Questions tagged [value-at-risk]

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30 votes
2 answers
17k views

What is the difference between the methods for calculating VaR?

There are three different commonly used Value at Risk (VaR) methods: Historical method Variance-Covariance Method Monte Carlo What is the difference between these approaches, and under what ...
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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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22 votes
3 answers
2k views

How are distributions for tail risk measures estimated in practice?

Let's say you want to calculate a VaR for a portfolio of 1000 stocks. You're really only interested in the left tail, so do you use the whole set of returns to estimate mean, variance, skew, and shape ...
18 votes
3 answers
18k 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 ...
18 votes
1 answer
575 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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16 votes
3 answers
5k views

How to compute the Value-at-Risk of the sum of two dependent lognormal random variables?

Hy I posted this question first at mathflow.net they suggested me this page, which I was not aware of. Question Let $(X_1,X_2)$ be a multivariate normal random vector ($X_1$ and $X_2$ need not be ...
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15 votes
3 answers
767 views

Extreme Value Theory possible for portfolios with options?

Say you have a portfolio with long exposure to a few linear assets (stock indices) and short exposure to a nonlinear asset (say call options on one of the linear assets). I am interested in ...
  • 321
13 votes
2 answers
1k views

Imposing Restrictions on Cointegrating Vectors, R example

The code given below estimates a VEC model with 4 cointegrating vectors. It is a reproducible code, so just copy and paste into your R console (or script editor). ...
  • 191
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 ...
  • 121
11 votes
3 answers
7k views

Where can I find a list of VaR and CVaR formulas for continuous distributions?

Where can I find more VaR and CVaR formulas for continuous distributions? I collected a list here:
  • 5,679
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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11 votes
2 answers
884 views

VaR for portfolio of funds

Let's assume we need to calculate a 1-day VaR for a portfolio of funds. Funds are traded, they can be bought and sold every day. We know exactly what the assets in each fund are. What is the right way ...
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11 votes
0 answers
606 views

Computing Value at Risk for portfolio in R [closed]

I know how to compute VaR with long positions using PerformanceAnalytics. What about a portfolio consisting in two equities A and B, 100 USD long positions in each, and 2 stock options for the same ...
10 votes
2 answers
9k 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 ...
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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9 votes
2 answers
951 views

CDS spread scenarios from historical market data

I'm searching for information on the best way to generate scenarios to be used in VaR or ES calculations, for CDS spreads. Given that we need significant historical data in order to achieve a decent ...
  • 503
8 votes
2 answers
2k views

Estimation of Empirical Expected Shortfall of a heavy tailed distribution

Assume that you have a portfolio for which you have estimated a parametric model to the underlying instruments, but the distribution of the portfolio as a whole is too complicated to compute ...
8 votes
1 answer
1k views

How to limit the nbr of cross-gamma calculations in a delta-gamma VaR calculation?

Many times, we want to calculate VaR using some parametric approach (delta-normal approximation for instance) when historical simulation or monte carlo are simply to slow. This is fine as long as only ...
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8 votes
2 answers
997 views

Risk neutrality correction for Monte Carlo Bootstrapping according to PRIIP regulation for products of category III

The PRIIP (packaged products) regulation prescribes Monte Carlo bootstrapping simulation for calculation of VaR for products of category III (non-linearly leveraged products). The idea is based on ...
8 votes
1 answer
743 views

Calculating VaR/CVaR on high frequency data and returns

As we converge on the minute time scale and below for our unit time interval, the return distributions tend to be leptokurtotic and more discretized (due to fixed values such as minimum price ...
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8 votes
1 answer
550 views

Which is a more appropriate choice of risk measurement in a utility function, CVaR or VaR?

What is the consensus on which risk measure to use in measuring portfolio risk? I am researching what is the best risk measure to use in a portfolio construction process for a long/short option-free ...
8 votes
0 answers
4k views

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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7 votes
3 answers
4k views

VaR implementation using quantlib?

I am thinking of writing a VaR framework for my existing system, using quantlib to do the bulk of the calculations. Despite several searches, I have not as yet come across a quantlib VaR ...
7 votes
2 answers
874 views

How to minimize the difference between a parametric VaR and a MC-VaR with lognormal assumption?

Given that we want to find the Value at Risk for a portfolio of stocks only, there are two main methods to proceed. In the problem, we also assume that stocks follow a geometric Brownian motion. A ...
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7 votes
1 answer
411 views

Portfolio VaR with Copula?

Let the portfolio be given by: $$X=X_1+X_2$$ $(X_1,X_2)$ are dependent through a Copula function $C(u_1,u_2)$, such that the joint distribution is given by: $$F(x_1,x_2)=C(F(x_1),F(x_2))$$ What is ...
  • 5,679
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 ...
7 votes
1 answer
2k views

Value-at-Risk formula when using skewed-t distribution

I am trying to find a formula for the skewed-t VaR. For example the VaR formula for a t-distribution is $$ \sqrt{\frac{df-2}{df}} \times \Sigma{t} \times \mbox{quantitle}(t-\mbox{dist}, 0.01) + \mu $$...
7 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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7 votes
1 answer
1k views

Overlapping Value-at-Risk Backtest Data an Issue?

