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Theory of rational option pricing

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.
Citations
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Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
TL;DR: In this paper, the authors present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties "coherent", and demonstrate the universality of scenario-based methods for providing coherent measures.
Abstract: In this paper we study both market risks and nonmarket risks, without complete markets assumption, and discuss methods of measurement of these risks. We present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties “coherent.” We examine the measures of risk provided and the related actions required by SPAN, by the SEC=NASD rules, and by quantile-based methods. We demonstrate the universality of scenario-based methods for providing coherent measures. We offer suggestions concerning the SEC method. We also suggest a method to repair the failure of subadditivity of quantile-based methods.

8,651 citations

Journal ArticleDOI
Steven L. Heston1
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

References
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Journal ArticleDOI
TL;DR: Efficient Capital Markets: A Review of Theory and Empirical Work Author(s): Eugene Fama Source: The Journal of Finance, Vol. 25, No. 2, Papers and Proceedings of the Twenty-Eighth Annual Meeting of the American Finance Association New York, N.Y. December, 28-30, 1969 (May, 1970), pp. 383-417 as mentioned in this paper
Abstract: Efficient Capital Markets: A Review of Theory and Empirical Work Author(s): Eugene F. Fama Source: The Journal of Finance, Vol. 25, No. 2, Papers and Proceedings of the Twenty-Eighth Annual Meeting of the American Finance Association New York, N.Y. December, 28-30, 1969 (May, 1970), pp. 383-417 Published by: Blackwell Publishing for the American Finance Association Stable URL: http://www.jstor.org/stable/2325486 Accessed: 30/03/2010 21:28

18,295 citations


"Theory of rational option pricing" refers background in this paper

  • ...By construction, dz is not serially correlated and in the notation of (24), () = - ga e 44 In [ 13 ] and [41 ], respectively....

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Journal ArticleDOI
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

Journal ArticleDOI
TL;DR: The authors tried to answer the question: When is a random variable Y "more variable" than another random variable X "less variable" by asking when a variable X is more variable than another variable Y.

3,655 citations


"Theory of rational option pricing" refers background in this paper

  • ...It should also be noted that it is the total risk, and not the systematic or portfolio risk, of the common stock which is important to warrant pricing. In [ 39 ],p. 225....

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Book
03 Jan 1960

1,004 citations

Journal ArticleDOI
TL;DR: This paper showed that the text, first written in 1964, is still relevant and relevant at the beginning of the 21st century, which is known to a generation of financial economists having marked the beginnings of the field known as financial econometrics.
Abstract: This work is known to a generation of financial economists having marked the beginnings of the field known as financial econometrics. This edition sets out to show that the text, first written in 1964, is still relevant is still relevant at the beginning of the 21st century.

886 citations