a formula which contains n-dimensional multivariate normal intecjrals.
Abstract: This paper applies the technique for valuing compound options to the risky coupon, bond problem. A formula is derived which contains n-dimensional multivariate normal intecjrals. It is shown that, for some compound option problems, the special correlation structure allows an application of an integral reduction which may simplify the numerical evaluation. The effects of various indenture restrictions on the formula are discussed, and a new formula for evaluating subordinated debt is presented.
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TL;DR: In this article, the authors developed a simple approach to valuing risky corporate debt that incorporates both default and interest rate risk, and used this approach to derive simple closed-form valuation expressions for fixed and floating rate debt.
Abstract: We develop a simple approach to valuing risky corporate debt that incorporates both default and interest rate risk. We use this approach to derive simple closed-form valuation expressions for fixed and floating rate debt. The model provides a number of interesting new insights about pricing and hedging corporate debt securities. For example, we find that the correlation between default risk and the interest rate has a significant effect on the properties of the credit spread. Using Moody's corporate bond yield data, we find that credit spreads are negatively related to interest rates and that durations of risky bonds depend on the correlation with interest rates. This empirical evidence is consistent with the implications of the valuation model.
2,306 citations
Book•
28 Jun 1987
TL;DR: In this article, the authors provide access to a broad area of research that is not available in separate articles or books of readings, such as the meaning and measurement of risk, general single-period portfolio problems, mean-variance analysis and the Capital Asset Pricing Model, the Arbitrage Pricing Theory, complete markets, multi period portfolio problems and the Intertemporal Capital Asset pricing model, the Black-Scholes option pricing model and contingent claims analysis, 'risk-neutral' pricing with Martingales, Modigliani-Miller and the capital structure of the firm, interest
Abstract: Based on courses developed by the author over several years, this book provides access to a broad area of research that is not available in separate articles or books of readings. Topics covered include the meaning and measurement of risk, general single-period portfolio problems, mean-variance analysis and the Capital Asset Pricing Model, the Arbitrage Pricing Theory, complete markets, multiperiod portfolio problems and the Intertemporal Capital Asset Pricing Model, the Black-Scholes option pricing model and contingent claims analysis, 'risk-neutral' pricing with Martingales, Modigliani-Miller and the capital structure of the firm, interest rates and the term structure, and others.
1,803 citations
Posted Content•
TL;DR: In this paper, the authors studied the spread between spot rates on corporate and government bonds and found that the spread can be explained in terms of three elements: (1) compensation for expected default of corporate bonds; (2) compensated for state taxes; and (3) compensating for the additional systematic risk in corporate bond returns relative to government bond returns.
Abstract: The purpose of this article is to explain the spread between spot rates on corporate and government bonds. We find that the spread can be explained in terms of three elements: (1) compensation for expected default of corporate bonds (2) compensation for state taxes since holders of corporate bonds pay state taxes while holders of government bonds do not, and (3) compensation for the additional systematic risk in corporate bond returns relative to government bond returns. The systematic nature of corporate bond return is shown by relating that part of the spread which is not due to expected default or taxes to a set of variables which have been shown to effect risk premiums in stock markets Empirical estimates of the size of each of these three components are provided in the paper. We stress the tax effects because it has been ignored in all previous studies of corporate bonds.
1,437 citations
TL;DR: In this article, the authors study the implications of imperfect information for term structures of credit spreads on corporate bonds and derive the conditional distribution of the assets, given accounting data and survivorship.
Abstract: We study the implications of imperfect information for term structures of credit spreads on corporate bonds. We suppose that bond investors cannot observe the issuer's assets directly, and receive instead only periodic and imperfect accounting reports. For a setting in which the assets of the firm are a geometric Brownian motion until informed equityholders optimally liquidate, we derive the conditional distribution of the assets, given accounting data and survivorship. Contrary to the perfect-information case, there exists a default-arrival intensity process. That intensity is calculated in terms of the conditional distribution of assets. Credit yield spreads are characterized in terms of accounting information. Generalizations are provided.
1,373 citations
TL;DR: In this article, the authors examined and explained the differences in the rates offered on corporate bonds and those offered on government bonds, and examined whether there is a risk premium in corporate bond spreads and, if so, why it exists.
