Pricing Asian Options with Floating Exercise Price Equal to the Arithmetic Mean: An Optimal Stochastic Control Approach

Abstract

This research characterizes the premium of a European-type +Asian put option with floating exercise price equal to the arithmetic mean, through the solution analysis to a stochastic optimal control problem in continuous time, that models the decision-making process of consumption-investment of a rational consumer in a finite horizon of planning with stochastic terminal date. The premium obtained is a partial differential equation of second order corresponding to the Black-Scholes-Merton equation, with the difference that this is established with fundamentals of economic rationality. Also, the Hamilton-Jacobi-Bellman partial differential equation is solved, which optimizes the stochastic optimal control problem.