Estimating Time-Varying Factors’ Variance in the String Term Structure Model With Stochastic Volatility

This paper presents a new string term structured model with stochastic volatility calibrated with futures and options market data. I use interest rate options to build a time series of the variance of the factors that drive the interest rates (level, slope, and curvature). In addition, the variance of the factors is governed by a mean-reverting stochastic volatility process, whose model’s parameters are estimated within a new framework through the minimization of the distance between the moments of the gamma distribution. I show the empirical application of the model in Brazil’s derivative market, where I present empirical evidence that the Interbank Deposit (DI) future market provides good predictive power for interest rates considering short- and mid-term maturities. However, for long-term maturities, the DI future market does not capture the posterior level of interest rates, suggesting an upward bias due to the hypothetical risk premium embedded in this market