Equações diferenciais estocásticas e as estratégias de hedging no mercado de opções

Abstract

The Stochastic Differential Equation models (SDEs) assume an important role in finances. The major part of these models try to help the investors with the risk management of the financial activities and they use SDEs for describing the evaluation of certain variables such as the price and the volatility of assets. In this sense, one of our goals for this dissertation is to study how the financial market works, with special attention to option price and hedging strategies. The second goal is to show the mathematical modeling process with SDEs and, then, explore the models as Black - Scholes - Merton and it version with many assets. Finally, we conclude by presenting applications in real data and some possibilities to extend the option price models.