The tag has no usage guidance.

learn more… | top users | synonyms

8
votes
3answers
2k 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 ...
7
votes
2answers
601 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 ...
6
votes
1answer
503 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 $$ \sqrt{\frac{df-2}{df}} \times \Sigma{t} \times \mbox{quantitle}(t-\mbox{dist}, 0.01) + \mu $$...
4
votes
1answer
179 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
1answer
191 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 ...
4
votes
1answer
92 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 ...
4
votes
2answers
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 ...
4
votes
1answer
302 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 ...
3
votes
1answer
63 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 ...
3
votes
2answers
385 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
1answer
347 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 ...
3
votes
2answers
71 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
2answers
59 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
1answer
50 views

Can I split my backtesting into multiple consecutive sub-periods?

I'm testing a model to estimate the VaR of a portfolio with different stocks. I used 1500 data to estimate some parameters, and now I have other 1500 data for backtesting purposes (for a total of 3000 ...
3
votes
0answers
45 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 ...
3
votes
0answers
316 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 ...
2
votes
1answer
620 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
3k 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
1k 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 ...
2
votes
2answers
44 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
71 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
49 views

Expected Shortfall alternative formulation

Define: $$q_\alpha(F_L)=F^{\leftarrow}(\alpha)=\inf\lbrace{x\in \mathbb{R}\mid F_L(x)\geq \alpha\rbrace}=VaR_\alpha(L)$$ I want to prove that: $$ES_\alpha = \frac{1}{1-\alpha}\mathbb{E}[\mathbb{1}_{...
2
votes
2answers
2k 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.
2
votes
1answer
374 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 ...
2
votes
0answers
49 views

Value-at-Risk Calculation with respect to the Capital Requirements

I want to calculate the Value-at-Risk at date $t$ in such a way that I minimize the capital requirements given as \begin{align} \text{CR}_{\,t+1\,:\,t+250} = \sum_{h=0}^{249}\max\left( -(3+k_{t})\...
2
votes
0answers
115 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 ...
2
votes
0answers
113 views

Beta distribution - Holding period

Let's say I have a risk factor that is defined between [0,1], such as recovery rates. Assuming I have daily data, I can estimate the "daily VaR", i.e. the tails over 1 day period, since the data is ...
1
vote
4answers
140 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?
1
vote
1answer
139 views

Calculate VaR for a liabilty taking a exponential distribution?

An insurance company faces the liability loss off $L = \begin{cases} 0, & \mbox{with probability } 0.75 \\ Z, & \mbox{with probability } 0.25\end{cases}$ where $Z\sim Exp(\mu)$. I want to ...
1
vote
2answers
316 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 ...
1
vote
1answer
64 views

Issues in estimating VaR with GARCH

I am currently trying to figure out how to estimate the value at risk using the rugarch package in R. I've come to a result, but it seems a bit excessive. Here's my code: ...
1
vote
2answers
60 views

Value-at-Risk “hiding risk in the tail” and diversification?

I have a question regarding Value-at-Risk and diversification? When one says that VaR "hides the risk in the tail", does one mean that if we for instance look at VaR at level p=0.05 say, we might get ...
1
vote
1answer
130 views

What is the difference between these two Expected Shortfall definitions?

I have come across different ways expected shortfall is defined. e.g. $$ES_a(X)=\frac{1}{1-a}\int_a^1VaR_b(X)db$$ and $$ES_a(X)=\frac{1}{a}\int_0^aVaR_b(X)db$$ e.g. on Wikipedia's article. Are these ...
1
vote
1answer
1k views

How to interpret/use VaR and Standard Deviation?

The parametric VaR is defined as follows: $$VaR=Z_a*Vol$$ Is this the best way to interpret how much risk is being taken on for a particular asset? How does one interpret volatility on its own if ...
1
vote
1answer
47 views

Value at risk in dollars vs. log returns

I have a quick question about this remark in Tsay's book "Analysis of Financial Time Series" (3rd edition). He says that $$ \text{dollar VaR} = \text{Value} \times \text{log return VaR} $$ and that ...
1
vote
1answer
71 views

Where can I find Value at Risk & Expected shortfall for ETF's?

I'm struggling to find VaR & ES data for ETF's on websites such yahoo finance & Morningstar. Where can I find this data? Thanks,
1
vote
1answer
126 views

Is Value-at-Risk translation invariant?

Let: $X=V_1-V_0R_0$ where $R_0$ is the interest rate. Then, is it so that this risk measure is Translation Invariant as: $\textit{VaR}_{\alpha}(X)=\textit{VaR}_{\alpha}(V_1-V_0R_0)=V_0+\textit{VaR}_{\...
1
vote
1answer
71 views

Value-at-Risk of the sum of three independent lognormal random variables with different confidence level

there are three Business units in a firm, each has operational VaR value which are independent from eachother. the quantile for each opVaR is different from the others. can I simply add the VaRs to ...
1
vote
1answer
234 views

Quantiles, Value-at-Risk and log normal random walks…

Sorry, that's probably quite a bunch of silly questions, but I just got lost a bit and need to dot all the i's and cross some t's :). Let's say we have a series of returns (like this one we may get ...
1
vote
1answer
160 views

regarding Basel II III model

I may have to get involved in some projects using Basel II, III model for risk modeling, to which I have no background. Are there any good book/tutorials to recommend? What are the underlying ...
1
vote
4answers
715 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 ...
1
vote
0answers
42 views

Problems in computing VaR with GARCH-GPD-copula approach

I use a time-varying Gaussian copula (with GARCH-filtered standardized residuals modeled semiparametrically with Gaussian kernel interior and GPD tails, i.e. generalized pareto distributed) to ...
1
vote
2answers
76 views

Parametric VaR of a portfolio including a swap

I am calcualting the parametric VaR of a portfolio that includes among other things an IRS swap that begins in the exact same day the valuation is done. Therefore, its NPV is 0 and I do not which ...
1
vote
1answer
124 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 ...
1
vote
0answers
163 views

How to backtest Value at Risk Models using Conditional and Unconditional tests?

I am trying to carry out backtesting on a number of Value at Risk figures i obtained using var/covar, historical, and monte carlo simulation. The two methods im using are the Kupiec test (...
1
vote
0answers
101 views

Simulating Option Positions VaR with Monte Carlo in Python

I'm trying to calculate VaR for overall option positions. Currently I do a MC simulation for the underlying, and derive the theoretical value of the option from those theoretically. Then I calculate ...
1
vote
1answer
146 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 ...
1
vote
0answers
272 views

Comparing Backtests of Value-at-Risk and Expected Shortfall

My goal is to test if ES (CVaR) empirically is a better risk measure than VaR for a set of given variables (assumed underlying distribution, confidence level, sample size) for different asset classes. ...
0
votes
1answer
41 views

Calculating VaR of an Incomplete Distribution

I am currently completing a multiple choice question that has stumped me. An asset has its price and its corresponding probability described as: 100, 0, -50, -70 and -90 with probabilities 50%, 12%...
0
votes
0answers
23 views

help with p&L vectors historical simulation

My question is about the calculation of the Value at Risk based on historical simulation. I have a table which contains the P&L-vectors of each day of one year. But I don't know what is contained ...