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Questions tagged [value-at-risk]

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Value At Risk Rigorous Definition

Reading a paper about VaR and don't understand what $a'$ is. The link to the paper is here: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.878.8823&rep=rep1&type=pdf. The relevant ...
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115 views

Delta-Gamma VaR approximation and cross-gamma

Suppose we have a portfolio of say two vanilla options (e.g. on two index futures). One option A with underlying X and a second option B with underlying Y. I'm trying to calculate the delta-gamma ...
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69 views

Why is infimum chosen to define value at risk as opposed to the minimum?

I believe that the VaR is defined as the infimum of the generalized inverse of the CDF of the loss function (something like that, please correct accordingly): $$\text{VaR}(\alpha)=\inf\{x: F_L(x)\geq \...
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64 views

Backtesting Value-At-Risk (20-days)

I calculate the 20-day returns of (rolling window) of historical stock prices of 2 years. Are there any problems (like autocorrelation) when I want to backtest the VaR (Value-at-Risk) model?
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46 views

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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46 views

Value at Risk calculation using univariate Markov switching multifractal

So I'm studying different ways for the Value at Risk calculation. Currently my attempt is in using the univariate Markov-Switching Multifractal framework. I've already estimated the $\hat{\sigma}_{t+...
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1answer
74 views

Standard market risk platform Value-at-Risk (VaR)

if possible, could you share publicly available methodological guides/pamphlets or post links to specialised websites which give sufficient detail of the basic assumptions, algorithms and possible ...
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52 views

Covariance matrix for risk factors of a FX Forward contract

Does it make sense to calculate log-returns of interest rates from a zero curve? Context: I'm trying to build a variance-covariance matrix for the risk factors of a USDBRL FX Forward maturing in 1 ...
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87 views

Estimating VaR of bond due to changes in the US yield curve

I am attempting estimate the 99% 10-day VaR of an investment grade bond due to changes in the US yield curve. The data provided is the daily prices of the bond over time. In addition I have the Daily ...
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1answer
54 views

Is scaling the standard deviations in the VaR formula (parametric) equivalent to scaling the VaR figure at the end?

I have come across people calculating parametric VaR who scaled the standard deviations by say square root of 10 to scale up to a 10 day horizon. Elsewhere I have seen textbooks suggesting that it is ...
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43 views

LogNormal VaR Formula Risk Metrics

https://web.mst.edu/~huwen/teaching_VaR_Weiqian_Li.pdf On page 6, the paper above mentions RiskMetrics would use the following VaR formula: ...
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1answer
77 views

VaR and Expected Shorfall estimations with negative shape parameter of a GPD (Extreme Value Theory )

So im trying to replicate an code from the Quantative Risk Management Book (https://github.com/qrmtutorial/qrm/blob/master/code/09_Market_Risk/09_Standard_methods_for_market_risk.R). But when i try a ...
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37 views

Implications of modeling operational risks without frequency distribution

When modeling operational risk, the Loss Distribution Approach (LDA) is widely used. Usually, we model the loss frequency distribution and the loss severity distribution and then aggregate both to ...
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1answer
82 views

Optimal Portfolios with Skewed and Heavy-Tailed Distributions

I am learning about portfolio theory and been using Markowitz. I wondered, however, if I can use distributional and asymmetric information of the returns to solve the problem. For instance, I have a ...
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34 views

VAR Monte Carlo GBM vs Selecting Normal Dist Returns

I am running a VaR calculation and have seen two ways of doing it in several places online. One simply assumes normal distribution of returns and selects n number of returns from the normal ...
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95 views

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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74 views

Calculating the Value-at-Risk when changing the confidence level

If I have a VaR estimate at a 95% confidence interval is 10, how do I calculate the approximate level of the VaR if the confidence level was raised to 99%, assuming a one-tailed normal distribution?
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62 views

VAR interpretation

I definitely struggle to understand the following interpretation of VAR (value at risk) provided by Jorion $$VAR(c)=E[X]−Q(X,c)$$ where $X$ is a random variable, $E[X]$ its expected value, $Q(X,c)$ ...
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67 views

Calculate VaR using method of historical simulation

A bank invests € $1.000.000$ in a hedge fund. The last 500 daily returns can be taken from a database. The worst 20 returns are -4.58 -2.95 -2.95 -2.93 -2.17 -2.08 -2.06 -1.98 -1.94 -...
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282 views

Do the minimum VaR and minimum ES portfolios lie on the mean-variance efficient frontier?

