Modeling the Volatility Risk Premium Term Structure in Swaptions

Despite the large body of evidence of a volatility risk premium embedded in option prices, little is known about its behavior over the cross-section of option maturities. This study introduces maturity term structure modeling in the literature of the volatility premium. My findings are consistent with a concave, upward sloping maturity term structure, constructed on the basis of delta-hedged swaption straddle portfolios in two major currency markets (USD and GBP). I extend the application of the Nelson-Siegel model to volatility premium term structure modeling using both linear estimation techniques and state space optimization by means of a Kalman filter. The model is found to be capable of accurately fitting the premium term structure in-sample through three latent factors that correspond to the structure’s level, slope and curvature. The factors are largely driven by movements in swaption implied volatility and to a lesser extent by dynamics in the forward swap rate and macroeconomic influences. Due to large randomness in the premia dynamics, out-ofsample forecasts of the term structure are inaccurate. The shape of the term structure is furthermore robust to alternative premium valuations, indicating that the Nelson-Siegel model can be successfully applied to a range of alternatively constructed volatility risk premium term structures.