<h3>Define the concept of Value-at-Risk (VaR)</h3>
Value-at- Risk (VaR) is a general measure of risk developed to equate risk across products and to aggregate risk on a portfolio basis. VaR is defined as the predicted worst-case loss with a specific confidence level (for example, 95%) over a period of time (for example, 1 day). For example, every afternoon, J.P. Morgan takes a snapshot of its global trading positions to estimate its DEaR (Daily-Earnings-at-Risk), which is a VaR measure defined as the 95% confidence worst-case loss over the next 24 hours due to adverse price moves.
<h3>Multiple Levels</h3>
The elegance of the solution is that it works on multiple levels, from the position-specific micro level to the portfolio-based macro level. VaR has become a common language for communication about aggregate risk taking, both within an organization and outside (for example, with analysts, regulators, and shareholders).


<h3>Benefits of VaR</h3>
<ul class="list2">
	<li>Measures risk, not notional exposure--relates risk to capacity</li>
	<li>Provides comparable risk measure across business groups</li>
	<li>Facilitates aggregation of risk--portfolio effects</li>
	<li>Can compare risk to daily profit and loss (P&amp;L)--reality check</li>
	<li>Facilitates stress testing--hidden concentration</li>
</ul>
<h3>Four Basic Questions</h3>

A VaR system seeks to answer:

1. How much can I lose? - Bottom line focus

2. Where would losses be concentrated? - Measure concentration by business group, region and risk type.

3. Which exposures offset each other? - highlight offsetting positions or hedges and diversifications.

4. How much return to expect? - Target appropriate return for risk taken.

<h3>Time Horizon</h3>

The application of the VaR concept is a fundamental component of the RiskMetrics® framework.
A VaR of USD 100 means that on average, only 1 day in 20 would you expect to lose more than
USD 100 due to market movements.

This definition of VaR uses a 5% risk level:
You would anticipate exceeding your VaR amount only 5% of the time (or, 95% of the
time you expect to lose less than your VaR amount) over a 1-day horizon.

Value at Risk (VaR)

We earlier saw how VaR can be calculated using the parametric method. We will now look at this method in detail, and also understand how VaR can be easily calculated using matrices.
 
<h3>VaR of a Single Asset</h3> 
 
<p class="definition">VaR of a single asset is the value of the asset multiplied by its volatility. Here, the volatility can be calculated at the desired confidence level.</p> 
 
<h2>Example:</h2> 
<p>An IBM stock is trading at $115 with a 1-year standard deviation of 20%.
 
In the normal distribution, 95% confidence level is 1.645 standard deviations away from the mean. 
 
Therefore, our VaR at 95% confidence level will be:
 
VaR (95%) = 115* 0.20 * 1.645
=  37.835

<div class="special-area">
<strong>Assumption of Normality</strong>

<p>A distribution is described as normal if there is a high probability that any observation
form the population sample will have a value that is close to the mean, and a low
probability of having a value that is far from the mean. The normal distribution curve
is used by many VaR models, which assume that asset returns follow a normal
pattern. A VaR model uses the normal curve to estimate the losses that an institution
may suffer over a given time period. Normal distribution tables show the probability
of a particular observation moving a certain distance from the mean.
 
<br><br>If we look along a normal distribution table we see that at -1.645 standard deviations,
the probability is 5%; this means that there is a 5% probability that an observation
will be at least 1.645 standard deviations below the mean. This level is used in many
VaR models.
</p> 
</div>

<h3>VaR of a Portfolio</h3>

<p>Generally VaR will not be calculated for a single position, but a portfolio of positions. 
In such a case will require the portfolio volatility.</p> 
 
<p>The portfolio volatility of a two-asset portfolio is given by:</p> 

<div  style="text-align:left;" class="formula"> 
<a href="https://financetrain.com/wp-content/uploads/2010/07/var_portfolio.gif"><img src="https://financetrain.com/wp-content/uploads/2010/07/var_portfolio.gif" alt="" title="var_portfolio" width="564" height="73" class="alignnone size-full wp-image-425" /></a>
 
<br><p>Where:</p> 
 
<ul class="list2" style="font-weight:normal;"> 
<li>$latex w_{1} $ is the weighting of the first asset</li> 
<li>$latex w_{2} $ is the weighting of the second asset</li> 
<li>$latex \sigma_{1} $ is the standard deviation or volatility of the first asset</li> 
<li>$latex \sigma_{2} $ is the standard deviation or volatility of the second asset</li> 
<li>$latex \rho $ is the correlation coefficient between the two assets</li> 
</ul> 
</div> 
 
