Estimating time-varying factors’ variance in the string-term structure model with stochastic volatility

This paper presents a novel term structure of interest rate (TSIR) model with stochastic volatility and jumps (SVJ) that combines the market framework proposed by Brace et al. (1997) with the string-shock framework of Santa-Clara and Sornette (2001). In this model, the factors’ variance is estimated through the eigendecomposition of a variance–covariance matrix obtained with a measure of market volatility derived from out-of-the-money option prices and historical correlations of interest rates traded in the futures market. The stochastic evolution of the factors’ variance is governed by the 4/2 model developed by Grasselli (2017), including jumps. A novel method is employed to estimate the parameters of the SVJ model that minimizes the distance between the sample moments and the moments of a gamma distribution. The empirical application of the model in the Brazilian derivatives market demonstrates its effectiveness in accurately capturing the volatility smile of interest rate options.