# 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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'...