<p> 
The VaR will then be given by:
</p> 
<div  style="text-align:left;" class="formula"> 
<a href="https://financetrain.com/wp-content/uploads/2010/07/var_formula.gif"><img src="https://financetrain.com/wp-content/uploads/2010/07/var_formula.gif" alt="" title="var_formula" width="261" height="48" class="alignnone size-full wp-image-430" /></a>
 
<br><p>Where:</p> 
 
<ul class="list2" style="font-weight:normal;"> 
<li>VaR <sub>(1 - $latex \alpha $)</sub> is the estimated VaR at the confidence level 100 × (1 - $latex \alpha $)%.</li> 
<li>$latex Z_{\alpha} $ represents the no. of standard deviations on the left side of the mean, at the required standard deviation.</li> 
 
</ul> </div>

<h3>VaR of a Portfolio - Example</h3>

<p>Let us assume that we want to calculate Parametric VaR at a 95% confidence level over a one-day horizon on a portfolio composed of two assets with the following assumptions:</p> 
 
<ul class="list2" style="font-weight:normal;"> 
<li>P = $100 million</li> 
<li>$latex w_{1} $ = 50%</li> 
<li>$latex w_{2} $ = 50%</li> 
<li>$latex \sigma_{1} $  = 3%</li> 
<li>$latex \sigma_{2} $ = 5%</li> 
<li>$latex \rho $ = 30%</li> 
</ul> 
 
<div  style="text-align:left;" class="formula"> 
<a href="https://financetrain.com/wp-content/uploads/2010/07/var_example.gif"><img src="https://financetrain.com/wp-content/uploads/2010/07/var_example.gif" alt="" title="var_example" width="638" height="94" class="alignnone size-full wp-image-433" /></a>
</div>

<h3>Portfolio of n Assets</h3>

<p>If the portfolio is bigger than 2 assets, the volatility of the portfolio is expressed using matrix notation:</p> 
 
 
<div  style="text-align:left;" class="formula"> 
<a href="https://financetrain.com/wp-content/uploads/2010/07/var_covar_formula.gif"><img src="https://financetrain.com/wp-content/uploads/2010/07/var_covar_formula.gif" alt="" title="var_covar_formula" width="480" height="124" class="alignnone size-full wp-image-434" /></a>
<br><p>Where:</p> 
 
<ul class="list2" style="font-weight:normal;"> 
<li >$latex w $ is the vector of the weights of the n assets.</li> 
<li>$latex w' $ is the transpose vector of $latex w $</li> 
<li>$latex \sum $ is the covariance matrix of the n assets</li> 
</ul> 
</div> 
<p>This is the reason why this method is also known as Variance Covariance method.</p> 

<h3>Variance Covariance Method - Examples</h3>

<h2>Example 1 – Two Asset Portfolio</h2> 
<p>This spreadsheet takes the same example above and recalculates the VaR using the matrices.</p> 
<p class="attachment"><a href='https://financetrain.com/wp-content/uploads/2010/07/Parametric-VaR.xls'>Two Asset Portfolio VaR <img src="https://financetrain.com/wp-content/uploads/2010/07/excel-icon-1281.png" alt="" title="excel-icon-128" width="128" height="128" class="alignnone size-full wp-image-437" /></a></p> 
<h2>Example 2 – Three Asset Portfolio</h2> 
<p>This spreadsheet shows the VaR calculation of a three-asset portfolio.</p> 
<p class="attachment"><a href='https://financetrain.com/wp-content/uploads/2010/07/Parametric_VaR_3_assets1.xls'>Three Asset Portfolio VaR <img src="https://financetrain.com/wp-content/uploads/2010/07/excel-icon-1281.png" alt="" title="excel-icon-128" width="128" height="128" class="alignnone size-full wp-image-437" /></a></p> 
<p>It is easy from there to expand the calculation to a portfolio of n assets. But be aware that you will soon reach the limits of Excel as we will have to calculate n(n-1)/2 terms for your covariance matrix.</p> 

Analytical Approach to Calculating VaR (Variance-Covariance Method)

The fundamental assumption of the Historical Simulations methodology is that you base your results on the past performance of your portfolio and make the assumption that the past is a good indicator of the near-future.  

