Forecasting Parameters in the SABR Model

Abstract

We present two approaches to forecast parameters in the SABR model. The first approach is the vector auto-regressive moving-average model (VARMA) for the time series of the in-sample calibrated parameters, and the second is based on machine learning techniques called epsilon-support vector regression (ε-SVR). Using daily data of S&P 500 ETF option prices from 2014 Jan 01 to 2018 Dec 31, we first calibrate the daily values of the model parameters from the training sample, then conduct out-of-sample forecasting of parameters and pricing of options. Both approaches produce good fits between the forecasted and calibrated parameters for out-of-sample dates. A comparison study shows that using forecasted parameters as inputs, the SABR model generates better pricing results than assuming constant parameters or using lag parameters. We also discuss the market conditions under which one approach outperforms the other.