Questions tagged [value-at-risk]

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18 votes
3 answers
17k views

Is there a step-by-step guide for calculating portfolio VaR using monte carlo simulations

I am trying to determine a step-by-step algorithm for calculating a portfolio's VaR using monte carlo simulations. It seems to me that the literature for this is extraordinarily opaque for something ...
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11 votes
3 answers
9k views

How does Cornish-Fisher VaR (aka modified VaR) scale with time?

I am thinking about the time-scaling of Cornish-Fisher VaR (see e.g. page 130 here for the formula). It involves the skewness and the excess-kurtosis of returns. The formula is clear and well ...
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10 votes
2 answers
8k views

How is the formula for the VEV (VaR-equivalent volatility) in the PRIIP document derived?

The recent regulation (page 32) on PRIIPs requires to compute a VaR-equivalent volatility defined as $$\mbox{VEV}=\frac{\sqrt{3.842-2\ln \mbox{VaR}}-1.96}{\sqrt{T}}$$ Does anyone have an idea how ...
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10 votes
2 answers
1k views

Empirical distribution function of overlapping time series data

If we model asset return volatility for periods of more than one (say more than one day) there is the square-root rule which holds true under some assumptions. The situation is more tricky if we look ...
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23 votes
5 answers
15k views

Portfolio optimisation with VaR or CVaR constraints using linear programming

I would like to optimize a portfolio allocation (maximizing the exposure or the expected return), but with VaR or CVaR contraints. (some parts of my portfolio cannot exceed a certain VaR) How can I ...
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  • 1,993
12 votes
4 answers
3k views

Are these steps correct to calculate Value-at-Risk with a Monte Carlo simulation?

I have a problem calculating VaR with the Monte Carlo Simulation. I followed the next steps and would like know if it is a right way to calculate VaR or if I need something more? The steps Generate ...
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  • 121
18 votes
1 answer
568 views

What approaches are there for stress testing a portfolio?

Wikipedia lists three of them: Extreme event: hypothesize the portfolio's return given the recurrence of a historical event. Current positions and risk exposures are combined with the historical ...
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  • 283
2 votes
1 answer
9k views

Historical Value At Risk on option portfolio

I am new to Value at Risk subject in fact everything related to quant. Can any body validate the Value at Risk Model on the option price ? I am using a below explained approach . our portfolio ...
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7 votes
2 answers
2k views

VaR mapping - Forward Foreign Currency Contract

I have a question about VaR mapping for FX forwards. Please bear with me while I outline the problem. Philippe Jorion's book discusses VaR mapping; a means to break down complex instruments into ...
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6 votes
1 answer
1k views

Question regarding the Category 3 PRIIP MRM calculation

My question is regarding the European Commission regulation on standardizing the information in the key information documents for PRIIPs. In the Annex IV of the regulation, one can find the ...
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  • 71
5 votes
2 answers
8k views

non-subadditivity of VaR

I have been reading up on VaR and get very confused by the subadditivity concept. On wikipedia, it says "VaR is not subadditive: VaR of a combined portfolio can be larger than the sum of the VaRs ...
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  • 235
2 votes
1 answer
263 views

Questions about VaR and CVaR. Is there any relation between $VaR_{\alpha}(X)$ and $VaR_{\alpha}(-X)$, or $CVaR_{\alpha}(X)$ and $CVaR_{\alpha}(-X)$?

I have some questions when dealing with Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). Is there any relationship between $VaR_{\alpha}(X)$ and $VaR_{\alpha}(- X)$, or $CVaR_{\alpha}(X)$ ...
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  • 47
1 vote
1 answer
5k views

VaR for FX forwards

I am trying to figure out some of the commonly used approaches to deal with FX forwards (in a currency portfolio containing spots, forwards and swaps) that would allow me to calculate the one day VaR ...
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1 vote
0 answers
591 views

Large deviations theory and extreme value theory

I'll enter into details of both, sooner or later, but for the moment I'm concerned about the differences (and relationships, if any) between these two theories. Can someone give me a brief, but still ...
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  • 575
0 votes
1 answer
2k views

Compute cross-gamma

I am trying to use delta-gamma method with montecarlo simulations to calculate the VAR of a portfolio consisting in options and equities. To use the method I need to compute a gamma matrix, that has ...
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5 votes
0 answers
761 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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  • 1,543
2 votes
3 answers
16k views

Why is Value at Risk non-negative?

When reading the book of Financial Risk Forecasting, I saw the following example. I am not very clear about two points marked with yellow and green respectively. ...
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1 vote
1 answer
376 views

Prove Subadditivity - Entropic Value at Risk

Any insight in how to prove the following risk measure is subadditive? $\rho_{1-\alpha}(X) = \inf_{z>0}\{z^{-1}\ln(\frac{E[e^{zX}]}{\alpha})\}$, with $\alpha \in ]0,1]$ I want to prove it is a ...
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1 vote
3 answers
930 views

Can a VaR equivalent Volatility (VEV) be negative?

As from title, can a VaR equivalent Volatility (VEV) as defined by KID/PRIIPS law be negative?
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0 votes
3 answers
1k views

Parametric/Analytical VaR

Suppose I want to calculate VaR for a known distribution with mean $\mu$, variance $\sigma^2$ and $\alpha$-quantile as, $VaR_{\alpha}$ = $\mu + \sigma q_{\alpha}$. For a Gaussian distribution it is ...
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  • 603
0 votes
2 answers
157 views

recalculate VaR from one currency to another

I have a strange question. For example, I have 95% VaR (1Y, delta-normal) for portfolio with one stock in same currency (for example, USD). What minimal information should I have for recalculation ...
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  • 221
0 votes
2 answers
141 views

Filtered Historical Simulation VaR for swaps

I am trying to understand how to calculate FHS VaR for a portofolio of vanilla swaps. I think I understand the main ideas behind FHS VaR and how to implement it for other assets such as equities. I ...
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  • 25
0 votes
1 answer
2k 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 ...
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  • 778
0 votes
1 answer
203 views

What does "1-month horizon" mean in VaR calculations

For a simple equity portfolio, I need to compute historical 1-year simulation VaR with a "1-month horizon". I imagine this means I need to compute the 1-month return of the portfolio at each point in ...
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  • 264
0 votes
0 answers
53 views

Backtesting Conditional Versus Unconditional forecast horizon with lag 2

Assume that we have a 10 year dataset from Tesla (toy example): ...
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