Questions tagged [var]

Value at Risk, a widely used risk measure of the risk of loss on a specific portfolio of financial assets.

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Normal VaR for short bond

So I'm short a GBP denominated zero-coupon bond which has a face value of 1 million pounds and a remaining maturity of 6 months. Furthermore, I have to assume that the daily return of a 6-month zero ...
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45 views

A forward contract to buy a foreign currency can be handled by a linear model

In Hull's book, he says that: "An example of a derivative that can be handled by the linear model is a forward contract to buy a foreign currency." Then he continues with, "For the ...
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How to prove the following relation of Conditional Value-at-Risk and Value-at-Risk and Conditional Tail Expectation?

How to prove the following relation of Conditional Value-at-Risk and Value-at-Risk and Conditional Tail Expectation????
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28 views

Simulated VaR with differently distributed processes

I am attempting to calculate the one-month 95th and 99th percentile profits for a two-year portfolio of energy-generating assets over the next three months. This means that the calculation has two ...
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36 views

the relationship between VaR(0.05) and mean?

What is the meaning of the difference between the quantile of prob=0.05 and mean for a sample form a specific distribution? In other words, I would like to understand the relationship between ...
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27 views

How to calculate VaR price space according to PRIIP flow diagram

My question is regarding the European regulation on standardizing the information in the KID's for PRIIPs. (https://esas-joint-committee.europa.eu/Publications/Technical%20Standards/JC%202017%2049%20(...
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56 views

Implied volatility surface modelling in filtered historical simulation

What is the best way to model implied volatility surface in filtered historical simulation (other than keeping it constant)? Is it appropriate to apply GARCH-like model to every point on the surface? ...
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61 views

Resources on VaR modelling for derivative portfolios?

I'm interested in finding resources related to historical VaR calculation for derivative portfolios where both spot and implied volatility changes are accounted for. The resources I've been able to ...
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41 views

Incremental/marginal contribution to VaR in a simulation setting

Estimating marginal contributions to VaR in a simulation setting is apparently quite difficult (see e.g. this blog post) due to issues with sampling variability. My question is whether the following ...
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34 views

Advantage of copula over estimation based on historical data

It seems to me hard to intuitively understand the concept of copulas and their advantages. For example, why would it be better to estimate value at risk of portfolio by modelling its asset returns ...
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58 views

Value at Risk (VaR): Normal distribution with gamma distributed volatility

If I was to do a 99% VaR calculation on a portfolio with normally distributed returns $\mathcal{N} (\mu,\sigma)$, the 99% VaR would be $\mu - 2.33\sigma$. Instead of having a constant volatility, let'...
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58 views

Why is VaR metric still used?

It is well know that VaR is not subaddtive measure which means that condition $$ \text{VaR}(X+Y) \leq \text{VaR}(X) + \text{VaR}(Y), $$ where $X$ and $Y$ are portfolios, is not satisfied. As a ...
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52 views

How do you handle implied volatility performing a VaR Monte-Carlo simulation using a stochastic volatility process calibrated on the underlying

Say you have a portfolio consisting of options each having a market implied volatility. If you now use some stochastic volatility model like GARCH to calibrate the real world volatility of the ...
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62 views

Portfolio VaR of a hedge portfolio (long index, short future): What total exposure to take to calculate VaR?

Imagine a portfolio is made of 20m USD invested in equities and -18m USD of MSCI World futures (sell 18m USD short). The annualised volatility of the 20m USD in equities (Equ.) is 15% and the ...
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36 views

Summing up two VaRs

I know that normally you can't just add two VaRs straight ahead and you need to use the formula with the sum of squares and the square root. However, in the marking scheme for the task in the image ...
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36 views

ES using historic simulation

Why is the data obtained from 91-100 days all eliminated from the calculation of the 1-day 95% ES? My interpretation is because the first day to calculate the 95% ES should be the 90th day? But I can'...
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121 views

Kupiec Test Backtesting VaR

I am currently analyzing the Kupiec test used for backtesting $VaR$. Suppose that I backtest a $VaR$ system for $n$ days (for example 250), with a confidence interval of $1-\alpha$ (for example a $1-\...
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Expected Shortfall for ARMA-GARCH Model

I need to find an analytical solution for the 99% confidence expected shortfall (CVaR) for a long position of 100 dollars at time $t$ for an asset with returns modeled by an ARMA(1,1)-GARCH(1,1) model ...
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Payment Gateways' market risk: where does it come from?

