Option pricing (original) (raw)

Theory of Financial Options: A Conceptual Review

1997

This essay discusses the basic option pricing models - including the Binomial discrete model, the Black-Scholes continuous model, and their variants - and their mathematical derivations. It also provides an empirical evidence of options pricing and mispricing of the underlying securities that are traded in the markets. Moreover, some applications of option products are explored both as the market instruments and as the tailor-made contingent-claim contracts. Risk reduction, while enhancing returns through financial engineering, active assets allocation, and portfolios management, is possible and makes more sense if individual investors are aware of and familiar with the basic option pricing tools and their exotic applications. Sophisticated investors such as speculators, and hedgers, who are well-informed and have been equipped with these analytical capabilities, already squeezed extra returns from their investments in real and financial assets, let alone the institutional traders who seek arbitrage opportunities around the globe. Until all heterogeneous market participants are fluent with the language of derivative products and fine-tuned their expectations accordingly, the normative assumptions underlying modern finance theory will prove to be relevant in the real world.

Option pricing: A simplified approach

Journal of Financial Economics, 1979

This paper presents a simple discrete-time model for valuing options. The fundamental economic principles of option pricing by arbitrage methods are particularly clear in this setting. Its development requires only elementary mathematics, yet it contains as a special limiting case the celebrated Black-Scholes model, which has previously been derived only by much more difficult methods. The basic model readily lends itself to generalization in many ways. Moreover, by its very construction, it gives rise to a simple and efficient numerical procedure for valuing options for which premature exercise may be optimal.

Theory of rational option pricing

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. 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 r estrictions 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.