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MRMM-5-the-art-of-term-structure-models-drift.html
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<!doctype html>
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<head>
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<title>Market Risk Measurement and Management | Chapter 5 | The Art of Term Structure Models: Drift</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 5</h1>
<h3>The Art of Term Structure Models: Drift</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>Model 1: Normal Distribution/No Drift</h2>
<p>dr = σdw</p>
<img src="images/MRMM5/normally-distributed-rates-and-no-drift.png" alt="rate tree with normally distributed rates and no drift" />
<aside class="notes">
'r' = the rate. 'σ√(dt)' is the standard deviation of the change in the rate. In practice, this model does not accurately reflect term structure rates and has a downward-sloping term structure due to the absence of drift and the effect of convexity.
</aside>
</section>
<section>
<h2>Model 2: Drift and Risk Premium</h2>
<p>dr = λdt + σdw</p>
<img src="images/MRMM5/drift-and-risk-premium.png" alt="rate tree incorporating drift and risk premium" />
<aside class="notes">
This model incorporates drift (interpreted as a risk premium) in order to build a more economically robust model.
</aside>
</section>
<section>
<h2>The Ho-Lee Model: Time-Dependent Drift</h2>
<p>dr = λ<sub>t</sub>dt + σdw</p>
<img src="images/MRMM5/the-ho-lee-model.png" alt="Ho-Lee rate tree" />
<aside class="notes">
In contrast to model 2, the drift is time-dependent.
</aside>
</section>
<section>
<h2>The Vasicek Model: Mean Reversion</h2>
<ul>
<li>dr = k(θ-r)dt + σdw</li>
<li>Non-recombining rate tree</li>
<aside class="notes">
'θ' is the long-run value (or central tendency) of the short-term rate and 'k' is a constant denoting the speed of mean reversion.
</aside>
</section>
<section>
<h1>THE END</h1>
<h3><a href="http://alchemistsacademy.com">AlchemistsAcademy.com</a></h3>
</section>
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