The below algorithm illustrates the straightforwardness of this methodology. It is called Full Valuation because we will re-price the asset or the portfolio after every run. This differs from a Local Valuation method in which we only use the information about the initial price and the exposure at the origin to deduce VaR.

<h2>Step 1 – Calculate the returns (or price changes) of all the assets in the portfolio between each time interval.</h2>

The first step lies in setting the time interval and then calculating the returns of each asset between two successive periods of time. 

Generally, we use a daily horizon to calculate the returns, but we could use monthly returns if we were to compute the VaR of a portfolio invested in alternative investments (Hedge Funds, Private Equity, Venture Capital and Real Estate) where the reporting period is either monthly or quarterly. 
 
Historical Simulations VaR requires a long history of returns in order to get a meaningful VaR. Indeed, computing a VaR on a portfolio of Hedge Funds with only a year of return history will not provide a good VaR estimate.

<h2>Step 2 – Apply the price changes calculated to the current mark-to-market value of the assets and re-value your portfolio.</h2>

Once we have calculated the returns of all the assets from today back to the first day of the period of time that is being considered – let us assume one year comprised of 265 days – we now consider that these returns may occur tomorrow with the same likelihood. For instance, we start by looking at the returns of every asset yesterday and apply these returns to the value of these assets today. That gives us new values for all these assets and consequently a new value of the portfolio. 
 
Then, we go back in time by one more time interval to two days ago. We take the returns that have been calculated for every asset on that day and assume that those returns may occur tomorrow with the same likelihood as the returns that occurred yesterday. 
 
We re-value every asset with these new price changes and then the portfolio itself. And we continue until we have reached the beginning of the period. 
 
In this example, we will have had 264 simulations.
 
<h2>Step 3 – Sort the series of the portfolio-simulated P&L from the lowest to the highest value.</h2>

After applying these price changes to the assets 264 times, we end up with 264 simulated values for the portfolio and thus P&Ls. 
 
Since VaR calculates the worst expected loss over a given horizon at a given confidence level under normal market conditions, we need to sort these 264 values from the lowest to the highest as VaR focuses on the tail of the distribution.
 
<h2>Step 4 – Read the simulated value that corresponds to the desired confidence level.</h2>

The last step is to determine the confidence level we are interested in – let us choose 99% for this example. 
 
One can read the corresponding value in the series of the sorted simulated P&Ls of the portfolio at the desired confidence level and then take it away from the mean of the series of simulated P&Ls. 
 
In other words, the VaR at 99% confidence level is the mean of the simulated P&Ls minus the 1% lowest value in the series of the simulated values. 
 
This can be formulated as follows: 

<div  style="text-align:left;" class="formula"> 
<a href="https://financetrain.com/wp-content/uploads/2010/07/var_historical.gif"><img src="https://financetrain.com/wp-content/uploads/2010/07/var_historical.gif" alt="" title="var_historical" width="277" height="56" class="alignnone size-full wp-image-448" /></a>
 
<p>Where:</p> 
 
<ul class="list2" style="font-weight:normal;"> 
<li>VaR (1 - $latex \alpha $) is the estimated VaR at the confidence level 100 × (1 - $latex \alpha $)%.</li> 
<li>$latex \mu $(R) is the mean of the series of simulated returns or P&Ls of the portfolio</li> 
<li>R$latex _{\alpha} $ is the worst return of the series of simulated P&Ls of the portfolio or, in other words, the return of the series of simulated P&Ls that corresponds to the level of significance $latex \alpha $</li> 
</ul> 
</div> 
 
<div class="special-area">
<strong>Need for Interpolation</strong>
We may need to proceed to some interpolation since there will be no chance to get a value at 99% in our example. Indeed, if we use 265 days, each return calculated at every time interval will have a weight of 1/264 = 0.00379. If we want to look at the value that has a cumulative weight of 99%, we will see that there is no value that matches exactly 1% (since we have divided the series into 264 time intervals and not a multiple of 100). Considering that there is very little chance that the tail of the empirical distribution is linear, proceeding to a linear interpolation to get the 99% VaR between the two successive time intervals that surround the 99th percentile will result in an estimation of the actual VaR. This would be a pity considering we did all that we could to use the empirical distribution of returns, wouldn’t it? Nevertheless, even a linear interpolation may give you a good estimate of your VaR. For those who are more eager to obtain the exact VaR, the Extreme Value Theory (EVT) could be the right tool for you. We will explain in another article how to use EVT when computing VaR. It is rather mathematically demanding and would require us to spend more time to explain this method. 
</div> 

Calculating VaR Using Historical Simulation

Monte Carlo Simulations correspond to an algorithm that generates random numbers that are used to compute a formula that does not have a closed (analytical) form – this means that we need to proceed to some trial and error in picking up random numbers/events and assess what the formula yields to approximate the solution. Drawing random numbers over a large number of times (a few hundred to a few million depending on the problem at stake) will give a good indication of what the output of the formula should be.

