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on Risk Management |
| By: | Pietro Bogani; Matteo Fontana; Luca Neri; Simone Vantini |
| Abstract: | Accurate computation of robust estimates for extremal quantiles of empirical distributions is an essential task for a wide range of applicative fields, including economic policymaking and the financial industry. Such estimates are particularly critical in calculating risk measures, such as Growth-at-Risk (GaR). % and Value-at-Risk (VaR). This work proposes a conformal framework to estimate calibrated quantiles, and presents an extensive simulation study and a real-world analysis of GaR to examine its benefits with respect to the state of the art. Our findings show that CP methods consistently improve the calibration and robustness of quantile estimates at all levels. The calibration gains are appreciated especially at extremal quantiles, which are critical for risk assessment and where traditional methods tend to fall short. In addition, we introduce a novel property that guarantees coverage under the exchangeability assumption, providing a valuable tool for managing risks by quantifying and controlling the likelihood of future extreme observations. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.00520 |
| By: | Enzo D'Innocenzo (University of Bologna); Andre Lucas (Vrije Universiteit Amsterdam and Tinbergen Institute); Bernd Schwaab (European Central Bank); Xin Zhang (Sveriges Riksbank) |
| Abstract: | We propose a robust semi-parametric framework for persistent time-varying extreme tail behavior, including extreme Value-at-Risk (VaR) and Expected Shortfall (ES). The framework builds on Extreme Value Theory and uses a conditional version of the Generalized Pareto Distribution (GPD) for peaks-over-threshold (POT) dynamics. Unlike earlier approaches, our model (i) has unit root-like, i.e., integrated autoregressive dynamics for the GPD tail shape, and (ii) re-scales POTs by their thresholds to obtain a more parsimonious model with only one time-varying parameter to describe the entire tail. We establish parameter regions for stationarity, ergodicity, and invertibility for the integrated time-varying parameter model and its filter, and formulate conditions for consistency and asymptotic normality of the maximum likelihood estimator. Using four exchange rate series, we illustrate how the new model captures the dynamics of extreme VaR and ES. |
| Keywords: | dynamic tail risk, integrated score-driven models, extreme value theory |
| JEL: | C22 G11 |
| Date: | 2024–11–08 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20240069 |
| By: | Livieri, Giulia; Radi, Davide; Smaniotto, Elia |
| Abstract: | Transition risk can be defined as the business-risk related to the enactment of green policies, aimed at driving the society towards a sustainable and low-carbon economy. In particular, when new green laws are released, companies are forced to comply with the new standards, incurring in costs which can undermine their financial stability. In this paper we derive formulas for the pricing of defaultable coupon bonds and Credit Default Swaps to empirically demonstrate that a jump-diffusion credit risk model in which the downward jumps in the firm value are due to tighter green laws can capture, at least partially, the transition risk. The empirical investigation consists in the model calibration on the CDS term-structure, performing a quantile regression to assess the relationship between implied prices and a proxy of the transition risk. Additionally, we show that a model without jumps lacks this property, confirming the jump-like nature of the transition risk. |
| Keywords: | derivatives; climate change; hypothesis testing; panel data; asset pricing; CDS spreads; credit risk; sustainable finance; transition risk |
| JEL: | G32 C32 C21 Q54 |
| Date: | 2024–04–18 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:123650 |
| By: | Tahir Choulli; Ella Elazkany; Mich`ele Vanmaele |
| Abstract: | This paper explores the application and significance of the second-order Esscher pricing model in option pricing and risk management. We split the study into two main parts. First, we focus on the constant jump diffusion (CJD) case, analyzing the behavior of option prices as a function of the second-order parameter and the resulting pricing intervals. Using real data, we perform a dynamic delta hedging strategy, illustrating how risk managers can determine an interval of value-at-risks (VaR) and expected shortfalls (ES), granting flexibility in pricing based on additional information. We compare our pricing interval to other jump-diffusion models, showing its comprehensive risk factor incorporation. The second part extends the second-order Esscher pricing to more complex models, including the Merton jump-diffusion, Kou's Double Exponential jump-diffusion, and the Variance Gamma model. We derive option prices using the fast Fourier transform (FFT) method and provide practical formulas for European call and put options under these models. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.21649 |