My understanding of VaR model back testing is thus: ~~ t: Calculate daily VaR using look back data over n past days t+1: Compare daily return against VaR, record breach if one occurred, repeat ...
7 votes
1 answer
2k views

Fitting distributions to financial data using volatility model to estimate VaR

I want to fit a distribution to my financial data using a volatility model to estimate the VaR. So in case of a normal distribution, this would be very easy, I assume the returns to follow a normal ...
7 votes
2 answers
3k views

Value at Risk for Futures Contracts

I would like to know how you would compute Value at Risk on a portfolio of futures i.e rates futures, commodity futures and equity. How do you deal with the discontinuous form of commodity futures for ...
6 votes
3 answers
165 views

Which lags or percentiles should be run in a batch when calculating Value-at-Risk?

Are there any "standard" VaR calculations run in a batch? For example, testing a VaR calculation with a lag of 1,2, 5 or 10 days over 2 years? Same question for the percentile, 1%, 2.5%, 5% etc.
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6 votes
1 answer
420 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 $$...
6 votes
1 answer
762 views

How to compute returns and daily VaR of a currency position?

I have a Forex trading account with a base currency USD. I am holding a position in EUR/JPY and would like to estimate my daily VaR. If I compute the EUR/JPY returns using the historic prices this ...
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6 votes
2 answers
545 views

PCA for stand alone equity VaR

I am trying to compute equity VaR, forex VaR and total VaR on an international portfolio (10 stocks x 4 countries). Since I am not interested in the risk disaggregation among diffrent countries I was ...
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6 votes
1 answer
9k views

How to calculate Credit VaR?

(source John Hull, Options Futures and Other Derivatives 8th edition) I can't follow why Hull calculates Credit VaR in the following manner. I thought CVaR was Unexpected Loss$_{confidence}$ - ...
5 votes
2 answers
2k views

Intuitive explanation for expectiles

I am looking for an intuitive explanation for expectiles. Here is a link to a paper about expectiles: Bellini and Di Bernardino: Risk Management with Expectiles, European Journal of Finance, May ...
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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5 votes
4 answers
939 views

How to determine what's driving the VaR?

I am given the following data: Historical (260 days) P&L vector of a portfolio. Specific P&L's for each investment in the portfolio, for the 10 days with the lowest P&L. The question ...
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5 votes
2 answers
492 views

Missing data in historical simulation VaR

A historical simulation approach to VaR estimation relies on the availability of historical data. What do we do when there is no data (say, spot price and implied volatility surface) as, for example, ...
5 votes
2 answers
2k views

VaR for corporate bonds

I am trying to create a simple risk calculation for the portfolio (ignoring correlations for the moment). I have some corporate bonds with limited daily price changes. Any one have ideas how I can get ...
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5 votes
2 answers
942 views

How to Calculate a Monte Calo VaR estimation error

I'm performing a Monte Carlo to calculate value at risk (with a 3 dimension risk factor) Now, I would like to calculate the error of the estimation of the VaR with respect to the number of simulations ...
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5 votes
1 answer
444 views

questions on VAR manipulation

The book of Financial Risk forecasting by Danielsson gives the following example about VAR manipulation. I have two questions: 1) If $0> VAR_1 > VAR_0$ , why the following figure plots it as $-...
5 votes
2 answers
169 views

Do correlated assets affect the price of a portfolio of derivatives?

I need to compute the value at risk of a given portfolio as an exercise for a class at university but I have trouble understanding how correlated assets affect the price of the portfolio. Could you ...
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5 votes
3 answers
3k views

Expected Shortfall (CVaR) Backtesting

I am writing my thesis on VaR and ES risk measurements and have encountered some issues with how to best test the accuracy of ES estimates. My understanding of the topic is that backtesting ES ...
  • 321
5 votes
1 answer
2k views

How do I compute Value at Risk of a European call option?

Consider a European call option on a non-dividend paying stock, where the option has strike K = 100 and expiry T = 0.25, i.e. the option expires 3 months from now. The option is on a single share. The ...
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5 votes
2 answers
519 views

quantiative risk measure how they are implemented in R and their use

So far I have just theoretical knowledge of risk measure and never used them in application. Therefore I have some basic question how risk measures are used in reality and how they are implemented in ...
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5 votes
2 answers
2k views

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 ...
  • 321
5 votes
0 answers
765 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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4 votes
3 answers
2k views

Do I need a copula to accurately estimate the VaR of a portfolio of risky assets?

I need to estimate the daily VaR of a portfolio of various exposures in $n$ risky assets (say equity futures). The simplest approach, I think, would be to just estimate VaR from a multivariate normal ...
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