Questions tagged [value-at-risk]

Value-at-Risk is a family of measures used to help the owner of a position to assess its "worst case value".

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VaR model Unconditional Coverage Tests: Is this extension of Kupiec POF test correct?

Background: Kupiec P. in 1995, published paper "Techniques for Verifying the Accuracy of Risk Management Models" on Journal of Derivatives, v3, P73-84, it's a Unconditional Coverage Tests designe for ...
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Stress Testing for VaR

I am trying to perform stress testing for VaR and have taken into consideration two methods:- 1. Sensitivity analysis 2. Historical scenario analysis. According to the Derivatives Policy group we ...
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772 views

VaR backtesting with overlapping time intervals

Of course the issue here is dependence: can it be removed or accounted for (in independence tests too, which of course would be troublesome)? There's a lot of literature on regression in this setting, ...
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Sharpe ratio with CVaR for denominator and different investor utility functions

I would like to model different type of investors, hence I need to find some kind of utility functions to optimize. Apart from very abstract exponential utility function, I couldn't find any proper ...
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VAR FPCA analysis paper replication

I've been trying to replicate the following publication: CONSISTENT FUNCTIONAL PCA FOR FINANCIAL TIME-SERIES, Sebastian Jaimungal, Eddie K. H. Ng, 2007 but I havent been able to get the same results ...
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Joint Distribution of Correlated Variables with Markov Switching

I am modeling a portfolio of correlated assets whose lack of liquidity can be reasonably described by a Markov-switching model. That is, not only is movement size among assets correlated, but so is ...
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Implied volatility surface modelling in filtered historical simulation

What is the best way to model implied volatility surface in filtered historical simulation (other than keeping it constant)? Is it appropriate to apply GARCH-like model to every point on the surface? ...
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Expected Shortfall for ARMA-GARCH Model

I need to find an analytical solution for the 99% confidence expected shortfall (CVaR) for a long position of 100 dollars at time $t$ for an asset with returns modeled by an ARMA(1,1)-GARCH(1,1) model ...
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Extreme Value Theory for Value-at-Risk: Advantage versus historical simulation?

I started researching this topic and it is well covered in the literature. My understanding is that it uses a historical time series of returns of a given set of stocks and represent such ...
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Modelling approaches for interest rate risk in the banking book (IRRBB)

I am having a hard time researching papers that deal with the measurement of market risk in the banking book. The trading book as I see it is similar to asset management and as the name says the ...
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Parametric VaR of a portfolio of a stock and an option on that stock

I understand how to calculate the parametric VaR of a stock and an option separately. But I don't understand how one can calculate the VaR of a portfolio of a stock and an option on that stock using ...
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'GARCH - extreme value theory - copula' approach to estimate risk measures in R

I'm reading about this approach of using GARCH-EVT-copula methodology to separate univariate and joint estimation and then estimate for example VaR and ES. I wanted to try something similar, but my ...
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Intraday Value at Risk approximations

We use full valuation of derivatives portfolios using scenarios from historical data. For simple contracts, this is relatively fast. For contracts requiring monte carlo simulation, this becomes ...
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Do you roll back the maturities and schedules when backtesting VaR for portfolios of bonds, options or future contracts?

I want to backtest VaR models which are applied to portfolios of products which have maturities (options and futures) and even schedules (bonds). I have a question which never came up when backtesting ...
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Martingale corrections to historical Value at Risk?

I am looking for a bit of advice. I have recently used to a new firm, which uses Value at Risk in a manner that is unfamiliar from previous places I have worked that I find less than ideal. Previous, ...
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Estimator for Conditional value at risk (average value at risk)

I am following a book: Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization by Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi I'm learning about average value at risk. ...
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Methods for calculating Expected shortfall

Let B1, B2 be two defaultable zero-coupon bonds maturing in 1 year, each with a face value of $100. Assume: each bond is priced at 90 dollars each bond has a 4% probability to default within 1 year ...
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VaR of ARCH model

Consider the following: $r_t = \theta r_{t-1}+u_t$ $u_t=\sigma_t\epsilon_t$ $\sigma^2_t=\omega+\alpha u^2_{t-1}$ $-1<\theta<1,\omega>0,\alpha \in(0,1)$ What is the 99% 2-day VaR of a ...
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Monte Carlo VAR with differente asset classes

I have found a very useful post regarding the use of Monte Carlo simulaton to obtain portfolio Value at risk, based on Cholesky decomposition, random variates, etc. This post I'm talking about is: Is ...
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RiskMetrics VAR calculations and conditional distribution of sum of log returns

According to Tsay's book in Chapter 7, for the Risk Metrics model: A nice property of such a special random-walk IGARCH model is that the conditional distribution of a multiperiod return is ...
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Pricing default risk in cryptos

I'm looking to figure out how to price "insurance" against a counter-party defaulting in an OTC cryptocurrency transaction. I think the first measure would be to calculate VaR? I'm planning on ...
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VaR decomposition of non-normal portfolio by g-and-h distribution

According to Doowoo Nam (2013), VaR of non-normal portfolio returns approximated by g-and-h distribution can be decomposed pretty much in the same way as the VaR of a portfolio with normal returns. ...
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Problems in computing VaR with GARCH-GPD-copula approach

I use a time-varying Gaussian copula (with GARCH-filtered standardized residuals modeled semiparametrically with Gaussian kernel interior and GPD tails, i.e. generalized pareto distributed) to ...
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How to fit a VAR + GARCH in R

I should create a VAR model with Garch error in R but i don't know how to do it and which package to use. The Vector Autoregressive model (or VECM) should also have covariates in it. Then I should ...
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Value-at-Risk Calculation with respect to the Capital Requirements