Abstract: The purpose of this article is to explain the spread between rates on corporate and government bonds. We show that expected default accounts for a surprisingly small fraction of the premium in corporate rates over treasuries. While state taxes explain a substantial portion of the difference, the remaining portion of the spread is closely related to the factors that we commonly accept as explaining risk premiums for common stocks. Both our time series and cross-sectional tests support the existence of a risk premium on corporate bonds. THE PURPOSE OF THIS ARTICLE is to examine and explain the differences in the rates offered on corporate bonds and those offered on government bonds ~spreads!, and, in particular, to examine whether there is a risk premium in corporate bond spreads and, if so, why it exists. Spreads in rates between corporate and government bonds differ across rating classes and should be positive for each rating class for the following reasons: 1. Expected default loss—some corporate bonds will default and investors require a higher promised payment to compensate for the expected loss from defaults. 2. Tax premium—interest payments on corporate bonds are taxed at the state level whereas interest payments on government bonds are not. 3. Risk premium—The return on corporate bonds is riskier than the return on government bonds, and investors should require a premium for the higher risk. As we will show, this occurs because a large part of the risk on corporate bonds is systematic rather than diversifiable. The only controversial part of the above analyses is the third point. Some authors in their analyses assume that the risk premium is zero in the corporate bond market.1
1,233 citations
References
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TL;DR: In this paper, a theoretical valuation formula for options is derived, based on the assumption that options are correctly priced in the market and it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks.
Abstract: If options are correctly priced in the market, it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks. Using this principle, a theoretical valuation formula for options is derived. Since almost all corporate liabilities can be viewed as combinations of options, the formula and the analysis that led to it are also applicable to corporate liabilities such as common stock, corporate bonds, and warrants. In particular, the formula can be used to derive the discount that should be applied to a corporate bond because of the possibility of default.
28,434 citations
TL;DR: In this article, the American Finance Association Meeting, New York, December 1973, presented an abstract of a paper entitled "The Future of Finance: A Review of the State of the Art".
Abstract: Presented at the American Finance Association Meeting, New York, December 1973.(This abstract was borrowed from another version of this item.)
11,225 citations
Book•
12 Sep 2011
TL;DR: In this paper, the authors deduced a set of restrictions on option pricing formulas from the assumption that investors prefer more to less, which are necessary conditions for a formula to be consistent with a rational pricing theory.
Abstract: The long history of the theory of option pricing began in 1900 when the French mathematician Louis Bachelier deduced an option pricing formula based on the assumption that stock prices follow a Brownian motion with zero drift. Since that time, numerous researchers have contributed to the theory. The present paper begins by deducing a set of restrictions on option pricing formulas from the assumption that investors prefer more to less. These restrictions are necessary conditions for a formula to be consistent with a rational pricing theory. Attention is given to the problems created when dividends are paid on the underlying common stock and when the terms of the option contract can be changed explicitly by a change in exercise price or implicitly by a shift in the investment or capital structure policy of the firm. Since the deduced restrictions are not sufficient to uniquely determine an option pricing formula, additional assumptions are introduced to examine and extend the seminal Black-Scholes theory of option pricing. Explicit formulas for pricing both call and put options as well as for warrants and the new "down-and-out" option are derived. The effects of dividends and call provisions on the warrant price are examined. The possibilities for further extension of the theory to the pricing of corporate liabilities are discussed.
9,635 citations
TL;DR: In this article, an intertemporal model for the capital market is deduced from portfolio selection behavior by an arbitrary number of investors who aot so as to maximize the expected utility of lifetime consumption and who can trade continuously in time.
Abstract: An intertemporal model for the capital market is deduced from the portfolio selection behavior by an arbitrary number of investors who aot so as to maximize the expected utility of lifetime consumption and who can trade continuously in time. Explicit demand functions for assets are derived, and it is shown that, unlike the one-period model, current demands are affected by the possibility of uncertain changes in future investment opportunities. After aggregating demands and requiring market clearing, the equilibrium relationships among expected returns are derived, and contrary to the classical capital asset pricing model, expected returns on risky assets may differ from the riskless rate even when they have no systematic or market risk. ONE OF THE MORE important developments in modern capital market theory is the Sharpe-Lintner-Mossin mean-variance equilibrium model of exchange, commonly called the capital asset pricing model.2 Although the model has been the basis for more than one hundred academic papers and has had significant impact on the non-academic financial community,' it is still subject to theoretical and empirical criticism. Because the model assumes that investors choose their portfolios according to the Markowitz [21] mean-variance criterion, it is subject to all the theoretical objections to this criterion, of which there are many.4 It has also been criticized for the additional assumptions required,5 especially homogeneous expectations and the single-period nature of the model. The proponents of the model who agree with the theoretical objections, but who argue that the capital market operates "as if" these assumptions were satisfied, are themselves not beyond criticism. While the model predicts that the expected excess return from holding an asset is proportional to the covariance of its return with the market
6,294 citations
TL;DR: In this paper, the authors examined the structure of option valuation problems and developed a new technique for their solution and introduced several jump and diffusion processes which have not been used in previous models.
3,062 citations