A new class of risk measures called cash sub-additive risk measures is introduced to assess the risk of future financial, nonfinancial and insurance positions. The debated cash additive axiom is relaxed into the cash sub-additive axiom to preserve the original difference between the numeraire of...

In this paper, we introduce two classes of indices which can be used to measure the market perception concerning the degree of dependency that exists between a set of random variables, representing different stock prices at a fixed future date. The construction of these measures is based on the...

We extend the Rothschild and Stiglitz (1970, 1971) notion of increasing risk to families of random variables and in this way link their approach to the concept of stochastic processes which are increasing in the convex order. These processes have been introduced in seminal work by Strassen...

We introduce a methodology to extract the downside and upside implied volatilities from European options. Our proposed methodology is based on partitioning the total implied volatility into downside and upside portions. We extract the downside and upside volatilities for S&P 500 for the years...

This paper investigates the risk exposure for options and proposes MaxVaR as an alternative risk measure which captures the risk better than Value-at-Risk especially. While VaR is a measure of end-of-horizon risk, MaxVaR captures the interim risk exposure of a position or a portfolio. MaxVaR is...

The forward-looking nature of option market data allows one to derive economically-based and model-free risk measures. This article proposes an extensive analysis of the performances of option-implied VaR and CVaR, and compare them with classical risk measures for the S&P500 Index. Delivering...

Eigenfunction and quadrature methods have been extensively used in asset pricing as a forecasting tool. In contrast, their application to systemic risk has been limited. With the advent of high frequency options panels we document a battery of measures that can be used to measure and forecast...

This essay explores the link between the exponential probability density function and the present value function coupled with moment theory to derive important non probabilistic parameters from the Present value function in which are then used to derive a measure of the volatility of interest...

The paper contributes to the stochastic volatility literature by developing simulation schemes for the conditional distributions of the price of long term bonds and their variability based on non-standard distributional assumptions and volatility concepts; itillustrates the potential value of...