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Questions tagged [value-at-risk]

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10
votes
2answers
6k 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
3answers
7k 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 ...
9
votes
2answers
704 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 ...
8
votes
2answers
1k 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
2answers
505 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 ...
7
votes
1answer
797 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
1answer
1k 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
1answer
1k 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 ...
6
votes
1answer
350 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 ...
6
votes
1answer
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 ...
4
votes
2answers
2k 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 ...
4
votes
2answers
5k views

Does one use the covariance or correlation matrix in cholesky decomposition to generate correlated samples

Can we interchangeably use Cholesky decomposition of covariance and correlation matrix to generate simulations? If not, in which situations do we use one or the other and why? Thanks in advance.
4
votes
1answer
365 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 $-...
4
votes
2answers
4k views

Difference between VaR and credit VaR?

Quick question: is there a difference between credit VaR and VaR or are they the same thing?
4
votes
1answer
425 views

Confidence Interval on Monte-Carlo-CVaR

I use the Monte-Carlo Simulation for the computation of VaR and CVaR and wish to compute the 95% Confidence Interval of my result(not the confidence level of VaR). In the case of VaR this is simple ...
4
votes
1answer
2k views

Value at Risk Monte-Carlo using Generalized Pareto Distribution(GPD)

I have created a VBA program to calculate VaR by using Monte Carlo, I have simulated Brownian Motion. This method might be ok for 100% equity portfolio, but let's say this portfolio may have fixed ...
4
votes
2answers
399 views

How to add Risks-Not-In-VaR (RNIV) to VaR under Basel III

I am trying to generate/prove the magnitude of the over-conservativeness of the regulatory VaR (internal models) under Basel III against what a more accurate VaR would be. However, I can't seem to ...
4
votes
1answer
495 views

Market risk stress testing?

I am doing a research for a paper for market risk stress testing. In fact I found some information on the web about this important topic such as: Stress Testing from Art to Science Stress Testing ...
4
votes
1answer
295 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 ...
4
votes
1answer
735 views

Backesting VaR on overlapping intervals to year's end

Let us assume that each month of the year (up to November) we calculate a VaR (say 99%) with holding period to the end of the year. Thus the holding period starts with 12 months and goes down to 1 ...
3
votes
2answers
605 views

Expected Shortfall Formula in terms of P

Let $X$ be a continuous random variable and $Q_x$ is the associated quantile function. Show that expected shortfall $ES_X[p]$ at the confidence level $p$ which is defined as $$ES_X[p]=\Bbb E[X|X\leq ...
3
votes
2answers
858 views

CVaR/VaR Ratio as alpha goes to 1

I am having trouble taking the following limit of CVaR/VaR for a normal distribution as alpha approaches 1: $\lim_{\alpha \to 1} \frac{\mu + \sigma \frac{\phi^{-1}(\alpha)}{1-\alpha}}{\mu + \sigma \...
3
votes
2answers
217 views

Value at Risk - What if an account has never suffered from a negative return

I want to implement an algorithm that calculates an account's 95% value at risk on a monthly return base. The case I want to describe in this question is rather academic and will probably never happen ...
3
votes
2answers
576 views

Determining the portfolio return distribution to calculate CVaR/ES

I'm trying to do a portfolio optimization with an expected shortfall constraint. For this, it is necessary to know the distribution of expected portfolio returns. When doing this empirically, my plan ...
3
votes
1answer
314 views

Can portfolio Value-at-Risk be calculated analytically for multivariate t-distributed returns?

It is widely known that VaR is generally not sub-additive in all but the most restrictive cases (typically when a Gaussian return distribution is assumed, which fails when it matters the most). ...
3
votes
1answer
154 views

Risk Compensation

I try to understand the different ways to compensate for risk. In the CAPM, when we plot the excess return against the risk, we find that portfolios of interest lie on the efficient frontier (i.e. ...
3
votes
1answer
133 views

Portfolio optimization w.r.t. value at risk: introductory or survey references

I am looking for references introducing the problem of portfolio optimization when the target characteristic is value at risk. A textbook treatment would be great. Surveys on the topic are also ...
3
votes
1answer
124 views

CVaR formulation

I am a research intern and I am working on a topic about a profit maximization of a risk-averse newsvendor by using Conditional Value-at-Risk.The problem is that I found different expressions of CVaR. ...
3
votes
2answers
151 views

CVaR reformulation correct?

