Determinação entrópica do preço racional da opção européia simples ordinária sobre ação e bond: uma aplicação da teoria da informação em finanças em condição de incerteza / Entropic approach to rational pricing of the simple ordinary option of european-type over stock and bond: an application of information theory in finance under uncertainty

AUTOR(ES)
DATA DE PUBLICAÇÃO

1999

RESUMO

This thesis integrates Finance and Information Theory in order to create an alternative environment to the calculation of the rational price of the simple ordinary European option over stocks and bonds. One of the features of this new environment is to allow us to continue using the Newtonian calculus instead of the stochastic one. It creates a precise and complete mathematical notation for the Information Theory and integrates it with the Finance Theory under uncertainty conditions. It integrates Gulko’s (1998 and 1998a) and Yang’s (1997) entropic approaches to the calculation of the rational price of the simple ordinary European option. It precisely defines the uncertainty-price-neutral world (risk-neutral world), the martingale world, the informationally efficient world and the entropic world and their implications to the Investment Science and, more specifically, to the calculation of the rational price of ordinary assets and derivatives. It demonstrates with details the Black-Scholes-Merton formula of the rational price of the simple ordinary European option, improves the mathematical notation, simplifies it (by eliminating the martingale approach) and completes the demonstration done by Baxter &Rennie (1998). It breaks a succession of works that established a mistaken way to calculate the price of the simple ordinary European option. This mistake had its origin, much probably, in an edition of Brealey &Myers, who erroneously used a result from Cox &Rubinstein (1985). This result facilitates the calculation of the rational price of the simple ordinary European option by using a table that avoids the direct usage of the Black-Scholes-Merton formula. Brealey &Myers (since the 1991 fourth edition), Luehrman (in his two 1998 articles in HBR and in a 1995 case in HBS) and Edleson (1994 case published in HBS) teach that the percentage value found in this table must be multiplied by the price of the asset, when in reality it should have been multiplied by the present value of the strike price. The most important results of this thesis for Finance are: (i) development of a robust and economic alternative method, based on the maximum-entropy principle of the Information Theory and on Pearson’s Distribution System, to the calculation of a unique uncertainty-price-neutral probability measure (risk-neutral probability), (ii) achievement of a practical formula to the calculation of the rational price of the simple ordinary European option on stocks, (iii) validation of the Black-Scholes-Merton formula on stocks, (iv) achievement of an adequate formula to the calculation of the rational price of the simple ordinary European option on bonds, (v) estimation of the implied entropic volatility of the price of an asset and (vi) definition and estimation of the entropic value-at-risk. There are still two important results to the Information Theory and to Economics: (i) a more precise distinction between uncertainty and risk and (ii) development of the forecast informational gain, an enhancement of the result of Theil (1967) and Benish (1999) by using the Kullback-Leibler divergence concept.

ASSUNTO(S)

derivativo opção entropy entropia option rational price risk-neutral density funtion preço racional densidade neutralizadora do preço da incerteza teoria da informação information theory derivative

ACESSO AO ARTIGO

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