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<!doctype html>
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<title>Drip-fixed-income by lakshmiDRIP</title>
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<h1>Drip-fixed-income</h1>
<p>DRIP Fixed Income</p>
<p class="view"><a href="https://github.com/lakshmiDRIP/DRIP-Fixed-Income">View the Project on GitHub <small>lakshmiDRIP/DRIP-Fixed-Income</small></a></p>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP-Fixed-Income/zipball/master">Download <strong>ZIP File</strong></a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP-Fixed-Income/tarball/master">Download <strong>TAR Ball</strong></a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP-Fixed-Income">View On <strong>GitHub</strong></a></li>
</ul>
</header>
<section>
<p align="center"><img src="https://github.com/lakshmiDRIP/DRIP/blob/master/DRIP_Logo.gif?raw=true" width="100"></p>
<p><strong>v2.63</strong> <em>1 March 2017</em></p>
<p>DRIP Fixed Income is a collection of Java libraries for Instrument/Trading Conventions, Treasury Futures/Options, Funding/Forward/Overnight Curves, Multi-Curve Construction/Valuation, Collateral Valuation and XVA Metric Generation, Calibration and Hedge Attributions, Statistical Curve Construction, Bond RV Metrics, Stochastic Evolution and Option Pricing, Interest Rate Dynamics and Option Pricing, LMM Extensions/Calibrations/Greeks, Algorithmic Differentiation, and Asset Backed Models and Analytics.</p>
<p>DRIP Fixed Income is composed of the following main libraries:</p>
<ul>
<li>Instrument/Trading Conventions Library</li>
<li>Treasury Futures/Options Library</li>
<li>Funding/Forward/Overnight Curve Library</li>
<li>Multi-Curve Construction/Valuation Library</li>
<li>Collateral and XVA Metrics Library</li>
<li>Position Horizon Analyzer Library</li>
<li>Statistical Curve Construction Library</li>
<li>Bond RV Metrics Library</li>
<li>Stochastic Evolution and Option Pricing Library</li>
<li>Interest Dynamics and Option Pricing Library</li>
<li>LMM Extensions, Calibration, and Greeks Library</li>
<li>Algorithmic Differentiation Library</li>
<li>Asset Backed Model Library</li>
</ul>
<p>For Installation, Documentation and Samples, and the associated supporting Numerical Libraries please check out <a href="https://github.com/lakshmiDRIP/DRIP">DRIP</a>.</p>
<h2>
<a id="drip-core-technical-specifications" class="anchor" href="#drip-core-technical-specifications" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>DRIP Core Technical Specifications</h2>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/DRIPSpecification/AssetAllocation/AssetAllocation_v2.56.pdf">Asset Allocation Library</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/DRIPSpecification/FixedIncome/FixedIncomeAnalytics_v2.58.pdf">Fixed Income Analytics</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/DRIPSpecification/TransactionCost/TransactionCostAnalytics_v2.57.pdf">Transaction Cost Analytics</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/DRIPSpecification/XVA/XVAAnalytics_v2.62.pdf">XVA Analytics</a></li>
</ul>
<h2>
<a id="drip-supporting-technical-specifications" class="anchor" href="#drip-supporting-technical-specifications" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>DRIP Supporting Technical Specifications</h2>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/DRIPSpecification/SplineBuilder/SplineBuilder_v0.82.pdf">Spline Builder Library</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/DRIPSpecification/NumericalOptimization/NumericalOptimization_v2.05.pdf">Numerical Optimization Library</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/DRIPSpecification/StatisticalLearning/StatisticalLearningLibrary_v0.80.pdf">Statistical Learning Library</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/DRIPSpecification/MachineLearning/MachineLearningLibrary_v0.92.pdf">Machine Learning Library</a></li>
</ul>
<h2>
<a id="additional-documentation" class="anchor" href="#additional-documentation" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Additional Documentation</h2>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP">DRIP GitHub Source</a></li>
<li><a href="https://lakshmidrip.github.io/DRIP/Javadoc/index.html">DRIP API Javadoc</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/ReleaseNotes">DRIP Release Notes</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/DRIPSpecification">DRIP Technical Specifications</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/External">DRIP External Specifications</a></li>
<li>User guide is a work in progress!</li>
</ul>
<h2>
<a id="samples-bondsasset-backed" class="anchor" href="#samples-bondsasset-backed" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Samples (Bonds/Asset Backed)</h2>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/assetbacked">Asset Backed Analytics</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/bond">Bond Core Analytics</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/bondapi">Bond RV Measures</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/bondfixed">Fixed Coupon Bond Analytics</a></li>
