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Questions tagged [value-at-risk]

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Value-at-Risk theory papers

I am looking for some papers related to the value-at-risk theory. I would like to focus on mathematical aspects of VaR. I would like to read something about modern approaches to VaR (maybe using ...
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56 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 ...
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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 ...
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Does it make sense to subtract VaR from spot shocks?

I have a model to compute the Event Risk (in dollars) from a shock to the spot price of an asset. I also have the 10-day VaR PnL for the same assets returns. These two numbers are then aggregated to ...
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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 \...
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Methods for calculating Expected shortfall

Let B1, B2 be two defaultable zero-coupon bonds maturing in 1 year, each with a face value of $100. Assume: each bond is priced at 90 dollars each bond has a 4% probability to default within 1 year ...
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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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How does CVaR change when the mean and variance of the loss distribution change?

I have a CVaR constraint in my optimization problem and I want to change the mean and standard deviation of loss distribution during each iteration. How can I get the new CVaR based on the old CVaR ...
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VaR of ARCH model

Consider the following: $r_t = \theta r_{t-1}+u_t$ $u_t=\sigma_t\epsilon_t$ $\sigma^2_t=\omega+\alpha u^2_{t-1}$ $-1<\theta<1,\omega>0,\alpha \in(0,1)$ What is the 99% 2-day VaR of a ...
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1answer
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Value-at-risk and Equity delta

How to validate value-at-risk calculation on an equity portfolio using equity sensitivities? I don't have trouble doing that for rates instruments or options but I don't know which underlying risk ...
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Monte Carlo VAR with differente asset classes

I have found a very useful post regarding the use of Monte Carlo simulaton to obtain portfolio Value at risk, based on Cholesky decomposition, random variates, etc. This post I'm talking about is: Is ...
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Scenario generation for Value at risk: How to interpret the scenarios

This is a a simple and rather pratical approach and not theoretical. Let's assumes I have generated 250 scenarios for a given fixed portfolio. Hence we assume that the asset returns can result in 250 ...
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1answer
60 views

Computing Montecarlo VaR for a single asset

I'm trying to understand the procedure to compute the Value-at-Risk for a single asset by implementing the Montecarlo technique. Here it follows the procedure step-by-step in 5 points: selecting the ...
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1answer
140 views

Variance-Covariance VaR: how to get the volatility?

Because the variance-covariance VaR assumes that the returns are normally distributed, in theory it is easy to get VaR by simply finding the mean and the volatility (standard deviation) of the ...
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1answer
104 views

Delta-Gamma VaR question on inputs (do I need only one delta or the delta for the past 500 days?)

When calculating a VaR using the Delta-Gamma approach, I am supposed to use this formula: ∆(V) = Delta * ∆(X) + 0.5 * Gamma * ∆(X)² where: ∆(V) = change in value of the asset in portfolio ∆(X) = ...
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Procedures to follow when VaR model fails backtest

I was wondering what the correct procedure is to follow when a VaR model fails a backtest (either conditional coverage and/or independence tests)? Assuming I am restricted to using a historical VaR ...
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2answers
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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)+...
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Pricing default risk in cryptos

I'm looking to figure out how to price "insurance" against a counter-party defaulting in an OTC cryptocurrency transaction. I think the first measure would be to calculate VaR? I'm planning on ...
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1answer
58 views

Value at Risk for normal r.v. with shock (regimes)

I am struggling to understand how was this simple Value-at-Risk calculated. It's Example 1 in Daníelsson, Jón, et al. "Fat tails, VaR and subadditivity." Journal of econometrics 172.2 (2013): 283-291 (...
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References for Risk Adjusted Portfolio Optimization

I'm trying to formulate BL portfolios which use Mean VaR, Mean CVaR optimization to calculate risk-adjusted equilibrium returns. Can someone point me to any references on this topic? I'm looking for ...
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1answer
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How to calculate $\frac{\partial\ \text{CVaR}_{\alpha}(\min(X,d))}{\partial d}$ and $\frac{\partial\ \text{VaR}_{\alpha}(\min(X,d))}{\partial d}$?

How to calculate $\frac{\partial\ \text{CVaR}_{\alpha}(\min(X,d))}{\partial d}$ and $\frac{\partial\ \text{VaR}_{\alpha}(\min(X,d))}{\partial d}$? Here, $\text{CVaR}$ is short for Conditional Value-...
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How to compute a single Value-at-Risk (a single quantile) of portfolio returns taking into account correlation between individual returns?

Introduction My goal is to retrieve a single Value-at-Risk (VaR) of a N(0, H) random variable $X$ at the $\alpha \in (0,1)$ confidence level where H is a known d-dimensional positive definite matrix ...
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Hedger's utility function associated with minimizing value at risk

What must be the general shape of a hedger's utility function if the hedger is minimizing value at risk? What is a simple example of such a utility function?
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Does it make sense to simulate from the multidimensional GBM?

Suppose I have times series data on 3 assets and I do $N$ simulations (GBM) first for each of assets individually and then from a multidimensional GBM since their log-returns are correlated (I use ...
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1answer
138 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 ...
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1answer
156 views

Negative VaR equivalent Volatility (VEV) and its meaning?

