scholarly journals Interval Estimation of Value-at-Risk Based on Nonparametric Models

Econometrics ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 47 ◽  
Author(s):  
Hussein Khraibani ◽  
Bilal Nehme ◽  
Olivier Strauss
Keyword(s):  
At Risk ◽  
Stock Returns ◽  
Value At Risk ◽  
Convex Sets ◽  
Convex Set ◽  
Interval Estimation ◽  
Kernel Estimation ◽  
Cumulative Distribution ◽  
Computation Method ◽  
Interval Valued

Value-at-Risk (VaR) has become the most important benchmark for measuring risk in portfolios of different types of financial instruments. However, as reported by many authors, estimating VaR is subject to a high level of uncertainty. One of the sources of uncertainty stems from the dependence of the VaR estimation on the choice of the computation method. As we show in our experiment, the lower the number of samples, the higher this dependence. In this paper, we propose a new nonparametric approach called maxitive kernel estimation of the VaR. This estimation is based on a coherent extension of the kernel-based estimation of the cumulative distribution function to convex sets of kernel. We thus obtain a convex set of VaR estimates gathering all the conventional estimates based on a kernel belonging to the above considered convex set. We illustrate this method in an empirical application to daily stock returns. We compare the approach we propose to other parametric and nonparametric approaches. In our experiment, we show that the interval-valued estimate of the VaR we obtain is likely to lead to more careful decision, i.e., decisions that cannot be biased by an arbitrary choice of the computation method. In fact, the imprecision of the obtained interval-valued estimate is likely to be representative of the uncertainty in VaR estimate.

scholarly journals Optimisation of Time-Varying Asset Pricing Models with Penetration of Value at Risk and Expected Shortfall

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 394
Author(s):  
Adeel Nasir ◽  
Kanwal Iqbal Khan ◽  
Mário Nuno Mata ◽  
Pedro Neves Mata ◽  
Jéssica Nunes Martins
Keyword(s):  
At Risk ◽  
Asset Pricing ◽  
Stock Returns ◽  
Value At Risk ◽  
Expected Shortfall ◽  
Time Varying ◽  
Pricing Models ◽  
Asset Pricing Model ◽  
Asset Pricing Models ◽  
Market Beta

This study aims to apply value at risk (VaR) and expected shortfall (ES) as time-varying systematic and idiosyncratic risk factors to address the downside risk anomaly of various asset pricing models currently existing in the Pakistan stock exchange. The study analyses the significance of high minus low VaR and ES portfolios as a systematic risk factor in one factor, three-factor, and five-factor asset pricing model. Furthermore, the study introduced the six-factor model, deploying VaR and ES as the idiosyncratic risk factor. The theoretical and empirical alteration of traditional asset pricing models is the study’s contributions. This study reported a strong positive relationship of traditional market beta, value at risk, and expected shortfall. Market beta pertains its superiority in estimating the time-varying stock returns. Furthermore, value at risk and expected shortfall strengthen the effects of traditional beta impact on stock returns, signifying the proposed six-factor asset pricing model. Investment and profitability factors are redundant in conventional asset pricing models.

scholarly journals How Risky Are the Options? A Comparison with the Underlying Stock Using MaxVaR as a Risk Measure

Risks ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 76
Author(s):  
Saswat Patra ◽  
Malay Bhattacharyya
Keyword(s):  
At Risk ◽  
Stock Returns ◽  
Value At Risk ◽  
Risk Measure ◽  
Stock Index ◽  
Risk Exposure ◽  
Index Options ◽  
Significance Level ◽  
Significance Levels ◽  
Better Than

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 a more stringent risk measure as it assesses the risk during the risk horizon. For a 30-day maturity option, we find that MaxVaR can be 40% higher than VaR at a 5% significance level. It highlights the importance of MaxVaR as a risk measure and shows that the risk is vastly underestimated when VaR is used as the measure for risk. The sensitivity of MaxVaR with respect to option characteristics like moneyness, time to maturity and risk horizons at different significance levels are observed. Further, interestingly enough we find that the MaxVar to VaR ratio is higher for stocks than the options and we can surmise that stock returns are more volatile than options. For robustness, the study is carried out under different distributional assumptions on residuals and for different stock index options.

scholarly journals Effects of asset frequency components on value-at-risk in emerging and developed markets

2020 ◽  
Vol 40 (1) ◽  
pp. 145
Author(s):  
Milton Biage ◽  
Pierre Joseph Nelcide
Keyword(s):  
At Risk ◽  
Stock Returns ◽  
Value At Risk ◽  
Financial Assets ◽  
Back Testing ◽  
Window Technique ◽  
Rolling Window ◽  
Frequency Components ◽  
Daily Stock Returns ◽  
Daily Returns

<p>Value-at-Risk was estimated using the technique of wavelet decomposition with goal to analyze the frequency components' impacts on variances of daily stock returns, and on  forecasts. Daily returns of twenty-one shares of the Ibovespa and daily returns of twenty-two shares of the DJIA were used. The  model was applied to the reconstructed returns to model and establish the prediction of conditional variance, applying the rolling window technique. The Value-at-Risk was then estimated, and the results showed that the DJIA shares showed more efficient market behavior than those of Ibovespa. The differences in behavior induces to affirm that VaRs, used in the analysis of financial assets from different markets with different governance premises, should be estimated by series of returns reconstructed by aggregations of components of different frequencies. A set of back-testing was applied to confront the estimated , which demonstrated that the estimation of  models are consistent.</p>

scholarly journals Dynamic value at risk estimation for BELEX15

2011 ◽  
Vol 8 (1) ◽  
Author(s):  
Emilija Nikolić-Đorić ◽  
Dragan Đorić
Keyword(s):  
At Risk ◽  
Stock Returns ◽  
Long Memory ◽  
Value At Risk ◽  
Stock Exchange ◽  
Risk Estimation ◽  
Value Theory ◽  
Garch Models ◽  
Measurement Models ◽  
Standardized Residuals

