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MRMM-9-var-mapping.html
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<!doctype html>
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<head>
<meta charset="utf-8">
<title>Market Risk Measurement and Management | Chapter 9 | VaR Mapping</title>
<meta name="description" content="Financial Risk Manager Part 2 Study Materials">
<meta name="author" content="MacLane Wilkison">
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<body>
<div class="reveal">
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<div class="slides">
<section>
<h1>Chapter 9</h1>
<h3>VaR Mapping</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>
<p><em>A process by which the current values of the portfolio positions are replaced by exposures on the risk factors</em></p>
</section>
<section>
<h2>Mapping for Risk Measurement</h2>
<img src="images/MRMM9/mapping-instruments-on-risk-factors.png" alt="mapping instruments on risk factors diagram" />
<aside class="notes">
Mapping is a method for simplifying many postitions by aggregating them across a set of primitive risk factors.
</aside>
</section>
<section>
<h2>Mapping Fixed-Income Portfolios</h2>
<ul>
<li>Primary mapping techniques:</li>
<ul>
<li>Principal mapping</li>
<li>Duration mapping</li>
<li>Cash-flow mapping</li>
</ul>
</ul>
<aside class="notes">
With principal mapping, one risk factor is chosen that corresponds to the average portfolio maturity. With duration mapping, one risk factor is chosen that corresponds to the portfolio duration. With cash-flow mapping, the portfolio cash flows are grouped into maturity buckets.
</aside>
</section>
<section>
<h2>Mapping Linear Derivatives</h2>
<ul>
<li>Forward contracts</li>
<ul>
<li>f<sub>t</sub> = S<sub>t</sub>e<sup>-yτ</sup>-Ke<sup>-rτ</sup> = F<sub>t</sub>e<sup>-rτ</sup>-Ke<sup>-rτ</sup> = (F<sub>t</sub>-K)e<sup>-rτ</sup></li>
<li>Long forward contract = long foreign currency spot + long foreign currency bill + short US dollar bill</li>
</ul>
<li>Commodity forwards</li>
<ul>
<li>Convenience yield - benefit from holding the cash product</li>
</ul>
<li>Forward rate agreements</li>
<ul>
<li>(1+R<sub>2</sub>τ<sub>2</sub>=(1+R<sub>1</sub>τ<sub>1</sub>)[1+F<sub>1,2</sub>(τ<sub>2</sub>-τ<sub>1</sub>)]</li>
</ul>
<li>Interest rate swaps</li>
</ul>
<aside class="notes">
Forward contracts: 'S<sub>t</sub>' = spot price of one unit of the underlying cash asset, 'K' = contracted forward rate, 'F<sub>t</sub>' = current forward rate, 'r' = risk-free rate, 'y' = income flow on the asset, 'τ' = time to maturity. Forward rate agreements are forward contracts that allow users to lock in an interest rate at some future date. The long locks in a borrowing rate, the short locks in a lending rate.
</aside>
</section>
<section>
<h2>Mapping Options</h2>
<ul>
<li>Black-Scholes: c = Se<sup>-r*τ</sup>N(d<sub>1</sub>)-Ke<sup>-rτ</sup>N(d<sub>2</sub>)</li>
<ul>
<li>d<sub>1</sub> = [ln(Se<sup>-r*τ</sup>/Ke<sup>-rτ</sup>)]/(σ√τ) + (σ√τ)/2</li>
<li>d<sub>2</sub> = d<sub>1</sub> - σ√τ</li>
</ul>
</ul>
<aside class="notes">
'K' = exercise price of option.
</aside>
</section>
<section>
<h1>THE END</h1>
<h3><a href="http://alchemistsacademy.com">AlchemistsAcademy.com</a></h3>
</section>
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