</ul>
<h2>
<a id="samples-curvesurface-construction" class="anchor" href="#samples-curvesurface-construction" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Samples (Curve/Surface Construction)</h2>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/forward">Forward Rate Curve</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/forwardratefuturesfeed">Forward Re-constitution</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/forwardvolatility">Forward Rate Volatility</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/funding">Funding Curve Construction</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/fundingfeed">Funding Re-constitution</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/fundinghistorical">Funding Historical Metrics</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/fx">FX Curve Construction</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/govvie">Govvie Curve Construction</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/multicurve">Multi Curve Construction</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/option">Option Surface Construction</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/overnight">Overnight Curve Construction</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/overnightfeed">Overnight Re-constitution</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/overnighthistorical">Overnight Historical Metrics</a></li>
</ul>
<h2>
<a id="samples-rates-products-valuation" class="anchor" href="#samples-rates-products-valuation" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Samples (Rates Products Valuation)</h2>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/bloomberg">Bloomberg Curve Analytics</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/cms">Constant Maturity Swap</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/piterbarg2012">Collateralized Curve Valuation</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/cross">Cross Currency Stream</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/dual">Dual Currency Swap</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/fedfund">Fed Fund Swap</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/fixfloat">Fix Float Swap</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/fixfloatpnl">IRS Horizon Attribution</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/floatfloat">Float Float Swap</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/forwardratefutures">Forward Rate Futures</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/forwardratefuturespnl">Forward Horizon Attribution</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/fra">Floating Rate Agreement</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/ois">Overnight Index Swap</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/oisapi">OIS Valuation Metrics</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/xccy">Cross Currency Definitions</a></li>
</ul>
<h2>
<a id="samples-treasury-bondfutures" class="anchor" href="#samples-treasury-bondfutures" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Samples (Treasury Bond/Futures)</h2>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/treasury">G10 Treasury Runs</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/treasuryfeed">Treasury Re-constitution</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/treasurypnl">Treasury Horizon Attribution</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/treasuryfutures">Treasury Futures Runs</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/treasuryfuturesfeed">Futures Re-constitution</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/treasuryfuturesapi">Treasury Futures Metrics</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/treasuryfuturespnl">Futures Horizon Attribution</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/treasuryfuturesrisk">Treasury Futures KRD</a></li>
</ul>
<h2>
<a id="samples-interest-rate-options" class="anchor" href="#samples-interest-rate-options" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Samples (Interest Rate Options)</h2>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/capfloor">IR Cap/Floor</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/fixfloatoption">Fix Float Option</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/hjm">HJM Model Dynamics</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/hullwhite">Hull White Dynamics</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/lmm">LMM Model Dynamics</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/sabr">SABR Model Dynamics</a></li>
</ul>
<h2>
