Asian options as a rational response to post-covid market volatility

Abstract

In this paper, using a stochastic dynamic general equilibrium model and an economic rationality approach, we maximize a HARA-type utility for a rational economic agent that can use its resources to finance consumption or to invest in a portfolio. By managing its risk, the economic agent avoids losses while hedging his portfolio. The portfolio includes a risk-free bond, a stock, and a long position in an Asian put option whose underlying price is an n-day mean of the stock’s price. After ten thousand simulations, we proved that our strategy results in higher portfolio values when compared to other buy-and-hold strategies. In addition, we deducted a valuation formula for the Asian option from the solution process of a differential equations system. The proposed solution is consistent with the Black-ScholesMerton model