Questions tagged [value-at-risk]
The value-at-risk tag has no usage guidance.
128
questions
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46 views
Block maxima estimation of Expected Shortfall
I want to calculate the expected shortfall of a return series with the block maxima (BM, link) method in Extreme Value Theory, however I can't seem to find out how this should be done. All papers I'...
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2answers
82 views
understanding Value-at-Risk correclty
The are several types how to calculate the VaR. I am focussing on the method of calculation the VaR in percentage.
$VaR=I*z*std*\sqrt{t}$
This gives the VaR in €.
I have the z-value, the daily ...
3
votes
1answer
116 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. ...
0
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2answers
49 views
From risk limits to pnl projection?
As a fresh risk manager, today I got an assignment to check whether our risk measurements / limits are setup properly (whether the limits are so tight that affect our p&l) . Better if I can ...
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0answers
32 views
Approximation of portfolio VaR (after mapping) when Delta and Gamma both equal zero
As titled, I am having trouble estimating the VaR of a portfolio mapped as a function of a single risk factor $S$, in the form :
$$V(S) = S^3 - 30S^2 + 300S + 150$$
with current value $S = 10$.
$S$...
4
votes
2answers
125 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 ...
1
vote
1answer
80 views
PCA on a portfolio of spot and forward contracts
I have a portfolio of spot and FX forwards on various currencies all based to AUD. I need to able to quantify how the changes in amount, tilt and curvature of the AUD curve would impact my p/l.
...
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44 views
How can I manually calculate the VAR of a call and put portfolio?
How would I solve the following question? Im unsure how to estimate the stock price using MCS.
0
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1answer
76 views
Historical Simulation of Bond, Stock and Option Portfolio
If I have a portfolio consisting of
1-one stock of unit price equal to S,
2-one 9% coupon American bond with 20 years to maturity and a par value of $1000,
3-and one European call option on the ...
1
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0answers
23 views
How to measure specific risk charge?
IFRS requires banks to compute different risks including market risk based on Basel iii.
To do so, the capital requirement is defined as follows:
$$max(VaR_{t−1},m_c × VaR_{avg}) + SRC$$
$SRC$ is ...
2
votes
1answer
67 views
Modified Sharpe ratio
I would like to model different type of investors, hence I need to find some kind of utility functions to optimize. Apart from very abstract exponential utility function, I couldn't find any proper ...
1
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1answer
87 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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0answers
58 views
Opposite of Value-at-Risk. Criteria for Optimization
I'm trying to optimize portfolio of undervalued and portfolio of overvalued stocks. I have simulated scenarios of stock returns, and based on them I would like to find optimal weights. One criteria is ...
1
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0answers
44 views
Risk Measure-identication
Let X be a variable with existing moment generating function $M_x(z)=E[e^{zX}]$.
Define the following risk measure: $\rho_{\alpha}(X)=inf_{z>0}(z^{-1}ln(\frac{M_x(z)}{1-\alpha}))$
Does anyone know ...
1
vote
2answers
80 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 ...
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0answers
46 views
Compute the VaR from NPV (Net present value)? [closed]
A client is evaluating an investment in
Indochina requiring an initial expenditure (period 0) of 10,000, and
which then in periods 1 and 2 gives a benefit V1 and V2. Assume
that the discount rate to ...
0
votes
2answers
79 views
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 ...
2
votes
1answer
69 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 ...
2
votes
1answer
167 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 ...
1
vote
0answers
41 views
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 ...
3
votes
1answer
99 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 \...
2
votes
0answers
81 views
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
...
4
votes
1answer
198 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 ...
2
votes
0answers
40 views
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 ...
1
vote
1answer
89 views
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 ...
1
vote
0answers
73 views
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 ...
0
votes
1answer
70 views
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 ...
1
vote
1answer
68 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 ...
0
votes
1answer
250 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 ...
0
votes
1answer
234 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) = ...
0
votes
2answers
77 views
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 ...
2
votes
2answers
95 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
0answers
54 views
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 ...
1
vote
1answer
65 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 (...
0
votes
1answer
91 views
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-...
2
votes
1answer
149 views
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 ...
1
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0answers
30 views
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?
0
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0answers
41 views
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 ...
2
votes
1answer
198 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 ...
1
vote
1answer
196 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?
1
vote
1answer
47 views
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_{\...
2
votes
1answer
194 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 ...
1
vote
1answer
103 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 ...
1
vote
1answer
101 views
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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0answers
53 views
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?
1
vote
1answer
116 views
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 ...
1
vote
1answer
123 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 ...
1
vote
2answers
96 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
$w$:...
0
votes
1answer
179 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 \...
2
votes
0answers
44 views
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. ...