<a href="https://financetrain.com/wp-content/uploads/2010/07/roulette.jpg"><img class="alignright size-medium wp-image-467" title="roulette" src="https://financetrain.com/wp-content/uploads/2010/07/roulette-298x300.jpg" alt="" width="298" height="300" /></a>It is believed actually that the name of this method stems from the fact that the uncle of one of the researchers (the Polish mathematician Stanislaw Ulam) who popularized this algorithm used to gamble in the Monte Carlo casino and/or that the randomness involved in this recurring methodology can be compared to the game of roulette.

We will now look at how Monte Carlo simulation can be applied to Value at Risk.

As we know, Monte Carlo Simulations correspond to an algorithm that generates random numbers that are used to compute a formula that does not have a closed (analytical) form – this means that we need to proceed to some trial and error in picking up random numbers/events and assess what the formula yields to approximate the solution. Drawing random numbers over a large number of times (a few hundred to a few million depending on the problem at stake) will give a good indication of what the output of the formula should be.

In the section, we will present the algorithm, and apply it to compute the VaR for a sample stock.

Computing VaR with Monte Carlo Simulations is very similar to Historical Simulations. The main difference lies in the first step of the algorithm – instead of using the historical data for the price (or returns) of the asset and assuming that this return (or price) can re-occur in the next time interval, we generate a random number that will be used to estimate the return (or price) of the asset at the end of the analysis horizon.
<h2>Step 1 – Determine the time horizon t for our analysis and divide it equally into small time periods, i.e. dt = t/n).</h2>
For illustration, we will compute a monthly VaR consisting of twenty-two trading days. Therefore n = 22 days and $latex \delta t $ = 1 day. In order to calculate daily VaR, one may divide each day per the number of minutes or seconds comprised in one day – the more, the merrier.

The main guideline here is to ensure that $latex \delta t $ is large enough to approximate the continuous pricing we find in the financial markets. This process is called discretization, whereby we approximate a continuous phenomenon by a large number of discrete intervals.
<h2>Step 2 – Draw a random number from a random number generator and update the price of the asset at the end of the first time increment.</h2>
It is possible to generate random returns or prices. In most cases, the generator of random numbers will follow a specific theoretical distribution. This may be a weakness of the Monte Carlo Simulations compared to Historical Simulations, which uses the empirical distribution. When simulating random numbers, we generally use the normal distribution.

In this article, we use the standard stock price model to simulate the path of a stock price from the ith day as defined by:
<div class="formula" style="text-align: left;"><a href="https://financetrain.com/wp-content/uploads/2010/07/stock_path_disc.gif"><img class="alignnone size-full wp-image-471" title="stock_path_disc" src="https://financetrain.com/wp-content/uploads/2010/07/stock_path_disc.gif" alt="" width="452" height="60" /></a>&nbsp;

Where:
<ul class="list2" style="font-weight: normal;">
	<li>R<sub>i</sub> is the return of the stock on the ith day</li>
	<li>S<sub>i</sub> is the stock price on the ith day</li>
	<li>S<sub>i+1</sub> is the stock price on the i+1th day</li>
	<li>$latex \mu $ is the sample mean of the stock price</li>
	<li>$latex \delta t $ is the timestep</li>
	<li>$latex \sigma $ is the sample volatility (standard deviation) of the stock price</li>
	<li>$latex \epsilon $ is a random number generated from a normal distribution</li>
</ul>
</div>
At the end of this step/day ($latex \delta t $ = 1 day), we have drawn a random number and determined S<sub>i+1</sub> since all other parameters can be determined or estimated.
<h2>Step 3 – Repeat Step 2 until reaching the end of the analysis horizon T by walking along the N time intervals.</h2>
At the next step/day ($latex \delta t $ = 2), we draw another random number and determine S<sub>i+2</sub> from S<sub>i+1</sub> using the same equation. We repeat this procedure until we reach T and can determine S<sub>i+T</sub>. In our example, S<sub>i+22</sub> represents the estimated (terminal) stock price in one month time of the sample share.
<h2>Step 4 – Repeat Steps 2 and 3 a large number M of times to generate M different paths for the stock over T.</h2>
So far, we have generated one path for this stock (from i to i+22). Running Monte Carlo Simulations means that we build a large number M of paths to take account of a broader universe of possible ways the stock price can take over a period of one month from its current value (S<sub>i</sub>) to an estimated terminal price <sub>i+T</sub>. Indeed, there is no unique way for the stock to go from S<sub>i</sub> to S<sub>i+T</sub>. Moreover, S<sub>i+T</sub> is only one possible terminal price for the stock amongst an infinity. Indeed, for a stock price being defined on (a set of positive numbers), there is an infinity of possible paths from S<sub>i</sub> to S<sub>i+T</sub>.