The mean-variance efficient frontier holds the minimum variance portfolio, but in the graph above it shows that the minimum VaR (Value-at-Risk) and minimum ES (CVaR) portfolios (expected shortfall/...
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1answer
254 views

VaR and Expected Shortfall for Geometric Brownian Motion

Given that $dS_t=\mu S_tdt+\sigma S_tdW_t$ ,a risk free rate r and defining Value at Risk and Expected Shortfall as $VaR_{t,a}=S_0e^{rt}-x$ where $x$ is the amount such that $P(S_t\leq x)=1-a$ ($a:$...
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148 views

Is there Cornish-Fisher volatility, given that there is Cornish-Fisher Value-at-Risk?

The Cornish-Fisher expansion is used to approximate the quantile $q_\alpha$ of a return distribution in order to extend the traditional Value-at-Risk (VaR) measure $$VaR = \mu(X) + \sigma(X) q_\alpha $...
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94 views

Someone help me understand why for portfolio variance or Parametric Value at Risk we have to compute the covariance matrix?

I understand that portfolio variance is computed through $w'Cw$, where w is the vector of weights, $C$ being the covariance matrix. However, what I don't get is this: why can't this portfolio variance ...
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1answer
248 views

Code (Python or R) references for operational risk models (AMA/COM)

I have to build an operational risk model and to be compliant with Basell II and III regulations I thought of using AMA (Advanced measurement approach) or COM (change of measurement). We have no ...
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1answer
52 views

A simple question about VaR estimation

"A 99% VaR using 1,000 (simulation) replications should be expected to have only 10 observations in the left tail, which is not a large number. The VaR estimate is derived from the 10th and 11th ...
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1answer
109 views

Mean-EVaR efficient frontier

Entropic Value-at-Risk (EVaR) is an alternative and more efficient risk measure than conditional Value-at-Risk (CVaR). EVaR serves as an upper bound to both VaR and CVaR. Below is a graph of the mean-...
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1answer
109 views

Does Value-at-Risk have any mathematical equivalence to copulas?

Portfolio Value-at-Risk estimated using the copula approach often just means generating artificial data sampled from a parametric copula('s joint multivariate distribution) as a model fit over the ...
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49 views

Multi-period Basel/Vasicek formula

I need to apply Basel/Vasicek formula to a 20-years horizon, both from a 20-years cumulative perspective and year-on-year basis. Please find below the formula of the Basel Capital (ie. unexpected loss)...
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35 views

Covariance of Individual Return and Portfolio Return

Hi guys, Is it possible to get the covariance between the individual return and portfolio return given the correlation matrix, volatility matrix, weights matrix and return matrix? I know how to get ...
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1answer
205 views

MonteCarlo Value at Risk for a bonds portfolio

As mentioned in the title, I am trying to calculate MC VaR for a portfolio consisting entirely of bonds. I already modeled the zero curve using Vasicek and Cox,Ingersoll & Ross models. Next steps ...
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1answer
55 views

Good ways to select best decision among N decisions, each with a profit/loss distribution? [closed]

I'm working on a problem where an asset owner (e.g., owner of a factory, power plant, etc.) can take a number of possible decisions (say 10). Each of those 10 decisions entails certain actions, but ...
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1answer
64 views

Do stationary prices need to be differenced for VaR?

I have a time series of electricity futures prices that I have shown to be stationary via the Augmented Dickey Fuller test (alpha = 0.05). Does that mean that, in calculating their individual values-...
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1answer
50 views

Can I say VAR is a prediction report?

