Modelo de Vasicek com Volatilidade Estocástica

Osvaldo Paulo Israel Cançado Assunção

Keywords: volatilidade estocástica | Análise Assintótica | Taxa de Juros | Vasicek | CIR

In this work we obtain closed formulas to price bonds using two popular models for the interest rate, Vasicek and CIR. We then expand these models, adding a two-factor stochastic volatility, following the work of J-P. Fouque, G. Papanicolaou, R. Sircar and K. Solna. We use perturbation theory and asymptotical analysis to obtain closed formulas for the bond price. Finally, we fit those models to brazilian market data, proving that the model with stochastic volatility, though more complicated, gets better results. The improvement on the results, however, does not come with an increased computational cost, since the closed formula obtained is simple and easy to implement, which is of great value to financial institutions.

Anexos:

• pfcosvaldocorrected.pdf