It is an industry standard to run at least 10,000 simulations even if 1,000 simulations provide an efficient estimator of the terminal price of most assets. In this paper, we ran 1,000 simulations for illustration purposes.
<h2>Step 5 – Rank the M terminal stock prices from the smallest to the largest, read the simulated value in this series that corresponds to the desired (1-$latex \alpha $)% confidence level (95% or 99% generally) and deduce the relevant VaR, which is the difference between S<sub>i</sub> and the ath lowest terminal stock price.</h2>
Let us assume that we want the VaR with a 99% confidence interval. In order to obtain it, we will need first to rank the M terminal stock prices from the lowest to the highest.

Then we read the 1% lowest percentile in this series. This estimated terminal price, S<sub>i+T</sub><sup>1%</sup> means that there is a 1% chance that the current stock price S<sub>i</sub> could fall to S<sub>i+T</sub><sup>1%</sup> or less over the period in consideration and under normal market conditions.

If S<sub>i+T</sub><sup>1%</sup> is smaller than Si (which is the case most of the time), then S<sub>i</sub> - S<sub>i+T</sub><sup>1%</sup> will corresponds to a loss. This loss represents the VaR with a 99% confidence interval.

In the next post, we will show you an example where we will apply the above steps to calculate the value at risk of an asset.

Calculating VaR using Monte Carlo Simulation

<p>In the previous post, we learned the algorithm to compute VaR using Monte Carlo Simulation. Let us compute VaR for one share to illustrate the algorithm.</p>
<p>We apply the algorithm to compute the monthly VaR for one stock. We will only consider the share price and thus work with the assumption we have only one share in our portfolio. Therefore the value of the portfolio corresponds to the value of one share.</p>
<p>The following assumptions are made:</p>
<table class="mytable" style="margin-left: 10px; width: 300px;" cellspacing="0">
<tbody>
<tr>
<td class="first-row">Current share price</td>
<td class="first-row">$20</td>
</tr>
<tr>
<td>Drift</td>
<td>10%</td>
</tr>
<tr>
<td class="alt">Volatility</td>
<td class="alt">20%</td>
</tr>
</tbody>
</table>
<p>Members  can download the attached spreadsheet below that shows the calculation of VaR using Monte Carlo Simulation.</p>

Monte Carlo Simulation - Example

Financial Institutions are often faced with risks other than normal market risk. That is especially true with derivative transactions. In derivative transactions, institutions need to increase their estimate of allowable loss amount by incorporating the following risks:
<ul>
	<li>Pre-settlement      risk</li>
	<li>Settlement      risk</li>
</ul>
Pre-settlement risk is the risk that a counterparty will default on a derivative transaction prior to the contract’s settlement at expiration (payment risk).

Settlement risk is a risk that a counterparty will default on a derivative transaction on the counterparty’s settlement (closing risk).

Attempts to mitigate these risks are known as bilateral payment netting and bilateral closing netting. By recognizing these risks institutions are attempting to estimate a value for this risk component and incorporate it into their calculations.

Aside from the trading business of financial institutions, recent attempts have been made to apply VaR concepts to the loan side.

A loan made to counterparty exposes a financial institution to credit risk. Credit risk is defined as the risk resulting from uncertainty in a counterparty’s ability or willingness to meet its contractual obligation.

