Long-term risk with stochastic interest rates

In continuous-time arbitrage-free markets we study the impact on pricing of the intertemporal aggregation of exposures to short-term rates variability across increasingly large investment horizons. When interest rates are... [ view full abstract ]

In continuous-time arbitrage-free markets we study the impact on pricing of the intertemporal aggregation of exposures to short-term rates variability across increasingly large investment horizons. When interest rates are constant, the instantaneous rate drives both risk-neutral prices and the evolution of pricing kernels. However, no ex-ante measurable financial variable is known to play an analogous dual role when rates are stochastic. Without assuming any specific dynamics for interest rates, we show how pure-discount bond yields address this issue when the forward measure is employed. Our analysis is consistent with long-term risk convergences when the horizon under consideration becomes arbitrarily large.