This paper presents a new method to validate risk models: the Risk Map. This method jointly accounts for the number and the magnitude of extreme losses and graphically summarizes all information about the performance of a risk model. It relies on the concept of a super exception, which is...

We find that option-implied information such as forward-looking variance, skewness and the variance risk premium are sensitive to the way the volatility surface is constructed. For some state-of-the-art volatility surfaces, the differences are economically surprisingly large and lead to...

We introduce a new measure of systemic risk, the change in the conditional joint probability of default, which assesses the effects of the interdependence in the financial system on the general default risk of sovereign debtors. We apply our measure to examine the fragility of the European...

This paper investigates whether multivariate crash risk (MCRASH), defined as exposure to extreme realizations of multiple systematic factors, is priced in the cross-section of expected stock returns. We derive an extended linear model with a positive premium for MCRASH and we empirically confirm...

Artículo de revista ; The European Central Bank’s and the Federal Reserve’s announcements of unconventional monetary policies have contributed to significantly reducing market perceptions of the probability of extreme macro-financial events. This phenomenon has arisen in periods of intense...

Este documento evalúa el impacto de los anuncios de medidas de política monetaria no convencionales de cuatro grandes bancos centrales (la Reserva Federal, el Banco Central Europeo, el Banco de Inglaterra y el Banco de Japón) sobre las probabilidades de futuras caídas bursátiles. Estas...

Summary of Banco de España Working Paper no. 2127

This article analyzes the tail behavior of energy price risk using a multivariate approach, in which the exposure to energy markets is given by a portfolio of oil, gas, coal, and electricity. To accommodate various dependence and tail decay patterns, this study models energy returns using...