THE DEPENDENCE STRUCTURE OF RUNNING MAXIMA AND MINIMA: RESULTS AND OPTION PRICING APPLICATIONS

We provide general results for the dependence structure of running maxima (minima) of sets of variables in a model based on (i) Markov dynamics; (ii) no Granger causality; (iii) cross-section dependence. At the time series level, we derive recursive formulas for running minima and maxima. These formulas enable to use a "bootstrapping" technique to recursively recover the pricing kernels of barrier options from those of the corresponding European options. We also show that the dependence formulas for running maxima (minima) are completely defined from the copula function representing dependence among levels at the terminal date. The result is applied to multivariate discrete barrier digital products. Barrier Altiplanos are simply priced by (i) bootstrapping the price of univariate barrier products; (ii) evaluating a European Altiplano with these values.     

Diamonds and precious metals for reduction of portfolio tail risk

ABSTRACT

We study the performance of diamonds compared to gold and other precious metals in mitigating the tail risk of a diversified equity market portfolio over the period June 2007 to October 2018. Our results display a diversification benefit of some diamond indices, which also improve the portfolio reward-to-risk ratio. To corroborate this evidence, we study the dependence structure and tail dependence of diamonds and a broad equity market portfolio and compare it to the dependence obtained with gold and other precious metals. Results from fitting a bivariate copula show that the average left tail dependence reaches its minimum when diamonds are used. We also show that using shares of diamond-mining companies does not provide the same benefits.     

Climate change management: a resilience strategy for flood risk using Blockchain tools

Decisions in Economics and Finance - This work aims to offer a contribution in the analysis and management, from an economic and financial point of view, of the flood risk, and extended to the...     

Optimal hedge ratio under a subjective re-weighting of the original measure

In this article we study a risk-minimizing hedge ratio with futures contracts, where the risk of the hedged portfolio is measured through a spectral risk measure (SRM), thus incorporating the degree of agent’s risk aversion. We empirically estimate the optimal hedge ratio (OHR) using a long time series of UK and US equity indices, the EURUSD and EURGBP exchange rates and four liquid commodities (Brent crude oil, corn, gold and copper), to represent different asset classes. Comparing the results with common OHRs (such as the minimum variance and the minimum expected shortfall), we find that the agent’s risk aversion has a material impact, and should not be ignored in risk management.