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8
votes
3answers
501 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 ...
8
votes
2answers
142 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 ...
4
votes
0answers
217 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 ...
3
votes
2answers
97 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
537 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 ...
2
votes
1answer
714 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
1answer
153 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
1answer
160 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
63 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 ...
2
votes
0answers
222 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 ...
1
vote
1answer
521 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
2answers
83 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. ...
1
vote
1answer
69 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
135 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
195 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. ...