scholarly journals NONPARAMETRIC ESTIMATION OF CONDITIONAL VALUE-AT-RISK AND EXPECTED SHORTFALL BASED ON EXTREME VALUE THEORY

2016 ◽  
Vol 34 (1) ◽  
pp. 23-67 ◽  
Author(s):  
Carlos Martins-Filho ◽  
Feng Yao ◽  
Maximo Torero
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Monte Carlo Study ◽  
Value Theory ◽  
Expected Shortfall ◽  
Scale Model ◽  
Conditional Value At Risk ◽  
Strong Mixing ◽  
Finite Sample ◽  
Nonparametric Estimators

We propose nonparametric estimators for conditional value-at-risk (CVaR) and conditional expected shortfall (CES) associated with conditional distributions of a series of returns on a financial asset. The return series and the conditioning covariates, which may include lagged returns and other exogenous variables, are assumed to be strong mixing and follow a nonparametric conditional location-scale model. First stage nonparametric estimators for location and scale are combined with a generalized Pareto approximation for distribution tails proposed by Pickands (1975, Annals of Statistics 3, 119–131) to give final estimators for CVaR and CES. We provide consistency and asymptotic normality of the proposed estimators under suitable normalization. We also present the results of a Monte Carlo study that sheds light on their finite sample performance. Empirical viability of the model and estimators is investigated through a backtesting exercise using returns on future contracts for five agricultural commodities.

scholarly journals Backtesting Marginal Expected Shortfall and Related Systemic Risk Measures

2020 ◽  
Author(s):  
Denisa Banulescu-Radu ◽  
Christophe Hurlin ◽  
Jérémy Leymarie ◽  
Olivier Scaillet
Keyword(s):  
At Risk ◽  
Financial Institutions ◽  
Systemic Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Expected Shortfall ◽  
Conditional Value At Risk ◽  
Finite Sample ◽  
Marginal Expected Shortfall

This paper proposes an original approach for backtesting systemic risk measures. This backtesting approach makes it possible to assess the systemic risk measure forecasts used to identify the financial institutions that contribute the most to the overall risk in the financial system. Our procedure is based on simple tests similar to those generally used to backtest the standard market risk measures such as value-at-risk or expected shortfall. We introduce a concept of violation associated with the marginal expected shortfall (MES), and we define unconditional coverage and independence tests for these violations. We can generalize these tests to any MES-based systemic risk measures such as the systemic expected shortfall (SES), the systemic risk measure (SRISK), or the delta conditional value-at-risk ([Formula: see text]CoVaR). We study their asymptotic properties in the presence of estimation risk and investigate their finite sample performance via Monte Carlo simulations. An empirical application to a panel of U.S. financial institutions is conducted to assess the validity of MES, SRISK, and [Formula: see text]CoVaR forecasts issued from a bivariate GARCH model with a dynamic conditional correlation structure. Our results show that this model provides valid forecasts for MES and SRISK when considering a medium-term horizon. Finally, we propose an early warning system indicator for future systemic crises deduced from these backtests. Our indicator quantifies how much is the measurement error issued by a systemic risk forecast at a given point in time which can serve for the early detection of global market reversals. This paper was accepted by Kay Giesecke, finance.

Single-Index Expectile Models for Estimating Conditional Value at Risk and Expected Shortfall*

2020 ◽  
Author(s):  
Rong Jiang ◽  
Xueping Hu ◽  
Keming Yu
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Real Data ◽  
Expected Shortfall ◽  
Conditional Value At Risk ◽  
Finite Sample ◽  
Single Index ◽  
Index Model ◽  
Index Approach ◽  
The One

Abstract This article develops a single-index approach for modeling the expectile-based value at risk (EVaR). EVaR has an advantage over the conventional quantile-based VaR (QVaR) of being more sensitive to the magnitude of extreme losses. EVaR can also be used for calculating QVaR and expected shortfall (ES) by exploiting the one-to-one mapping from expectiles to quantiles and the relationship between VaR and ES. We develop an asymmetric least squares technique for estimating the unknown regression parameter and link function in a single-index model, and establish the asymptotic normality of the resultant estimators. Simulation studies and real data applications are conducted to illustrate the finite sample performance of the proposed methods.

