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MRMM-11-non-parametric-approaches.html
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<!doctype html>
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<title>Market Risk Measurement and Management | Chapter 11 | Non-parametric Approaches</title>
<meta name="description" content="Financial Risk Manager Part 2 Study Materials">
<meta name="author" content="MacLane Wilkison">
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<section>
<h1>Chapter 11</h1>
<h3>Non-parametric Approaches</h3>
<p>
<small>Created for <a href="http://alchemistsacademy.com">Alchemists Academy</a> by <a href="http://alchemistsacademy.com/about">MacLane Wilkison</a></small>
</p>
</section>
<section>
<h2>Introduction</h2>
<ul>
<li>Non-parametric approaches aim to estimate risk measures without making strong assumptions about the relevant distribution</li>
<li>Assumes the near future will be similar to the recent past</li>
</ul>
</section>
<section>
<h2>Compiling Historical Simulation Data</h2>
<ul>
<li>P/L<sub>t</sub> = Σw<sub>i</sub>R<sub>i,t</sub></li>
<li>This is the P/L we <em>would have</em> earned on our current portfolio had we held it throughout the historical sample period</li>
</ul>
</section>
<section>
<h2>Estimation of Historical Simulation VaR and ES</h2>
<ul>
<li>Basic HS - plotting data on a simple histogram and reading off the VaR from the results</li>
<li>Bootstrapped HS - resampling from existing historical data set with replacement</li>
<li>HS using non-parametric density estimation - treats data as if it were drawn from some unspecified empirical distribution function</li>
</ul>
</section>
<section>
<h2>Estimating Confidence Intervals for HS VaR and ES</h2>
<ul>
<li>Order-statistics approach - provides a complete distribution function from which the confidence interval can be read</li>
<li>Bootstrap approach - produces a bootstrapped histogram of resampled estimates rom which the confidence interval can be read</li>
</ul>
</section>
<section>
<h2>Weighted Historical Simulation</h2>
<ul>
<li>Equal-weighted approach</li>
<li>Age-weighted approach: w<sub>i</sub> = [λ<sup>i-1</sup>(1-λ)]/(1-λ<sup>n</sup>)</li>
<li>Volatility-weighted approach</li>
<li>Correlation-weighted approach</li>
<li>Filtered approach</li>
</ul>
<aside class="notes">
The age-weighted approach discounts older observations in favor of new ones (λ is the decay rate). This approach has for major advantages: (1) allows a generalization of traditional HS as a special case with zero decay, (2) an appropriate choice for λ can make the esimates more responsive to large loss observations, (3) reduces distortions caused by events that are unlikely to recur, (4) enables the sample set to grow over time, eliminating ghost effects and improving efficiency. The volatility-weighted approach has several advantages: (1) accounts for volatility in a natural and direct way, (2) produces risk estimates that are appropriately sensitive to current volatility estimates, (3) allows us to obtain estimates that can exceed the maximum loss in our historical data set, (4) empirically, it produces superior estimates. The filtered approach combines the benefits of HS with the power and flexibility of conditional volatility models by bootstrapping returns within a conditional volatility framework.
</aside>
</section>
<section>
<h2>Overview of Non-parametric Methods</h2>
<img src="images/MRMM11/advantages-and-disadvantages.png" alt="advantages and disadvantages of non-parametric methods" />
</section>
<section>
<h1>THE END</h1>
<h3><a href="http://alchemistsacademy.com">AlchemistsAcademy.com</a></h3>
</section>
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