<a id="samples-stochastic-volatility-pricing" class="anchor" href="#samples-stochastic-volatility-pricing" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Samples (Stochastic Volatility Pricing)</h2>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/stochasticvolatility">Stochastic Volatility Pricing</a></li>
</ul>
<h2>
<a id="samples-automatic-differentiation-sensitivity" class="anchor" href="#samples-automatic-differentiation-sensitivity" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Samples (Automatic Differentiation Sensitivity)</h2>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/sensitivity">Product/Curve Sensitivity</a></li>
</ul>
<h2>
<a id="samples-credit-productscurves" class="anchor" href="#samples-credit-productscurves" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Samples (Credit Products/Curves)</h2>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/credit">Credit Curve Analytics</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/creditfeed">CDX Re-constitution</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/credithistorical">CDX Historical Metrics</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/creditindexpnl">CDX Horizon Attribution</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/creditoption">CDS/CDX Option</a></li>
</ul>
<h2>
<a id="xva-metrics-estimation" class="anchor" href="#xva-metrics-estimation" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Samples (XVA Metrics Estimation)</h2>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/piterbarg2010">Funding Beyond Discounting</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/burgard2011">Dynamic XVA Portfolio Evolution</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/burgard2012">CVA Numeraire Estimaton</a></li>
</ul>
<h2>
<a id="features" class="anchor" href="#features" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Features</h2>
<h3>
<a id="instrumenttrading-conventions-library" class="anchor" href="#instrumenttrading-conventions-library" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Instrument/Trading Conventions Library</h3>
<h4>
<a id="associations-and-exchanges" class="anchor" href="#associations-and-exchanges" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Associations and Exchanges</h4>
<ul>
<li>Associations</li>
<li>Exchanges</li>
</ul>
<h4>
<a id="date-conventions" class="anchor" href="#date-conventions" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Date Conventions</h4>
<ul>
<li>Day Count Conventions</li>
<li>Business Day Conventions</li>
</ul>
<h4>
<a id="overnight-and-ibor-like-indexes" class="anchor" href="#overnight-and-ibor-like-indexes" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Overnight and IBOR-like Indexes</h4>
<ul>
<li>IBOR Indexes - Introduction</li>
<li>Main IBOR Indices</li>
<li>Other IBOR Indices</li>
<li>Overnight Index Definitions</li>
<li>Overnight Index Committees and Meeting Dates</li>
</ul>
<h4>
<a id="over-the-counter-instruments" class="anchor" href="#over-the-counter-instruments" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Over the Counter Instruments</h4>
<ul>
<li>Forward Rate Agreement</li>
<li>Interest Rate Swaps</li>
<li>Vanilla IRS</li>
<li>Interest Rate Swaps (Basis Swaps: IBORfor IBOR)</li>
<li>Cross Currency Swaps (IBOR for IBOR)</li>
<li>Constant Maturity Swaps</li>
<li>Swap Indexes</li>
<li>Overnight Indexed Swaps</li>
<li>Swap Option</li>
<li>Forex and Forward Swaps</li>
</ul>
<h4>
<a id="exchange-traded-instruments" class="anchor" href="#exchange-traded-instruments" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Exchange Traded Instruments</h4>
<ul>
<li>Overnight Futures</li>
<li>Short-Term Interest Rate Futures (STIR Futures)</li>
<li>Currency Specific Futures</li>
<li>Interest Rate Futures Option - Premium</li>
<li>Interest Rate Futures Option - Margin</li>
<li>Bank Bill Futures - AUD Style</li>
<li>Deliverable Swap (IRS) Futures (PV Quoted)</li>
<li>Bond Futures (non AUD/NZD)</li>
<li>Country Specific Bond Futures - USD</li>
<li>Country Specific Bond Futures - Germany</li>
<li>Country Specific Bond Futures - Spain</li>
<li>Country Specific Bond Futures - UK</li>
<li>Country Specific Bond Futures - Japan</li>
<li>Options on Bond Futures (non AUD/NZD) - Premium</li>
<li>Options on Bond Futures (non AUD/NZD) - Margin</li>
<li>AUD-NZD Bond Futures</li>
</ul>
<h3>
<a id="treasury-futuresoptions-library" class="anchor" href="#treasury-futuresoptions-library" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Treasury Futures/Options Library</h3>
<h4>
<a id="treasury-futures-trading-and-hedging" class="anchor" href="#treasury-futures-trading-and-hedging" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Treasury Futures Trading and Hedging</h4>
<ul>
<li>Contract Detail Specifications</li>
</ul>
<h4>
<a id="identification-of-the-ctd-in-the-basket" class="anchor" href="#identification-of-the-ctd-in-the-basket" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Identification of the CTD in the Basket</h4>