A COMPARISON OF SOME UNIVARIATE MODELS FOR VALUE-AT-RISK AND EXPECTED SHORTFALL

2007 ◽  
Vol 10 (06) ◽  
pp. 1043-1075 ◽  
Author(s):  
CARLO MARINELLI ◽  
STEFANO D'ADDONA ◽  
SVETLOZAR T. RACHEV
Keyword(s):  
At Risk ◽  
Extreme Value Theory ◽  
Value At Risk ◽  
Value Theory ◽  
Extreme Value ◽  
Expected Shortfall ◽  
Stable Laws ◽  
Peaks Over Threshold ◽  
Threshold Method ◽  
Block Maxima

We compare in a backtesting study the performance of univariate models for Value-at-Risk (VaR) and expected shortfall based on stable laws and on extreme value theory (EVT). Analyzing these different approaches, we test whether the sum–stability assumption or the max–stability assumption, that respectively imply α–stable laws and Generalized Extreme Value (GEV) distributions, is more suitable for risk management based on VaR and expected shortfall. Our numerical results indicate that α–stable models tend to outperform pure EVT-based methods (especially those obtained by the so-called block maxima method) in the estimation of Value-at-Risk, while a peaks-over-threshold method turns out to be preferable for the estimation of expected shortfall. We also find empirical evidence that some simple semiparametric EVT-based methods perform well in the estimation of VaR.

USING EXTREME VALUE THEORY TO EVALUATE CONDITIONAL VAR FOR RISK MANAGEMENT IN ELECTRICITY MARKETS

2016 ◽  
Vol 78 (10) ◽  
Author(s):  
M. T. Askari ◽  
Z. Afzalipor ◽  
A. Amoozadeh
Keyword(s):  
At Risk ◽  
Electricity Markets ◽  
Extreme Value Theory ◽  
Value At Risk ◽  
Risk Model ◽  
Test System ◽  
Value Theory ◽  
Extreme Value ◽  
Conditional Value At Risk ◽  
Bidding Strategy

In a deregulated power market, generation companies attempt to maximize their profits and minimize their risks. This paper proposes a risk model for bidding strategy of generation companies based on EVT-CVaR method. Extreme Value Theory can overcome shortcomings of traditional methods in computing financial risk based on value-at-risk and conditional value-at-risk method. Also, generalized Pareto distribution is suggested to model tail of an unknown distribution and parameters of the GPD are estimated by likelihood moment method. Numerical results for risk assessment using the proposed approach are presented for IEEE 30-bus test system. According to the findings, this method can be used as a robust technique to calculate the risk for bidding strategy of generation companies.

Essays on measuring systemic risk

2019 ◽  
Author(s):  
Χριστόφορος Κωνσταντάτος
Keyword(s):  
At Risk ◽  
Systemic Risk ◽  
Value At Risk ◽  
Expected Shortfall ◽  
Conditional Value At Risk ◽  
Lehman Brothers ◽  
Marginal Expected Shortfall

