The Volatility of Long-Term Bond Returns:Persistent Interest Shocks and Time-Varying Risk Premiums

We develop an almost affine term-structure model with a closed-form solution for factor loadings in which the spot rate and the risk price are fractionally integrated processes with different integration orders. This model is used to explain two stylized facts. First, predictability of longterm excess bond returns requires sufficient volatility and persistence in the risk price. Second, the large volatility of long-term bond returns requires persistence in the spot rate. Decomposing long-term bond returns, we find that the expectations component from the level factor is more volatile than returns themselves and that the risk premium correlates negatively with level-factor innovations

Robust long-term interest rate risk hedging in incomplete bond markets

Pricing ultra-long-dated pension liabilities under the market-consistent valuation is challenged by the scarcity of the long-term market instruments that match or exceed the terms of pension liabilities. We develop a robust self-financing hedging strategy which adopts a min–max expected shortfall hedging criterion to replicate the long-dated liabilities for agents who fear parameter misspecification.We introduce a backward robust least squares Monte Carlo method to solve this dynamic robust optimization problem. We find that both naive and robust optimal portfolios depend on the hedging horizon and the current funding ratio. The robust policy suggests taking more risk when the current funding ratio is low. The yield curve constructed by the robust dynamic hedging portfolio is always lower than the naive one but is higher than the model-based yield curve in a low-rate environment

An empirical application of stochastic volatility models

This paper studies the empirical performance of stochastic volatility models for twenty years of weekly exchange rate data for four major currencies. We concentrate on the effects of the distribution of the exchange rate innovations for both parameter estimates and for estimates of the latent volatility series. The density of the log of squared exchange rate innovations is modelled as a flexible mixture of normals. We use three different estimation techniques: quasi-maximum likelihood, simulated EM, and a Bayesian procedure. The estimated models are applied for pricing currency options. The major findings of the paper are that: (1) explicitly incorporating fat-tailed innovations increases the estimates of the persistence of volatility dynamics; (2) the estimation error of the volatility time series is very large; (3) this in turn causes standard errors on calculated option prices to be so large that these prices are rarely significantly different from a model with constant volatility

Robust hedging in incomplete markets

We considered a pension fund that needs to hedge uncertain long-term liabilities. We modeled the pension fund as a robust investor facing an incomplete market and fearing model uncertainty for the evolution of its liabilities. The robust agent is assumed to minimize the shortfall between the assets and liabilities under an endogenous worst-case scenario by means of solving a min–max robust optimization problem. When the funding ratio is low, robustness reduces the demand for risky assets. However, cherishing the hope of covering the liabilities, a substantial risk exposure is still optimal. A longer investment horizon or a higher funding ratio weakens the investor's fear of model misspecification. If the expected equity return is overestimated, the initial capital requirement for hedging can be decreased by following the robust strategy

A Bayesian analysis of the unit root in real exchange rates

We propose a posterior odds analysis of the hypothesis of a unit root in real exchange rates. From a Bayesian viewpoint the random walk hypothesis for real exchange rates is a posteriori as probable as a stationary AR(1) process for four out of eight time series investigated. The French franc/German mark is clearly stationary, while the Japanese yen/US dollar is most likely a random walk. In contrast, classical tests are unable to reject the unit root for any of these series