<ul>
<li>The Conversion Factor</li>
<li>Old vs. Active Treasury</li>
<li>Market Parameters Influencing the CTD Calculation</li>
<li>Impact of Yield Curve Changes</li>
</ul>
<h4>
<a id="valuation-of-treasury-futures-contract" class="anchor" href="#valuation-of-treasury-futures-contract" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Valuation of Treasury Futures Contract</h4>
<ul>
<li>Futures Contract and Mark-To-Market</li>
<li>Role of the Clearing Corporation</li>
<li>Delivery Options for the Underlying</li>
<li>Implied Basis for the Futures</li>
<li>Net Basis For Treasury Futures</li>
</ul>
<h3>
<a id="fundingforwardovernight-curve-library" class="anchor" href="#fundingforwardovernight-curve-library" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Funding/Forward/Overnight Curve Library</h3>
<h4>
<a id="curve-builder-features" class="anchor" href="#curve-builder-features" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Curve Builder Features</h4>
<ul>
<li>Discount Curves</li>
</ul>
<h4>
<a id="curve-construction-methodology" class="anchor" href="#curve-construction-methodology" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Curve Construction Methodology</h4>
<ul>
<li>Approach</li>
<li>State Span Design Components</li>
<li>Curve Calibration From Instruments/Quotes</li>
<li>Calibration Considerations</li>
</ul>
<h4>
<a id="curve-construction-formulation" class="anchor" href="#curve-construction-formulation" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Curve Construction Formulation</h4>
<ul>
<li>Segment Linear Discount Curve Calibration</li>
<li>Curve Jacobian</li>
</ul>
<h4>
<a id="stream-based-calibration" class="anchor" href="#stream-based-calibration" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Stream Based Calibration</h4>
<ul>
<li>Latent State Formulation Metric (LSFM)</li>
<li>Stream Inference Setup</li>
<li>Coupon Period Based Calibration Specification</li>
<li>Stream Based Calibration Specification</li>
<li>Calibration of Multi-Stream Components</li>
</ul>
<h4>
<a id="spaning-splines" class="anchor" href="#spaning-splines" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Spaning Splines</h4>
<ul>
<li>Setup and Formulation</li>
<li>Challenges with the Spanning Spline Approach</li>
</ul>
<h4>
<a id="monotone-descreasing-splines" class="anchor" href="#monotone-descreasing-splines" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Monotone Descreasing Splines</h4>
<ul>
<li>Exponential Rational Basis Spline</li>
<li>Exponential Mixture Basis Set</li>
</ul>
<h4>
<a id="hagan-west-2006-smoothness-preserving-spanning-spline" class="anchor" href="#hagan-west-2006-smoothness-preserving-spanning-spline" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Hagan-West (2006) Smoothness Preserving Spanning Spline</h4>
<ul>
<li>Monotone/Convexity Preserving Estimator</li>
<li>Positivity Preserving</li>
<li>Ameliorating Estimator</li>
<li>Harmonic Spline Extension to the Framework above</li>
<li>Minimal Quadratic Estimator</li>
</ul>
<h4>
<a id="extrapolation-in-curve-construction" class="anchor" href="#extrapolation-in-curve-construction" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Extrapolation in Curve Construction</h4>
<h4>
<a id="multi-pass-curve-construction" class="anchor" href="#multi-pass-curve-construction" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Multi-Pass Curve Construction</h4>
<ul>
<li>Bear-Sterns Multi-Pass Curve Building Techniques</li>
</ul>
<h4>
<a id="transition-spline-or-stitching-spline" class="anchor" href="#transition-spline-or-stitching-spline" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Transition Spline (Or Stitching Spline)</h4>
<ul>
<li>Stretch Modeling using Transition Splines</li>
<li>Stretch Partition/Isolation in Transition Splines</li>
<li>Knot Insertion vs. Transition Splines</li>
<li>Overlapping Stretches</li>
</ul>
<h4>
<a id="penalizing-exactcloseness-of-fit-and-curvature-penalty" class="anchor" href="#penalizing-exactcloseness-of-fit-and-curvature-penalty" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Penalizing Exact/Closeness of Fit and Curvature Penalty</h4>
<h4>
<a id="indextenor-basis-swaps" class="anchor" href="#indextenor-basis-swaps" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Index/Tenor Basis Swaps</h4>
<ul>
<li>Component Layout and Motivation</li>
<li>Formulation</li>
</ul>
<h4>
<a id="multi-stretch-merged-curve-construction" class="anchor" href="#multi-stretch-merged-curve-construction" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Multi-Stretch Merged Curve Construction</h4>
<ul>
<li>Merge Stretch Calibration</li>
</ul>
<h4>
<a id="latent-state-manifest-measure-sensitivity" class="anchor" href="#latent-state-manifest-measure-sensitivity" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Latent State Manifest Measure Sensitivity</h4>
<ul>
<li>Float-Float Manifest Measure Sensitivities</li>