Η παρούσα διατριβή ερευνά διάφορα μέτρα συστημικού κινδύνου, αναγνωρίζοντας – προσδιορίζοντάς τα συστημικά τραπεζικά ιδρύματα της Ευρωπαϊκής Νομισματικής Ένωσής (Ευρωζώνης). Επίσης εξετάζει τις ακραίες κινήσεις της τιμής των μετοχών των τραπεζικών ιδρυμάτων της Ευρωζώνης. Η παρούσα αποτελείται από τρία κεφάλαια εστιάζοντας στα τραπεζικά ιδρύματα των Ηνωμένων Πολιτειών και της Ευρωζώνης. Το Κεφάλαιο 2 συγκρίνει τα συστημικά μέτρα τα επονομαζόμενα (i) Delta Conditional Value at Risk, (ii) Marginal Expected Shortfall και (iii) Systemic RISK. Τα αποτελέσματα καταδεικνύουν ότι τα τραπεζικά ιδρύματα της ζώνης του ευρώ συνεισφέρουν τον υψηλότερο κίνδυνο στο χρηματοπιστωτικό σύστημα (συμβολή στον συστημικό κίνδυνο). Επιπροσθέτως είναι και τα πιο ευάλωτα τραπεζικά ιδρύματα σε περίπτωση ύφεσης. Τα τραπεζικά ιδρύματα με τις υψηλότερες αναμενόμενες απώλειες σε περίπτωση ακραίων γεγονότων είναι κυρίως τα τραπεζικά ιδρύματα των ΗΠΑ. Το Κεφάλαιο 3 διερευνά τον συστημικό κίνδυνο που διαχέεται μεταξύ των τραπεζικών ιδρυμάτων των Ηνωμένων Πολιτειών και της Ευρωζώνης κάνοντας χρήση του μέτρου Conditional Value at Risk. Τα αποτελέσματα καταδεικνύουν ότι δύο από τα μεγαλύτερα γερμανικά τραπεζικά ιδρύματα συγκαταλέγονται στα πιο ευάλωτα τραπεζικά ιδρύματα της ζώνης του ευρώ στον συστημικό κινδύνου που προέρχονται από τα αντίστοιχα αμερικανικά τραπεζικά ιδρύματα, επίσης παρατηρείτε υψηλός βαθμός έκθεσης των αμερικανικών τραπεζικών ιδρυμάτων στα τρία μεγαλύτερα γαλλικά τραπεζικά ιδρύματα. Το Κεφάλαιο 4 ερευνά τη δομή εξάρτησης των ουρών των είκοσι τεσσάρων μεγαλύτερων τραπεζών στη ζώνη του ευρώ πριν και μετά την κατάρρευση της Lehman Brothers. Τα αποτελέσματα καταδεικνύουν ότι στη μετά κρίση περίοδο το επίπεδο της ακραίας συσχέτισης αυξάνεται σημαντικά στα τραπεζικά ιδρύματα του πυρήνα του ευρώ. Επίσης, μεταξύ των χωρών που λαμβάνουν δέσμη μέτρων διάσωσης τα μεγαλύτερα τραπεζικά ιδρύματα σε Ελλάδα και Ιρλανδία παρατηρείτε ότι μείωσαν την ακραία συσχέτιση με τα αντίστοιχα τραπεζικά ιδρύματα της ζώνης του ευρώ.

scholarly journals Computing value-at-risk and expected shortfall in operational risk

2021 ◽  
Author(s):  
Desire Issiaka Bakassa-Traore
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Operational Risk ◽  
Expected Shortfall ◽  
Conditional Value At Risk ◽  
Basel Committee ◽  
Loss Distribution Approach ◽  
Capital Charge ◽  
Heavy Tailed

Operational Risk has become more popular in the past fifteen years. The Basel committee realized its importance and banks have to allocate more capital charge, yet this is still not enough. With these new rules, banks have put in place new procedures to compute their risk measures and allocate enough capital charge to avoid bankruptcy. The Basel committee under Basel II has proposed different approaches to compute risk measures for Operational Risk, namely the Basic Indicator Approach, the Advanced Measurement Approach and the Standardized Approach. In our research, we will study the case of Loss Distribution Approach, which has been discussed before, and will contribute to the field by using a heavy-tailed distributed severity: g-and-h distributed. Then, we will analyze and test some methods to compute the value-at-risk( VaR) and conditional value-at-risk or expected shortfall (CVaR).

scholarly journals Extreme Risk, Value-At-Risk And Expected Shortfall In The Gold Market

2014 ◽  
Vol 14 (1) ◽  
pp. 107
Author(s):  
Knowledge Chinhamu ◽  
Chun-Kai Huang ◽  
Chun-Sung Huang ◽  
Delson Chikobvu
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Effective Means ◽  
Value Theory ◽  
Expected Shortfall ◽  
Extreme Stress ◽  
Extreme Risk ◽  
Gold Market ◽  
The Impact

Extreme value theory (EVT) has been widely applied in fields such as hydrology and insurance. It is a tool used to reflect on probabilities associated with extreme, and thus rare, events. EVT is useful in modeling the impact of crashes or situations of extreme stress on investor portfolios. It describes the behavior of maxima or minima in a time series, i.e., tails of a distribution. In this paper, we propose the use of generalised Pareto distribution (GPD) to model extreme returns in the gold market. This method provides effective means of estimating tail risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES). This is confirmed by various backtesting procedures. In particular, we utilize the Kupiec unconditional coverage test and the Christoffersen conditional coverage test for VaR backtesting, while the Bootstrap test is used for ES backtesting. The results indicate that GPD is superior to the traditional Gaussian and Students t models for VaR and ES estimations.

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