How arbitrage-free is the Nelson–Siegel model under stochastic volatility?

Abstract

This study examines the effect of no-arbitrage on the Nelson–Siegel (NS) model under stochastic interest-rate volatility. Unlike under constant volatility, in which only a constant (convexity-adjustment) term of a yield function differs with and without no-arbitrage, factor loadings also differ when the volatility is spanned by interest-rate factors. After controlling for the drift, we find that spanned volatility does not magnify the effect of no-arbitrage relative to constant volatility. The finding implies that enriching the NS model with stochastic volatility is of significant benefit as this better describes interest-rate data without increasing the cost of allowing arbitrage opportunities.