I want to calculate the Value-at-Risk at date $t$ in such a way that I minimize the capital requirements given as \begin{align} \text{CR}_{\,t+1\,:\,t+250} = \sum_{h=0}^{249}\max\left( -(3+k_{t})\...
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Testing Statistical Significance of Various Portfolio Simulations

I'm trying to determine which of my portfolio simulations/backtests if any are good enough to put some money into. I outline an approach below and I'm interested in knowing: What problems are there ...
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Beta distribution - Holding period

Let's say I have a risk factor that is defined between [0,1], such as recovery rates. Assuming I have daily data, I can estimate the "daily VaR", i.e. the tails over 1 day period, since the data is ...
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Fixed Income Var calculation

I'm trying to calculate var for a portfolio of fixed income securities. I initially want to just calculate undiversified VaR for each instrument. I'm doing the following for each instrument Take ...
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Comparing Backtests of Value-at-Risk and Expected Shortfall

My goal is to test if ES (CVaR) empirically is a better risk measure than VaR for a set of given variables (assumed underlying distribution, confidence level, sample size) for different asset classes. ...
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Energy Risk Quant--Any discussion boards for energy related quant topics?

Any discussion boards for energy related quant topics? Like VaR in energy portfolio, and pipeline option pricing.. just want to know where is the best discussion board for such energy specific topics. ...
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MonteCarlo Value At Risk for futures portfolio

I wanted to ask, suppose I have a portfolio of futures of gasoline and other oil products eg ULSD (Ultra Low Sulphur Diesel), WTI (West Texas Intermediate) for different months. I want to compute the ...
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How can I estimate value-at-risk of a long/short portfolio without making simplifying assumptions?

I have had a couple of long-standing questions about the mathematics behind a simple "vanilla" parametric VaR calculation and I'm hoping someone could clear up my confusion. Most likely I am ...
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How to calculate the gaussian VaR for a portfolio with 3 corporate bonds and 1 IRS payer?

As data I have the daily change of zero coupon spot rates for some vertex (0.25, 0.5, 1, 2..) and the daily change of z-spread for corporate bonds, also by vertex
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Backtesting Strategy in R for simple empirical value at risk

I am new in backtesting methodology and I want for start to keep things simple.Say that I have the following data: ...
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EWMA initial margin model risk

Let's say that someone wants to estimate the initial margin model (very simple one) with the exponential weighted moving average approach.For margin period of risk 2 days. ...
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How is a return-adjusted nearby created?

I am reading Value-at-Risk Second Edition – by Glyn A. Holton https://www.value-at-risk.net/futures-nearbys-and-distortions/ From 6.6.1 "The standard means of obtaining continual time series from ...
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Interpretation of Value at Risk

Let $X$ be a Loss random variable (Positive values of X represents Losses) and let $p \in (0,1)$. I know that the Value at Risk at level $p$ of $X$ is defined as: $$VaR_p(X) = inf{\{x \in \mathbb{R} : ...
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Value at risk, risk-neutral vs real-world probability measures

Does anyone know if there is any link between the Value at Risk of risk-neutral distribution and of the real-world distributions of asset rate of returns?
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Longer / Shorter period loss

I am struggling on I think a quite simple issue. Let's take a portfolio of 100 loans. If we assume they are independent, each loan’s default is a Bernoulli with parameter $p=0.01$ over a certain time ...
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Difference between Vasicek and Gordy models

I'm trying to understand what Gordy [1] added to Vasicek [2] model (the core of the IRB formula of Basel Accords). Is it correct to say the Vasicek shows that the portfolio loss conditional on $Y$ ...
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Advantage of copula over estimation based on historical data

It seems to me hard to intuitively understand the concept of copulas and their advantages. For example, why would it be better to estimate value at risk of portfolio by modelling its asset returns ...
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Lognormal asymmetry implication on Value at Risk

To examine the Value at Risk implications for a portfolio consisting of a spot and futures time series I have generated a 1-day monte carlo simulation. I was long in the spot and short in the future (...
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ES using historic simulation

Why is the data obtained from 91-100 days all eliminated from the calculation of the 1-day 95% ES? My interpretation is because the first day to calculate the 95% ES should be the 90th day? But I can'...
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Kupiec Test Backtesting VaR

I am currently analyzing the Kupiec test used for backtesting $VaR$. Suppose that I backtest a $VaR$ system for $n$ days (for example 250), with a confidence interval of $1-\alpha$ (for example a $1-\...
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Can value at risk be computed using downside deviation?

Value at risk is usually computed with a regular standard deviation. But can it be computed using downside deviation (semi-deviation) instead? Particularly if I want to consider a Var that includes ...
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Manually calculating and backtesting VaR and CVaR from DCC-GARCH R

I estimated a GARCH fit to the log returns of three series (CAC 40, a french real estate index and french T10 bond yield series) using rugarch. I then manually ...
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How to measure specific risk charge?

IFRS requires banks to compute different risks including market risk based on Basel iii. To do so, the capital requirement is defined as follows: $$max(VaR_{t−1},m_c × VaR_{avg}) + SRC$$ $SRC$ is ...
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Opposite of Value-at-Risk. Criteria for Optimization

I'm trying to optimize portfolio of undervalued and portfolio of overvalued stocks. I have simulated scenarios of stock returns, and based on them I would like to find optimal weights. One criteria is ...
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Risk Measure-identication

Let X be a variable with existing moment generating function $M_x(z)=E[e^{zX}]$. Define the following risk measure: $\rho_{\alpha}(X)=inf_{z>0}(z^{-1}ln(\frac{M_x(z)}{1-\alpha}))$ Does anyone know ...
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Does it make sense to subtract VaR from spot shocks?

I have a model to compute the Event Risk (in dollars) from a shock to the spot price of an asset. I also have the 10-day VaR PnL for the same assets returns. These two numbers are then aggregated to ...