Apreçamento de opções de IDI usando o modelo CIR

Abstract

The IDI option from the BM&F (Commodities and Futures Exchange) has unusual characteristics, that make its pricing different from common interest rate options. This paper develops a closed form formula for the pricing of these IDI options, using an arbitrage-free pricing approach. The model used considers only one stochastic factor: the short-term risk-free interest rate. The differential equation used to model the behavior of the interest rate comes from the CIR (COX INGERSOLL & ROSS, 1985) model, which has mean reversion property and does not allow negative nominal interest rates. It is also done a parameter estimation of the proposed model based on historic data, and then compares the theoretical price of the option based on these parameters with the market price and with the theoretical price considering the Vasicek (1977) model.