In June 2014, the European Central Bank (ECB) announced the implementation of new refinancing operations aimed at supporting bank lending to the non-financial private sector. This paper exhibits and prices options embedded in these Targeted Longer-Term Refinancing Operations. In particular, it...

This paper introduces a novel kind of interest-rate model offering simple analytical pricing formulas for swaps, futures, swaptions, caps and floors. The model is based on an original use of regime-switching features that makes it consistent with the non-linear behavior of interest rates. In...

We present a simple theory of business-cycle movements of option prices and volumes. This theory relies on time-varying heterogeneity between agents in their demand for insurance against aggregate risk. Formally, we build an infinite-horizon model where agents face an aggregate risk, but also...

In this study we compare the quality and information content of risk neutral densities obtained by various methods. We consider a non-parametric method based on a mixture of log-normal densities, the semi-parametric ones based on an Hermite approximation of Madan and Milne, or based on an...