Risk and Decision Analysis

In this work, the main theme is to investigate a novel generalized parametric exponential intuitionistic fuzzy divergence measure along with the study of its detailed properties for its authenticity. The applications of this newly developed generalized intuitionistic fuzzy divergence measure have been provided to multi-attribute decision making (MADM). Numerical verification has been illustrated to demonstrate the proposed method for solving multi-attribute decision making problem under fuzzy environment.

Since Basel 2, a financial institution can determine the capital required for credit risk by using internal models, which require the determination of Loss Given Default (LGD). LGD is also an important element in assets pricing. The dynamics of LGD can be evaluated directly or can be extracted from the dynamics of the recovery rate (RR). Observed LGDs/RRs present an asymmetric and bimodal distribution. In this article several models formalizing these features are employed: simple models and models modeling the unusual nature of LGDs/RRs (skewed regressions, adjusted regressions, inflated regressions). In sum, 25 models were retained for evaluating the dynamics of LGDs and RRs and 13 covariates. Performances of models were compared by using several classical and advanced metrics determined by using 10-fold cross-validation. According to obtained results, the best way to forecast LGDs is either to model and forecast it directly with the beta regression and with the zero-adjusted beta regression or drawn it from the fitted and forecasted RRs with its performing models. These latter models are the beta regression and the one-adjusted beta regression. As expected, most of the retained explanatory variables influence the dynamics of LGDs/RRs.

The article addresses theoretical issues, applied instruments and practical implementation of the behavioral valuation methodology. It formulates the range of specific correction parameters for beta coefficient, used in calculating CAPM-based discount rate in order to find behavioral discount rate and calculate stock’s market value, with regard to behavioral factors and risks associated with them.

The hypothesis that emotions influence the deviation of the beta coefficient used by irrational investors in the market from the beta coefficient used in the CAPM model was tested and confirmed. The range of deviations of the beta coefficient used by irrational investors in the market from the beta coefficient used in the CAPM model is presented. It can be used for specific practical applications in calculating the market value of shares.

The results of the studies described in the article are used in valuation, in corporate finance, in the stock market. It is especially important to use the tools of behavioral valuation in conditions of instability and crisis, a change in the market paradigm, market shifts, changes in the parameters of profitability and volatility of financial instruments. The use of behavioral valuation tools complements and expands the classic tools of traditional finance, improves the quality of value management solutions in modern markets.

Cryptocurrencies have emerged in the last decade as a new asset class unlikely to disappear despite its extraordinary volatility. Futures contracts on Bitcoins were introduced in December 2017 by the Chicago Mercantile Exchange followed by options in January 2020. Our goal in this paper is threefold: (i) present the main features of cryptocurrency spot and derivative markets; (ii) argue that the custody recently granted by large financial institutions to their large customers for their bitcoins shows that Bitcoins are very similar to commodities, allowing the extension to bitcoins of the convenience yield introduced by Working (American Economic Review, vol. 39, 1949, pp. 1254–1262) in the Theory of Storage; (iii) use the prices of options traded on the Deribit Exchange to build the volatility smiles and skews observed at different dates of 2019 for short and long dated maturities and compare them to smiles/skews of equity options.

In this paper, we consider the risk model perturbed by an independent diffusion process with a time delay in the arrival of the first claim. We derive the distribution of the counting process of the risk process, the integro-differential equations of the ruin probabilities and generalize its defective renewal equations. With claim amounts following exponential and mixed exponential distributions, explicit expressions and asymptotic properties of the ruin probabilities are derived. Numerical illustrations of the ruin probabilities are proposed when claim amounts are exponentially and mixed exponentially distributed. We extend the results to the case of the delayed renewal risk model with exchangeable risks which captures the possible dependence between inter-arrival times of the claims and derive the associated ruin probabilities.