In assessing credit risk from a counterparty, an institution must consider two issues:
<ul>
	<li>Credit      Quality: This encompasses both the likelihood of the counterparty      defaulting as well as possible recovery rates in the event of a default.</li>
	<li>Credit      Exposure: In the event of a default, what is the replacement cost of the      counterparty’s outstanding obligations likely to be?</li>
</ul>
Credit risk is typically reduced by collateralization. Under a collateralization arrangement, a party who owes an obligation to another party posts collateral. This collateral typically consists of cash versus securities to secure their obligation. One possible method for determining the VaR of a loan portfolio would be the Monte Carlo technique. This would generate random occurrences for various levels of default consequences that could be used to construct a probability distribution with its own mean and standard deviation. By attempting to evaluate credit risk, a VaR calculation can be performed on all assets and liabilities of a financial institution.

Apart from, this financial institutions are also using VaR to measure operational risk.

Application of VaR to Non-Market Areas

There are three major methodologies for calculating VaR.
<ul>
 	<li>Parametric</li>
 	<li>Monte Carlo</li>
 	<li>Historical</li>
</ul>
Note that the risk of nonlinear instruments (for example, options) is more complex to estimate than the risk of linear instruments (for example, traditional stocks, bonds, swaps, forwards, and futures), which can be approximated with simple formulas.

Financial instruments are nonlinear when their price does not change by a constant amount given a small movement in an underlying reference asset.

<strong>Brief Description</strong>

Brief description and use of each approach:<strong>
</strong>
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<th valign="top" width="197"><strong>Type</strong></th>
<th valign="top" width="197"><strong>Description</strong></th>
<th valign="top" width="197"><strong>Use</strong></th>
</tr>
<tr>
<td valign="top" width="197">Parametric</td>
<td valign="top" width="197">Estimates VaR with equation that specifies parameters (for example, volatility and correlation) as input.</td>
<td valign="top" width="197">Accurate for traditional assets and linear derivatives, but less accurate for nonlinear derivatives</td>
</tr>
<tr>
<td valign="top" width="197">Monte Carlo</td>
<td valign="top" width="197">Estimates VaR by simulating random scenarios and revaluing instruments in the portfolio</td>
<td valign="top" width="197">Appropriate for all types of instruments, linear or nonlinear</td>
</tr>
<tr>
<td valign="top" width="197">Historical</td>
<td valign="top" width="197">Estimates VaR by reliving history; we take actual

historical rates and revalue a portfolio for each

change in the market</td>
<td valign="top" width="197">Appropriate for all types of instruments, linear or non-linear</td>
</tr>
</tbody>
</table>
<strong>Advantages and Disadvantages</strong>
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<th valign="top" width="127"><strong>Type</strong></th>
<th valign="top" width="266"><strong>Advantages</strong></th>
<th valign="top" width="197"><strong>Disadvantages</strong></th>
</tr>
<tr>
<td valign="top" width="127">Parametric</td>
<td valign="top" width="266">Fast and simple to calculate</td>
<td valign="top" width="197">Less accurate for non-linear portfolios</td>
</tr>
<tr>
<td valign="top" width="127">Monte

Carlo</td>
<td valign="top" width="266">
<ul>
 	<li>Accurate for non-linear instruments</li>
 	<li>You get a full distribution of potential portfolios (not just a specific percentile)</li>
 	<li>You can use various distributional assumptions (normal, T-distribution, and so on)</li>
</ul>
</td>
<td valign="top" width="197">Takes a lot of computational power (and hence a

longer time to estimate results)</td>
</tr>
<tr>
<td valign="top" width="127">Historical</td>
<td valign="top" width="266">
<ul>
 	<li>Accurate for non-linear instruments</li>
 	<li>You get a full distribution of potential portfolios (not just a specific percentile)</li>
 	<li>No need to make distributional assumptions</li>
</ul>
</td>
<td valign="top" width="197">
<ul>
 	<li>You need a significant amount of daily rate history (at least a year, preferably much more)</li>
 	<li>You need significant computational power for revaluing the portfolio under each scenario.</li>
</ul>
</td>
</tr>
</tbody>
</table>
From a user's perspective, the important point to remember is that if you have significant nonlinear exposures in your portfolio, a simulation approach will generally be more accurate for estimating VaR than a parametric approximation--however, at the cost of greater complexity and computational requirements.

<strong>Three Approaches</strong>

All three approaches for estimating VaR have something to offer and can be used together to get a more robust estimate of VaR. For example, a parametric approach may be used to get an instant snapshot of risks taken during a trading day, while a simulation approach may be used to provide a fuller picture of risks (in particular, nonlinear risks) on a next-day basis.

Three Methodologies for Calculating VaR

Value at Risk

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