Companies like Square and Adyen and Paypal are flourishing. They facilitate payments between people and business in various currencies and provide small loans. However as they are not banks they are ...
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166 views

Credit VaR Formula

in Chapter 23 of Hull's Options, Futures, and Derivatives he has an example (i.e. example 23.4) which shows how the Credit VaR formula is applied. The answer in the formula is 0.128. I can't seem to ...
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186 views

Analytical portfolio optimization for VaR under multivariate normality

Given a set of assets with returns following a multivariate normal distribution with a known mean vector and a known covariance matrix, $$ r \sim N(\mu,\Sigma), $$ I want to find optimal portfolio ...
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212 views

Manually calculating and backtesting VaR and CVaR from DCC-GARCH R

I estimated a GARCH fit to the log returns of three series (CAC 40, a french real estate index and french T10 bond yield series) using rugarch. I then manually ...
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302 views

Calculate the historical simulation VaR of the portfolio using Python

Assume that we have 200 stocks in WeiBo (WB), 300 stocks in Netflix (NFLX), 250 stocks in Ford Motor Company (F) and 150 in Royal Dutch Shell (RDS-A) as of 31 August 2019 in the portfolio. I have ...
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Problem in calculating a simple VaR

In Alexander, Gordon J. and Alexandre M. Baptista (2006). Does the Basle Capital Accord reduce bank fragility? An assessment of the value-at-risk approach. Journal of Monetary Economics 53(7), ...
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219 views

Missing data in historical simulation VaR

A historical simulation approach to VaR estimation relies on the availability of historical data. What do we do when there is no data (say, spot price and implied volatility surface) as, for example, ...
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58 views

How to calculate value at risk in accordance with Basel?

I would greatly appreciate if you could let me know whether Value at Risk should be calculated for net open position (foreign currency assets-foreign currency liabilities) or for foreign currency cash?...
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135 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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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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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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71 views

A quick and dirty loss distribution and Credit VaR

I need to create a loss distribution for a credit portfolio as the first steps to estimate the portfolio Credit VaR. I have historical monthly account snapshots (payment history) of all accounts ...
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905 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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214 views

VaR equivalent volatility meaning

I have a hard time with interpreting VeV. I mean - I see its just standard deviation derived from Cornish-Fischer VaR, but I don't really know how to interpret it. The formula for VeV is: ...
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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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141 views

Do correlated assets affect the price of a portfolio of derivatives?

I need to compute the value at risk of a given portfolio as an exercise for a class at university but I have trouble understanding how correlated assets affect the price of the portfolio. Could you ...
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178 views

GJR-GARCH model using garchFit function

I'm trying to use the garchFit function described here in order to define a GJR-GARCH model to estimate volatility and then forecast VaR. I tried using ...
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114 views

Monte Carlo VaR w/ Multivariate Normal vs. Parametric

In Aladdin's Monte Carlo VaR, the default setting for the joint distribution of factor returns is multivariate normal. Given that normal distributions do not capture the fat tails seen in empirical ...
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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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932 views

What should the half-life be in EWMA when calculating VaR from EWMA?

If we want to calculate an $x$-day VaR ($x$ is some time period in days) from an Exponentially Weighted Moving Average (EWMA) of vector of returns, what should the half-life in the decay factor in ...
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116 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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142 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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297 views

RiskMetrics VAR calculations and conditional distribution of sum of log returns

According to Tsay's book in Chapter 7, for the Risk Metrics model: A nice property of such a special random-walk IGARCH model is that the conditional distribution of a multiperiod return is ...
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114 views

Value at Risk Calculation

In historical simulation VaR, if we have stale data for some of our risk factors, which means daily returns on a particular risk factor is 0 on multiple occasions. Is there any way to solve this other ...
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1answer
87 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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84 views

How long is considered `long-term'?

For a project I am doing I need to simulate the balance sheet of a pension fund. In order to do so I also need to simulate euro inflation. Since my inflation data is non-stationary, I model it using ...
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Extreme Value Theory for Value-at-Risk: Advantage versus historical simulation?

I started researching this topic and it is well covered in the literature. My understanding is that it uses a historical time series of returns of a given set of stocks and represent such ...
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49 views

VaR calculation using excel gives different value than VaR using R at all c values except at c=0.5

This is VaR calculation in excel using variance-covariance method. This is VaR calculation in R. ...
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213 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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59 views

Parametric VaR assumption question

Why do you have to make a correlation matrix when calculating the parametric value at risk, if one of the assumptions for this method to work is that the assets of the portfolio must be independently ...
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210 views

VaR for Options portfolio

I'm asked to estimate VaR for Options portfolio. Firstly, I wanna try to estimate VaR for AAPL stock european call option using Historical Simulation but I can't find any Historical Data. I tried ...
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78 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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