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We study the properties of a GEI model with nominal assets, outside money (injected into the economy as in Magill and Quinzii), and multiple currencies. We analyze the existence of monetary equilibria and the structure of the equilibrium set under two different assumptions on the determination of the exchange rates. If currencies are perfect substitutes, equilibrium allocations are indeterminate and, generically, sunspot equilibria exist. Generically, given a nonsunspot equilibrium, there are Pareto improving (and Pareto worsening) sunspot equilibria associated with an increase in the volatility of the future exchange rates. We interpret this property as showing that, in general, there is no clear-cut effect on welfare of the excess volatility of exchange rates, even when due to purely extrinsic phenomena.

It is well-known that stock prices fluctuate far more than dividends. Traditional valuation methods are not able to depict this fact. In this paper we incorporate excess volatility into a simple DCF model by considering an autoregressive cash flows process with random coefficients. We show that the model is free of arbitrage and that the transversality condition is met and we prove a valuation equation that differs from the classical Gordon-Shapiro version: Cost of capital (respectively dividend-price ratio) is stochastic and our model represents excess volatility. We discuss whether our assumptions are compatible with an equilibrium.

In rational beliefs (RB) models there is an observed empirical distribution for the stochastic process of state variables. Many different weakly asymptotic mean stationary (WAMS) processes could have generated this empirical distribution, i.e. are consistent with it, and each of them are therefore called a rational belief.We provide a general framework for using RB in general equilibrium models. Individual rational beliefs are assumed correlated by means of sunspots which at the aggregate level lead to excess volatility.The application adapts the proof by Duffie et al (1994) of the existence of a stationary ergodic RE equilibrium to the case where agents hold rational beliefs.

Purpose
The purpose of this paper is twofold: first, to propose a new robust volatility ratio (RVR) that compares the intraday high–low volatility with that of the intraday open–close volatility estimator; and second, to empirically test the proposed RVR on the cross-sectional (CS) average of the constituent stocks of India's BSE Sensex and US's Dow Jones Industrial Average index to find the evidence of "excess volatility."


Design/methodology/approach
The authors model the proposed RVR by assuming the logarithm of the price process to follow the Brownian motion. The authors have theoretically shown that the RVR is unbiased in the case of zero drift parameter. Moreover, the RVR is found to be an even function of the non-zero drift parameter.


Findings
The empirical results show that the analysis based on the RVR supports the existence of "excess volatility" in the CS average of the constituent stocks of India's BSE Sensex and US's Dow Jones index. In particular, the authors have observed that the CS average of individual constituent stocks of BSE Sensex is found to be more excessively volatile than the US's Dow Jones index during the period of the study from January 2008 to September 2016, based on multiple k-day time window analysis.


Practical implications
The study has implications for the policy makers and practitioners who would like to understand the volatility behavior in the asset returns based on the RVR of this study. In general, the proposed model can be used as a specification tool to find whether the stock prices follow the random walk behavior or excessively volatile.


Originality/value
The authors contribute to the existing volatility literature in finance by proposing a new RVR based on extreme values of asset prices and absolute returns. The authors implement the bootstrap technique on RVR to find the estimates of mean and standard error for multiple k-day time windows. The RVR can capture the excess volatility by comparing two independent volatility estimators. This is possibly the first study to find the CS average of all the constituent stocks of BSE Sensex based on the RVR.