We use Algorithmics RiskWatch where portfolios are analyzed by VaR over scenarios. Can I say that they are predictions reports? or descriptions reports?
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1answer
495 views

Correct way to calculate interest rate volatility for risk calculations

I'm trying to include interest rate derivatives in some Value at Risk calculations and am having trouble getting trustworthy values. My current approach is to look at the appropriate risk factor for ...
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1answer
157 views

Delta-normal VaR of portfolio of stock and call option

I have to calculate the 10-day 99% VaR of a portfolio that consists of a portfolio of 260 stocks of a company $K$ and that is short 500 call (European) options of the same company. I know that the ...
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1answer
299 views

Optimizing a portfolio whose risk is target expected shortfall

I want to maximize the return of a $n$-asset portfolio under known risk: $$\max_{\{w \in \mathbb{R}^{n}|w_{1}+...+w_{n}=1\}} \; \mathbb{E}\left[\sum_{i=1}^{n}w_{i}R_{i}\right]$$ under the constraint $$...
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1answer
73 views

Value at Risk under increasing function

There is an exercise I struggle to solve. I hope you can give me a hint. Let X be random variable taking values in $I\subset \mathbb{R}$. I have to show that the Value at Risk is invariant under any ...
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303 views

Decomposition of Contribution to Variance

$C$ is a $N\times N$ covariance matrix of stock returns. Assuming $w$ is a vector of positions in each asset, the total variance of the portfolio is $$w^TCw$$ The contribution to total variance of the ...
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65 views

What is the differential Value-at-Risk?

I am currently working on a Machine Learning Project, implementing portfolio optimization algorithms according to different risk measures. I have found sufficient information on Sharpe Ratio ...
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1answer
94 views

Cornish Fisher VaR Parameters Calibration

I am trying to calculate Cornish-Fisher (modified VaR), but I am in a trouble because when I am reading some articles, some authors calculate the Cornish-Fisher expansion taking parameters S and K, as ...
4
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1answer
99 views

CRRA Ultility， simple question

for CRRA, does increasing gamma leads to increase in risk-aversion? Looking at the curve, I think increasing gamma leads to less in risk-aversion (since the risk preimum is less). But in terms of ...
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1answer
233 views

Determining Value at Risk of a Poisson distribution

If my discrete random variable had a poisson distribution with both moments say equal to 10, how can I find the Value at Risk for a 95 percent confidence interval? I have seen that I need to ...
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2answers
393 views

How do you calculate value at risk on a portfolio of fixed income instruments

I'm curious about this question both for a parametric "Delta" style approach and a Monte Carlo full revaluation approach and I will lead one question into the next. Taking the "Delta" approach first. ...
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1answer
71 views

How are non-equity derivatives handled in monte carlo Value at Risk simulations

If you have a portfolio of stocks and options it's straight forward enough to generate correlated stock paths and evaluate the positions at the end of the time horizon, but what do you do if your ...
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1answer
123 views

Incremental/marginal contribution to VaR in a simulation setting

Estimating marginal contributions to VaR in a simulation setting is apparently quite difficult (see e.g. this blog post) due to issues with sampling variability. My question is whether the following ...
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1answer
453 views

How accurate is the square root of time rule for VaR for a portfolio containing several different types of instruments

Assuming that your value at risk model is based on normality assumptions, e.g. using a Delta-Gamma normal model does the approximation hold perfectly for a portfolio of stocks and options? What about ...
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0answers
28 views

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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1answer
210 views

Value at Risk (VaR): Normal distribution with gamma distributed volatility

If I was to do a 99% VaR calculation on a portfolio with normally distributed returns $\mathcal{N} (\mu,\sigma)$, the 99% VaR would be $\mu - 2.33\sigma$. Instead of having a constant volatility, let'...
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1answer
961 views

How does delta-gamma VaR work in practice and when can it be preferable to Monte-Carlo VaR?

So I will start off by just stating my understanding of the two methods through some examples and lead that into my question. Hopefully it is correct but if not then perhaps the answer to my question ...
4
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1answer
185 views

Value at Risk for portfolio with different maturities

I am new to StackExchange and relatively new to quantitative finance. I work at a commodity trading company and we have an extensive portfolio of futures and options on commodities (traded on the CME, ...

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