| By: | Alex Li |
| Abstract: | Predicting volatility in financial markets, including stocks, index ETFs, foreign exchange, and cryptocurrencies, remains a challenging task due to the inherent complexity and non-linear dynamics of these time series. In this study, I apply TimeMixer, a state-of-the-art time series forecasting model, to predict the volatility of global financial assets. TimeMixer utilizes a multiscale-mixing approach that effectively captures both short-term and long-term temporal patterns by analyzing data across different scales. My empirical results reveal that while TimeMixer performs exceptionally well in short-term volatility forecasting, its accuracy diminishes for longer-term predictions, particularly in highly volatile markets. These findings highlight TimeMixer's strength in capturing short-term volatility, making it highly suitable for practical applications in financial risk management, where precise short-term forecasts are critical. However, the model's limitations in long-term forecasting point to potential areas for further refinement. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.09062 |
| By: | Tomas Espana; Victor Le Coz; Matteo Smerlak |
| Abstract: | Markowitz's optimal portfolio relies on the accurate estimation of correlations between asset returns, a difficult problem when the number of observations is not much larger than the number of assets. Using powerful results from random matrix theory, several schemes have been developed to "clean" the eigenvalues of empirical correlation matrices. By contrast, the (in practice equally important) problem of correctly estimating the eigenvectors of the correlation matrix has received comparatively little attention. Here we discuss a class of correlation estimators generalizing Kendall's rank correlation coefficient which improve the estimation of both eigenvalues and eigenvectors in data-poor regimes. Using both synthetic and real financial data, we show that these generalized correlation coefficients yield Markowitz portfolios with lower out-of-sample risk than those obtained with rotationally invariant estimators. Central to these results is a property shared by all Kendall-like estimators but not with classical correlation coefficients: zero eigenvalues only appear when the number of assets becomes proportional to the square of the number of data points. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.17366 |
| By: | Barr, Nicholas |
| Abstract: | A response to pressures on pension finance caused by population ageing and economic turbulence has been a substantial move from traditional defined-benefit plans in which, at least in principle, all risk falls on the contributions side, to defined-contribution plans in which risk during accumulation all falls on the benefits side. This paper argues that both designs are ‘corner solutions’ and hence generally suboptimal, and goes on to set out a range of designs that offer different ways of sharing risk among workers, employers, future pensioners and current pensioners. |
| Keywords: | defined contribution; defined benefit; risk sharing; population ageing |
| JEL: | J1 |
| Date: | 2024–10–01 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:125669 |
| By: | A. H Nzokem |
| Abstract: | The paper proposes and implements a methodology to fit a seven-parameter Generalized Tempered Stable (GTS) distribution to financial data. The nonexistence of the mathematical expression of the GTS probability density function makes the maximum likelihood estimation (MLE) inadequate for providing parameter estimations. Based on the function characteristic and the fractional Fourier transform (FRFT), We provide a comprehensive approach to circumvent the problem and yield a good parameter estimation of the GTS probability. The methodology was applied to fit two heavily tailed data (Bitcoin and Ethereum returns) and two peaked data (S&P 500 and SPY ETF returns). For each index, the estimation results show that the six parameter estimations are statistically significant except for the local parameter ($\mu$). The goodness of fit was assessed through Kolmogorov-Smirnov, Anderson-Darling, and Pearson's chi-squared statistics. While the two-parameter geometric Brownian motion (GBM) hypothesis is always rejected, the Generalized Tempered Sable (GTS) distribution fits significantly with a very high P_value; and outperforms the Kobol, CGMY, and Bilateral Gamma distributions. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.19751 |