Empirical Pricing Analysis of Caps and Swaptions using Multi-Factor Models

The aim of this paper is to price caps and swaptions using multi-factor term structure models in a low interest rate environment. We price these products within the Heath-Jarrow-Morton framework, condition on the term structure, and investigate the pricing errors to detect possible modeling biases. The volatility functions are modeled using principal component analysis of up to three factors using interest-rate or option data with either constant or time-varying parameters. We use weekly data of US swaps, caps and swaptions from 2013-2019. The results show that option-based estimation outperforms interest-rate based estimation, and that the multi-factor models generally outperform one-factor models in pricing. We find that pricing errors vary over time, and are related to the term structure shape and level, and moneyness, but not to time-to-maturity, option expiry, and swap tenor. We further find that the low interest rate environment has a negative inuence on pricing errors.