Aplicação do modelo de volatilidade incerta para identificação de oportunidades de arbitragem

Resumo

The objective of this paper is to build a model that can identify arbitrage opportunities in the derivatives market. The idea of the model will be to replicate a financial contract using other instruments available in the financial market. The algorithm will apply the Uncertain Volatility Model in order to evaluate the price of the portfolio as a whole (replicated derivative, along with its replicating instruments). We will subtract from this price the cost of building such replicating portfolio, in order to derive the price at which we could trade the replicated contract. If this price differs from the price we observe in the market, then we will have found ourselves with an arbitrage opportunity. We shall use an optimization algorithm, together with the Uncertain Volatility Model, in order to get the portfolio that maximizes the profits of our strategy. One of the main pillars of our model lies in the fact that the pricing equation of options is not linear. In other words, the total price of a portfolio of options does not equal to the sum of the quantities of each of these options multiplied by their respective price. We will also build a Monte Carlo simulator, which will take as inputs the portfolio returned by the optimizer. The objective of this simulator will be to validate the profit as suggested by the arbitrage-identifying model. In order to apply the implemented algorithms in a real case, this study used data published on the B3 stock exchange website.

Ficha do documento

Tipo

Dissertação

Ano

2020

Instituição

Fundação Getulio Vargas

Fonte

Repositório da FGV

Idioma

Português

Acesso

Acesso aberto

Identificador

oai:repositorio.fgv.br:10438/29447

Temas

Economia

Palavras-chave

ArbitrageOptimizationUncertain volatility modelExplicit finite differences methodDerivatives pricingArbitragemOtimizaçãoModelo de volatilidade incertaMétodo de diferenças finitas explícitoApreçamento de derivativosEconomiaMercado de opções - BrasilDerivativos (Finanças) - PreçosVolatilidade (Finanças)Arbitragem comercialOtimização matemática