Un modelo macroeconómico con agentes de vida finita y estocástica: cobertura de riesgo de mercado con derivados americanos

Abstract

ResumenEn esta investigación se desarrolló un modelo de economía estocástica, pequeña y abierta, poblada por consumidores racionales idénticos que tienen vida finita, pero estocásti-ca; además, son adversos al riesgo y disponen de una riqueza inicial. Estos agentes enfrentan la decisión de distribuir su riqueza entre consumo e inversión en un portafolio de activos en un ambiente de riesgo de mercado y de política fiscal incierta. La cobertura se lleva a cabo mediante una opción americana de venta y su valuación se realiza en térmi-nos de cuánto está dispuesto a pagar el consumidor representativo por mantener dicho contrato a fin de cubrir un activo riesgoso contra caídas en su precio. El precio del contrato se determina en términos del premio al riesgo, el cual se caracteriza mediante la solución de una ecuación diferencial parcial lineal de segundo orden. Por último, se obtiene una formula de aproximación para el precio de la opción americana y se realiza un análisis de sensibilidad de dicho precio con respecto de sus parámetros.Palabras clave: decisiones de consumo y portafolio, valuación de productos derivados, política fiscal, riesgo de mercado, modelos de equilibrio. Clasificación jel: D91, G13, E62, D50, D81. AbstractThis paper develops a stochastic model of a small and open economy populated by identical rational consumers having finite life but stochastic, who are risk averse and have an initial wealth. These agents face the decision to allocate his wealth between consumption and investment in a portfolio of assets under an environment of risk market and uncertain fiscal policy. Hedging is performed via an American put option and its pricing is carried out in terms of how much the representative consumer is willing to pay to keep that contract to hedge a fall in the risky asset price. The option price is determined in terms of the risk premium, which is characterized by the solution of a second-order, linear partial differential equation. Finally, an approximated formula for the American option price is obtained, and a sensitive analysis of such a price with respect to its parameters is carried out.

Consumption and Portfolio Decisions of a Rational Agent That Has Access to an American Put Option on an Underlying Asset With Stochastic Volatility

“…In the valuation problem, we need not only to determine the value of the option at each instant, but also to know whether the option is exercise for each value of S t . Usually, this is done by setting a critical value S * for each of these moments ( [51]). Particularly, for the valuation through Monte Carlo method, we have considered the border of exercise S * defined by the stopping time, namely, when the maximum share price is attained in the planning horizon.…”