Risk and Decision Analysis

This paper examines whether the puzzling negative relationship between idiosyncratic volatility and next month performance is affected by the intensity of merger and acquisition (M&A) activity in the market. Our results show that the idiosyncratic volatility puzzle is stronger in periods of high M&A activity than in periods of low M&A activity. Further analysis shows that the negative relationship between idiosyncratic volatility and next month performance is the strongest in the high M&A activity sub-period spanning from 1982–1989. In contrast, M&A activity does not explain the negative relationship between the common factor in idiosyncratic volatility (CIV) and next month performance. M&A activity can in part explain the idiosyncratic volatility puzzle, but it does not subsume the negative relationship between CIV exposure and firm returns.

Contrary to the current regulatory trend regarding extreme risks, the purpose of this paper is to emphasize the necessity of considering the Value-at-Risk (VaR) with extreme confidence levels like 99.9%, as an alternative way of measuring risks in the “extreme tail”. Although the mathematical definition of the extreme VaR is trivial, its computation is challenging in practice, because the uncertainty of the extreme VaR may not be negligible for a finite amount of data. We begin to build confidence intervals around the unknown VaR. We build them using two different approaches, the first one uses the asymptotic Gaussian result and the second saddlepoint approach, the latter proves to be more robust when we use finite samples. We compare our approach with other methodologies which are based on bootstrapping techniques, focusing on the estimation of the extreme quantiles of a distribution. Finally, we apply these confidence intervals to perform a stress testing exercise with historical stock returns during the financial crisis, in order to identify potential violations of the VaR during periods of turmoil on financial markets.

In this paper, we provide several preservation results for Laplace transform ordering of residual lives (Lt-rl) under the reliability operations convolutions, mixtures and series systems. We also show that this order is preserved under completely monotone transformations.

The existing literature of fuzzy divergence measures provides a variety of such measures scoring one over the other and even having certain drawbacks. The main objective of the present communication is to remove such drawbacks and propose a modified fuzzy divergence measure along with the study of its detailed properties. The applications of this modified version of fuzzy divergence measure have been provided to the fields of medical diagnosis and multi-criteria decision making (MCDM) problem. Numerical verification has been illustrated to demonstrate the proposed method under fuzzy environment.

Option prices are characterized by wide bid-ask spreads, much wider than the spreads of their underlying assets. This note discusses the various attempts to rationalize and link the two markets’ spreads with each other and explains why their failures are mainly due to the inability to accommodate trading frictions in theoretical asset pricing models. It also presents in summary form the partial results from the stochastic dominance approach to option pricing under proportional transaction costs that provide bounds for the spreads for index call options.