Can a VaR equivalent Volatility (VEV) as defined by KID/PRIIPS law be negative and what does it mean if it has a negative value?
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1answer
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What is the relationship of Value-at-Risk of a random variable $X$ and a constant $D$ $VaR_{\alpha}(min(X,D))$and $VaR_{\alpha}(X)$?

Suppose $X$ is a nonnegative random variable and $D$ is a constant, what is the relationship of $\text{VaR}_{\alpha}(min(X,D))$ and $VaR_{\alpha}(X)$? Here, $VaR$ stands for Value-at-Risk as, $$ VaR_{\...
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1answer
97 views

Value at Risk for a plain vanilla interest rate swap

Hello I have question regarding the computations of the Value at Risk for a plain vanilla interest rate swap (i.e. same currency and fixed-for-floating). I have a data set consisting of the Swap ...
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1answer
79 views

Value-at-Risk and dividend payments

How should dividends be considered when computing Value-at-Risk for a stock portfolio using Historic data. To simplify let's consider a very simple portfolio of one long position on a stock. My VaR ...
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Difference between Standard VaR and VaR with partial set of Risk Factors

Ciao, I'm working on VaR and Expected Shortfall and this question came out. For a given portfolio VaR can be computed w.r.t. all the risk factors or just for a subset. Infact you can decide to 'freeze'...
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163 views

Delta- Gamma approximations for VaR

I was reading Delta- Gamma approximations for VaR from Phillipe Jorion-Value at Risk 3rd edition, I got stuck here, how do they derive equation $10.10$ from $10.9$. Also in eq. $10.9$ they have ...
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Definition of μ in Parametric Absolute Ex-Ante Risk

Parametric Value at Risk (of an investment fund) depends on the Gaussian Distribution and comes in two forms; Relative VaR (ie relative to the mean) and Absolute VaR. Both are calculated as ...
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1answer
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VaR of long options

I just had a chat with a risk manager who thinks that the daily VaR of a long option with a maturity under three months should be 'Premium of the Option' / 20 (assuming twenty days in a month) ...
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How can I find what Loss Given Default to use

I want to come up with the appropriate loss given default for a commodity derivative in my CVA calculation. would anyone know where I can find this information?
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1answer
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What is the name of this VaR calculation strategy?

Here's a question on a passage from this paper I'm reading. Here's the quote: Given the vector of portfolio weights $w$, and the estimate of the conditional variance, $\Sigma_{t,k}$, the ...
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1answer
118 views

Risk Management methods for Stock portfolio with ~30 stocks

What is ideal Risk Management method/methods s for stock portfolios with 25-30 stocks and around 50.000 USD invested in those stocks. Every stock bought will be kept in the portfolio for 1 to 12 ...
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2answers
91 views

Assigning Global VaR to portfolio members

Assuming that I calculate a parametric VaR of a portfolio with 3 assets, and I need to assign the amount each asset (equity) contributes to the VaR. Lets say that: $C$: Is the correlation matrix $w$:...
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1answer
126 views

Calculating Value at Risk (VaR) of a Stock position assuming geomtric brownian motion (GBM)

I want to calculate the VaR for a long position (S) in stockprices after one year. Therefore i tried two methods: analytical solution: $VaR = S\cdot p_0\cdot \sigma_d \cdot \Phi^{-1}(1-\alpha)\cdot \...
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0answers
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VaR decomposition of non-normal portfolio by g-and-h distribution

According to Doowoo Nam (2013), VaR of non-normal portfolio returns approximated by g-and-h distribution can be decomposed pretty much in the same way as the VaR of a portfolio with normal returns. ...
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1answer
212 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 ...
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1answer
212 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). ...
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1answer
133 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. ...
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Calculate VaR using the extreme value theory

I am trying to calculate the Value at Risk for different models. But I am now confused for some reason. Could you please help me? I calculate the 1% and 5% VaR (so negative numbers) and I am also ...
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1answer
66 views

Calculate standard deviation from the value at risk

I have the following data: VaR VaR% Expected return Am I right to think that I would be able to derive standard deviation from this? Using the formula: VaR%= ER-(zscore*SD), I should be able to ...
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542 views

Ratio between Expected Shortfall and Value at Risk for $t$-distribution

If $X$ is a random variable with $t$-distribution of parameter $\mathcal{v}$, how can I prove that $$ \lim_{\alpha \to 1^{-}} \frac{\mathrm{ES}_{\alpha}(X)}{\mathrm{VaR}_{\alpha}(X)} = \frac{\mathcal{...
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What's the relationship between $VaR_{\alpha}(X)$ and $VaR_{1-\alpha}(X)$ if the probability distribution function is not symmetric?

If the probability distribution function $f(x)$ is not symmetric, is there any relationship between $VaR_{\alpha}(X)$ and $VaR_{1-\alpha}(X)$? Here, $VaR$ is defined as $$ VaR_{\alpha}(X) := \inf\...
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1answer
522 views

VaR : Student-t GARCH

I have a question on the VaR estimation via the student t GARCH model. Under this framework, the one day ahead VaR estimate is calculated by the following formula: $$VaR_{p}=\mu_{t+1}+\sigma_{t+1}\...
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1answer
156 views

Questions abut 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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1answer
142 views

VaR Backtesting. High frequency of exceedances

I'm preparing for thesis defense and I've got simple question connected with Value at Risk backtesting. Portfolio VaR was calculated using historical simulation approach (250 days and 500days) and ...
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348 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 ...