This paper uses RiskMetrics, GARCH and IGARCH models to calculate daily VaR for Belgrade Stock Exchange index BELEX15 returns based on the normal and Student t innovation distribution. In the case of GARCH and IGARCH models VaR values are obtained applying Extreme Value Theory on the standardized residuals. The Kupiec's LR statistics was used to test the accuracy of risk measurement models. The main conclusions are: (1) when modelling value-at-risk it is very important to have a good model for volatility of stock returns; (2) both stationary and integrated GARCH models outperform RiskMetrics in estimating VaR; (3) although long memory volatility is present in the BELEX15 index, IGARCH models cannot outperform GARCH type models in VaR evaluations for this index.

scholarly journals Local Likelihood Density Estimation and Value-at-Risk

2010 ◽  
Vol 2010 ◽  
pp. 1-26 ◽  
Author(s):  
Christian Gourieroux ◽  
Joann Jasiak
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Stock Exchange ◽  
Local Approximation ◽  
Conditional Density ◽  
Conditional Value At Risk ◽  
Computation Method ◽  
Toronto Stock Exchange ◽  
Historical Simulation ◽  
Portfolio Returns

This paper presents a new nonparametric method for computing the conditional Value-at-Risk, based on a local approximation of the conditional density function in a neighborhood of a predetermined extreme value for univariate and multivariate series of portfolio returns. For illustration, the method is applied to intraday VaR estimation on portfolios of two stocks traded on the Toronto Stock Exchange. The performance of the new VaR computation method is compared to the historical simulation, variance-covariance, and J. P. Morgan methods.

scholarly journals APPLICATION OF K-RECORDS IN THE INTERVAL ESTIMATION OF THE VALUE AT RISK MEASURE (VAR)

2018 ◽  
Vol 17 (4) ◽  
pp. 41-50
Author(s):  
Marcin Dudziński ◽  
Ewa Wasilewska
Keyword(s):  
At Risk ◽  
Risk Management ◽  
Stock Prices ◽  
Value At Risk ◽  
Banking Sector ◽  
Risk Measure ◽  
Interval Estimation ◽  
Financial Supervision ◽  
Potential Losses

Value at Risk, or shorter – VaR, is a major tool used in the processes related to the risk management of banks and other monetary institutions, as well as in the tasks connected with financial supervision and scrutiny. The VaR measure may be interpreted as the minimum amount of equity that the company should own in order to be able to cover its potential losses. Although many methods leading to VaR estimation have been established so far, there is still no universal and faultless approach of VaR calculation. In our work, the method of VaR estimation consisting in determination of confidence intervals for VaR in terms of the so-called k-records has been described and used. The proposed approach is illustrated with use of an example from banking sector, concerning the stock prices of PKO BP Bank in the period between 13.01.2017 and 22.03.2018.

scholarly journals An extended TDM method under probabilistic interval-valued hesitant fuzzy environment for stock selection

PLoS ONE ◽  
2021 ◽  
Vol 16 (5) ◽  
pp. e0252115
Author(s):  
Qasim Noor ◽  
Tabasam Rashid ◽  
Syed Muhammad Husnine
Keyword(s):  
Decision Making ◽  
At Risk ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Value At Risk ◽  
Group Decision ◽  
Hesitant Fuzzy Set ◽  
Stock Selection ◽  
Decision Making Model ◽  
Interval Valued

Generally, in real decision-making, all the pieces of information are used to find the optimal alternatives. However, in many cases, the decision-makers (DMs) only want “how good/bad a thing can become.” One possibility is to classify the alternatives based on minimum (tail) information instead of using all the data to select the optimal options. By considering the opportunity, we first introduce the value at risk (VaR), which is used in the financial field, and the probabilistic interval-valued hesitant fuzzy set (PIVHFS), which is the generalization of the probabilistic hesitant fuzzy set (PHFS). Second, deemed value at risk (DVaR) and reckoned value at risk (RVaR) are proposed to measure the tail information under the probabilistic interval-valued hesitant fuzzy (PIVHF) environment. We proved that RVaR is more suitable than DVaR to differentiate the PIVHFEs with example. After that, a novel complete group decision-making model with PIVHFS is put forward. This study aims to determine the most appropriate alternative using only tail information under the PIVHF environment. Finally, the proposed methods’ practicality and effectiveness are tested using a stock selection example by selecting the ideal stock for four recently enrolled stocks in China. By using the novel group decision-making model under the environment of PIVHFS, we see that the best stock is E4 when the distributors focus on the criteria against 10% certainty degree and E1 is the best against the degree of 20%, 30%, 40% and 50% using the DVaR method. On the other hand when RVaR method is used then the best alternative is E4 and the worst is E2 against the different certainty degrees. Furthermore, a comparative analysis with the existing process is presented under the PHF environment to illustrate the effectiveness of the presented approaches.

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