Conditional Value at Risk (CVaR) is given as: $$CVaR_\alpha(X)=\frac{1}{\alpha}\int_{0}^{\alpha}VaR_\beta(X)d\beta=-E(X|X\leq-VaR_\alpha(X))=-\frac{1}{\alpha}\int_{-\infty}^{-VaR_\alpha(X)}x \cdot f(x)...
3
votes
1answer
800 views

Currency risk USD>EUR>EGP

Seeking input on hedging risk on USD to Euro with a 3rd component of payroll issued in Egyptian Pounds. We are a US corp invoicing a Germany entity in Euro with massive payroll being paid in Egyptian ...
3
votes
1answer
105 views

Value-at-Risk for a portfolio model with Gearing

My models: Say I want to construct a portfolio so I maximize my expected return while keeping my risk (measured by Value-at-Risk) lower than my risk target. $$\max \sum x_i \mu_i \\ VaR_{0.05} \leq \...
3
votes
1answer
475 views

Modeling tail data using Generalized Pareto distribution

I just estimated a ARMA(1,1)+GARCH(1,1)+Threshold order(1) equation for time series of stock prices. Now I'm going to estimate the residuals' marginal ...
3
votes
2answers
127 views

Do you know fast to compute, yet plausible risk attribution measures?

I am looking for a fast to compute, yet plausible risk attribution measure based on the risk measure used to compute overall risk. To be more specific, assume that my risk measure is the VaR of a ...
3
votes
3answers
3k views

Step By Step method to calculating VaR using MonteCarlo Simulations

In trying to find VaR for 5 financial assets with prices over a long period of time(2000 days worth of data) how would I do the following: Carry out monte-carlo simulation in order to find a VaR ...
3
votes
0answers
87 views

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 ...
2
votes
4answers
236 views

How to extrapolate VaR?

I have a model predicting 1-day VaR. How does 1-year VaR follow from it? Shall I just multiply by 365 or another method?
2
votes
2answers
192 views

1 day VaR vs 10 day VaR

Even while using historical simulation VaR, 1 day VaR is converted into 10 day VaR by multiplying 1 day VaR by Sqrt(10) for regulatory reporting purposes. What are the underlying assumptions for ...
2
votes
2answers
843 views

Historic Value at Risk - Ratios vs. Differences

Quick Summary on Historic VaR Let $S_0,...,S_n$ be the daily values of some stock (where $S_0$ is the current value). Then for $i=1,\ldots,n$ we let $$\hat r_i:=S_{i-1}/S_i \quad \text{and}\quad \hat ...
2
votes
1answer
309 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 ...
2
votes
1answer
923 views

Overestimating or underestimating risk?

This question might be silly, but I want to be sure of myself. If one has Value-at-Risk forecasts and there are zero VaR breaches (i.e. no return value is smaller than or equal to the VaR value) then ...
2
votes
2answers
682 views

Incremental VaR formula

According to a few resources online the formula of iVaR is : VaR (after adding the new element) - VaR (before) My question is how can this be correct given the lack of subadditivity of VaR? Meaning, ...
2
votes
1answer
4k views

Parametric VaR with Student-t distribution

Im using VaR to estimate parametric VaR. I have been able to do this using a Normal Distribution, however I want to also do this using a Student t-distribution and I'm unsure how to implement that in ...
2
votes
3answers
11k 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. ...
2
votes
1answer
189 views

The VaR of a portfolio with Student t returns

A portfolio consists of 300 stocks,150 of A and 150 of B, their annualized covariance matrix is as following: $\begin{pmatrix} 0.09 & 0.018\\ 0.018 & 0.04 \end{pmatrix}$ Thoese two stocks ...
2
votes
2answers
114 views

How to prove the following relation of Conditional Value-at-Risk and Value-at-Risk?

How to prove the following relation of Conditional Value-at-Risk $\text{CVaR}_{\alpha}(X)$ and Value-at-Risk $\text{VaR}_{\alpha}(X)$, \begin{equation} \text{CVaR}_{\alpha}(X) = \text{VaR}_{\alpha}(X)+...
2
votes
1answer
222 views

Volatility scenario generation for value-at-risk

I have the following problem: For a single name plain vanilla equity option calculate 1y VaR for given confidence level. Is there any state-of-the-art or current market practice known on how to ...
2
votes
1answer
187 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 $CVaR_{\alpha}(X)$ ...
2
votes
2answers
62 views

Maximization with risk-neutral investors and VaR constraints

In this paper, the authors make a simple model with: (1) A global bank, who is risk-neutral but has a Value-at-Risk constraint: $$\max_{x_t^B} E_t[x_t^B\prime R_{t+1}]$$ s.t. $$\alpha (Var(x_t^B\...
2
votes
1answer
123 views

How to measure the volatility of illiquid bond with no historical prices

The basket of corporate bonds that I am following barely traded after the issuance. Hence, there is no historical data to estimate the volatility. Can you suggest me a different approach to come up ...
2
votes
1answer
74 views

Historical VaR for shares in foreign currency

I'm currently studying John Hull's [1] example on historical value at risk for portfolio consisting of four stock indices. In this example Hull converts the prices of the stock indices to the home ...