Questions tagged [value-at-risk]

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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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0answers
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 ...
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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 ...
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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. ...
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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 ...
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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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2answers
123 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 ...
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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 $S = 10$. $S$...
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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.
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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 ...
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1answer
180 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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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 ...
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1answer
774 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 ...
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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 ...
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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 ...
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2answers
78 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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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 ...
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4answers
3k views

How can I calculate Value at Risk?

Is it possible calculate Value at Risk on an asset without a time horizon? What kind of variables do you need? Variables that are on the table are value, standard deviation, beta, market return, risk ...
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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 ...
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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 ...
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1answer
191 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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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 ...
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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 ...
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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 ...
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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 \...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
249 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
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 ...
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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 ...
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1answer
233 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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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 ...
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2answers
610 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, ...
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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)+...
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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-...
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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 ...
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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 (...
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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?
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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 ...
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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 ...
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1answer
195 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
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_{\...
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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 ...
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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 ...
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2answers
681 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 ...
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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) ...