Abstract

VENEGAS MARTINEZ, Francisco  and  RODRIGUEZ NAVA, Abigail. Consistency between minimization of variance and maximization of utility in pricing derivatives. Contad. Adm [online]. 2009, n.229, pp.9-30. ISSN 0186-1042.

This paper shows the consistency between the Markowitz-Sharpe's rationality premise (MS) used to solve decision problems about the assets integrating a portfolio and the Pareto-Walras-MarshaU's economic rationality premise (PWM) used to solve decision problems about the consumption of goods integrating a basket given a budget constraint incorporating assets. Both premises are based on the optimizing behavior of the agents. In the first case, investors minimize the variance of the assets returns of a portfolio subject to an expected return. In the second case, consumers maximize utility from the consumption of a generic good subject to a budget constraint incorporating the available assets in the economy. The consistency between the two postulates described above is shown as follows: under an environment of market risk generated by assets whose prices are driven by diffusion processes both postulates are used to value a European option. The main result is that both cases result in the same Black-Scholes-Merton (1973) partial differential equation that characterizes the option price, which agrees with the partial differential equation.

Keywords : Derivates; portfolios; rational behavior.

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