The Pricing of Options and Corporate Liabilities
01 May 1973-Journal of Political Economy (The University of Chicago Press)-Vol. 81, Iss: 3, pp 637-654
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.
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TL;DR: In this article, the authors draw on recent progress in the theory of property rights, agency, and finance to develop a theory of ownership structure for the firm, which casts new light on and has implications for a variety of issues in the professional and popular literature.
49,666 citations
Cites background or methods from "The Pricing of Options and Corporat..."
...2 Reviews of this literature are given by Peterson (1965), Alchian (1965, 1968), Machlup (1967), Shubik (1970), Cyert and Hedrick (1972), Branch (1973), Preston (1975)....
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...42 While we used the option pricing model above to motivate the discussion and provide some intuitive understanding of the incentives facing the equity holders, the option pricing solutions of Black and Scholes (1973) do not apply when incentive effects cause V to be a function of the debt/equity ratio as it is in general and in this example....
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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
Cites background or methods from "The Pricing of Options and Corporat..."
...INTRODUCTION THE VALUE OF a particular issue of corporate debt depends essentially on three items: (1) the required rate of return on riskless (in terms of default) debt (e....
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...Suppose the corporation has two classes of claims: (1) a single, homogenous class of debt and (2) the residual claim, equity....
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...Suppose further that the indenture of the bond issue contains the following provisions and restrictions: (1) the firm promises to pay a total of B dollars to the bondholders on the specified calendar date T;...
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...The initial condition follows from indenture conditions (1) and (2) and the fact that management is elected by the equity owners and hence, must act in their best interests....
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...Comparing terms in (2) and (1), we have that...
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TL;DR: In this paper, a closed-form solution for the price of a European call option on an asset with stochastic volatility is derived based on characteristi c functions and can be applied to other problems.
Abstract: I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset’s price is important for explaining return skewness and strike-price biases in the BlackScholes (1973) model. The solution technique is based on characteristi c functions and can be applied to other problems.
7,867 citations
Cites background from "The Pricing of Options and Corporat..."
...Many plaudits have been aptly used to describe Black and Scholes’ (1973) contribution to option pricing theory....
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...Standard arbitrage arguments [Black and Scholes (1973), Merton (1973)] demonstrate that the value of any asset U(S, v, t) (including accrued payments) must satisfy the partial differential equation (PDE) (6) The unspecified term (S, v, t) represents the price of volatility risk, and must be…...
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TL;DR: In this article, the authors derived a general form of the term structure of interest rates and showed that the expected rate of return on any bond in excess of the spot rate is proportional to its standard deviation.
6,160 citations
Cites methods from "The Pricing of Options and Corporat..."
...The development of the model is based on an arbitrage argument similar to that of Black and Scholes (1973) for option pricing....
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TL;DR: In this paper, a simple discrete-time model for valuing options is presented, which is based on the Black-Scholes model, which has previously been derived only by much more difficult methods.
5,864 citations
References
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TL;DR: In this paper, the authors present a body of positive microeconomic theory dealing with conditions of risk, which can be used to predict the behavior of capital marcets under certain conditions.
Abstract: One of the problems which has plagued thouse attempting to predict the behavior of capital marcets is the absence of a body of positive of microeconomic theory dealing with conditions of risk/ Althuogh many usefull insights can be obtaine from the traditional model of investment under conditions of certainty, the pervasive influense of risk in finansial transactions has forced those working in this area to adobt models of price behavior which are little more than assertions. A typical classroom explanation of the determinationof capital asset prices, for example, usually begins with a carefull and relatively rigorous description of the process through which individuals preferences and phisical relationship to determine an equilibrium pure interest rate. This is generally followed by the assertion that somehow a market risk-premium is also determined, with the prices of asset adjusting accordingly to account for differences of their risk.
17,922 citations
Journal Article•
TL;DR: In this article, the effect of financial structure on market valuations has been investigated and a theory of investment of the firm under conditions of uncertainty has been developed for the cost-of-capital problem.
Abstract: The potential advantages of the market-value approach have long been appreciated; yet analytical results have been meager. What appears to be keeping this line of development from achieving its promise is largely the lack of an adequate theory of the effect of financial structure on market valuations, and of how these effects can be inferred from objective market data. It is with the development of such a theory and of its implications for the cost-of-capital problem that we shall be concerned in this paper. Our procedure will be to develop in Section I the basic theory itself and to give some brief account of its empirical relevance. In Section II we show how the theory can be used to answer the cost-of-capital questions and how it permits us to develop a theory of investment of the firm under conditions of uncertainty. Throughout these sections the approach is essentially a partial-equilibrium one focusing on the firm and "industry". Accordingly, the "prices" of certain income streams will be treated as constant and given from outside the model, just as in the standard Marshallian analysis of the firm and industry the prices of all inputs and of all other products are taken as given. We have chosen to focus at this level rather than on the economy as a whole because it is at firm and the industry that the interests of the various specialists concerned with the cost-of-capital problem come most closely together. Although the emphasis has thus been placed on partial-equilibrium analysis, the results obtained also provide the essential building block for a general equilibrium model which shows how those prices which are here taken as given, are themselves determined. For reasons of space, however, and because the material is of interest in its own right, the presentation of the general equilibrium model which rounds out the analysis must be deferred to a subsequent paper.
15,342 citations
TL;DR: In this article, the problem of selecting optimal security portfolios by risk-averse investors who have the alternative of investing in risk-free securities with a positive return or borrowing at the same rate of interest and who can sell short if they wish is discussed.
Abstract: Publisher Summary This chapter discusses the problem of selecting optimal security portfolios by risk-averse investors who have the alternative of investing in risk-free securities with a positive return or borrowing at the same rate of interest and who can sell short if they wish. It presents alternative and more transparent proofs under these more general market conditions for Tobin's important separation theorem that “ … the proportionate composition of the non-cash assets is independent of their aggregate share of the investment balance … and for risk avertere in purely competitive markets when utility functions are quadratic or rates of return are multivariate normal. The chapter focuses on the set of risk assets held in risk averters' portfolios. It discusses various significant equilibrium properties within the risk asset portfolio. The chapter considers a few implications of the results for the normative aspects of the capital budgeting decisions of a company whose stock is traded in the market. It explores the complications introduced by institutional limits on amounts that either individuals or corporations may borrow at given rates, by rising costs of borrowed funds, and certain other real world complications.
9,970 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 paper, the effect of differences in dividend policy on the current price of shares in an ideal economy characterized by perfect capital markets, rational behavior, and perfect certainty is examined.
Abstract: In the hope that it may help to overcome these obstacles to effective empirical testing, this paper will attempt to fill the existing gap in the theoretical literature on valuation. We shall begin, in Section I , by examining the effects the effects of differences in dividend policy on the current price of shares in an ideal economy characterized by perfect capital markets, rational behavior, and perfect certainty. Still within this convenient analytical framework we shall go on in Section II and III to consider certain closely related issues that appear to have been responsible for considerable misunderstanding of the role of dividend policy. In particular, Section II will focus on the longstanding debate about what investors "really" capitalize when they buy shares; and Section III on the much mooted relations between price, the rate of growth of profits, and the rate of dividends per share. Once these fundamentals have been established, we shall proceed in Section IV to drop the assumption of certainty and to see the extent to which the earlier conclusions about dividend policy must be modified. Finally, in Section V , we shall briefly examine the implications for the dividend policy problem of certain kinds of market imperfections.
6,265 citations