Derivativos de renda fixa no Brasil: modelo Hull-White

Abstract

The Brazilian fixed income market, when compared to the international standards of developed countries, is characterized by high interest rates and huge volatility. These features turn the modeling of financial engineering into an extremely challenging task. It is not trivial to calibrate interest rate models that capture the stylized facts for the different regimes observed for the Brazilian market. We implement the Hull-White model, with one factor, for the IDI-BM&F option market. The critical aspect of this task is to implement the algorithm to match the market prices to the theoretical ones. The procedure allows us to estimate, endogenously, both the mean-reverting speed and the short rate volatility parameter. Despite the scarcity of IDI options daily data, we show that it is possible to calibrate the Hull-White model in a very robust fashion for the periods of financial stability. We also show that in periods with huge volatility — specifically during the recent Argentinean contagion effect in the Brazilian fixed income market—the model renders unstable parameters. Nowadays, this issue is relevant because the Central Bank has started using derivatives to perform both the monetary and exchange rate policies. Our work contributes, providing practical alternative ways for implementing the Hull-White model for the Brazilian fixed income market.