<li>Multi-reset Floating Period</li>
</ul>
<h4>
<a id="ois-valuation-and-curve-construction" class="anchor" href="#ois-valuation-and-curve-construction" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>OIS Valuation and Curve Construction</h4>
<ul>
<li>Base Framework and Environment Setup</li>
<li>OIS Valuation Extensions and Approximations</li>
<li>OIS-FX Basis Swap Valuation and Approximations</li>
<li>Arithmetic Accrual Convexity Correction</li>
<li>Composed Period Latent State Loadings</li>
</ul>
<h4>
<a id="spline-based-credit-curve-calibration" class="anchor" href="#spline-based-credit-curve-calibration" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Spline Based Credit Curve Calibration</h4>
<h3>
<a id="multi-curve-constructionvaluation-library" class="anchor" href="#multi-curve-constructionvaluation-library" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Multi-Curve Construction/Valuation Library</h3>
<h4>
<a id="correlated-multi-curve-build-out" class="anchor" href="#correlated-multi-curve-build-out" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Correlated Multi-Curve Build-out</h4>
<ul>
<li>Standard FRA Setup</li>
<li>Standard FRA Options</li>
<li>No arbitrage and Counter-party Risk Based Standard FRA Formulation</li>
<li>Market FRA Setup</li>
<li>Futures</li>
<li>Multi-Curve Swap Valuation</li>
</ul>
<h4>
<a id="cross-currency-basis-swap" class="anchor" href="#cross-currency-basis-swap" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Cross Currency Basis Swap</h4>
<ul>
<li>Product Details and Valuation</li>
<li>Building the CCS Discount Curve</li>
<li>Custom CCBS Based Curve Construction SKU</li>
<li>Mark-To-Market Cross-Currency Swap Valuation</li>
<li>Mark-To-Market Cross-Currency Swap - Valuation Formulation</li>
<li>Absolute/Relative MTM Application</li>
<li>Per-Trade Risk Isolation Components</li>
</ul>
<h3>
<a id="collateral-and-xva-metrics-library" class="anchor" href="#collateral-and-xva-metrics-library" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Collateral and XVA Metrics Library</h3>
<h4>
<a id="collateral-agreements-and-derivatives-valuation" class="anchor" href="#collateral-agreements-and-derivatives-valuation" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Collateral Agreements and Derivatives Valuation</h4>
<ul>
<li>Two Collateralized Assets</li>
<li>Setup pf the Collateral Curve Dynamics</li>
<li>Collateralized Black-Scholes Formulation</li>
<li>Collateralization and Funding Derivative Valuation</li>
<li>Collateral PDE Formulation</li>
<li>Formward Contract Valuation</li>
<li>European Style Options</li>
<li>Cross-Currency Model</li>
<li>Collateral Choice Model</li>
</ul>
<h4>
<a id="cva-and-funding-adjustments-pde" class="anchor" href="#cva-and-funding-adjustments-pde" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>CVA and Funding Adjustments PDE</h4>
<ul>
<li>Counterparty Risk and Funding Costs</li>
<li>Notation, Symbology, and Key PDE's</li>
<li>Model Setup and the Derivation of the Bilateral Risky PDE</li>
<li>Using VHat (T, S) and Mark-To-Market at Default</li>
<li>Using V (T, S) and Mark-To-Market at Default</li>
<li>Funding and Default Payoff Examples</li>
<li>Counter-party Funding and PDE Extensions</li>
<li>Balance Sheet and Funding Cost Management</li>
<li>Unified Framework for Bilateral Counterpart Risk and Funding Adjustments</li>
<li>Simple Model for the Impact of Derivative Asset on Balance Sheet and Funding</li>
<li>Balance Sheet Management to Mitigate Funding Costs</li>
<li>Funding Strategies and Costs Impact</li>
<li>Generalized Semi-replication and Pricing PDE</li>
<li>Semi-replication</li>
<li>Examples of Different Bond Portfolios</li>
<li>The Perfect Replication - FCA Vanishes</li>
<li>Semi-replication with no Shortfall at own Default</li>
<li>Set-offs</li>
<li>Semi-replication with a Single Bond</li>
<li>Burgard and Kjaer (2013) Case Study</li>
</ul>
<h4>
<a id="accounting-for-otc-derivatives-funding-adjustments-and-re-hypothecation-option" class="anchor" href="#accounting-for-otc-derivatives-funding-adjustments-and-re-hypothecation-option" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Accounting for OTC Derivatives: Funding Adjustments and Re-hypothecation Option</h4>
<ul>
<li>Status of Currenct FCA/FBA Accounting</li>
<li>Comaprison between FCA/FBA and FVA/FDA</li>
<li>OTC vs. Repo Markets</li>
<li>Modus Operandi of Funding Desks</li>
<li>MTM and the Asset Liability Symmetry</li>
<li>Rigorous Framework for Funding Costs</li>
<li>Funding Set VM RHO Computation</li>
<li>Shortcomings of Traditional CVA Systems</li>
<li>Addressing the Shortcomings of FCA/FBA Accounting</li>
<li>Valuation Adjustment Estimation Framework Setup</li>
<li>OTC Bookds Funding Set Decomposition</li>
<li>Inconsistent Booking under the FCA/FBA</li>
<li>Improvements Offered by the FVA/FDA Accounting</li>
<li>CET1 Deductions</li>
<li>"Going Concern" or Defaulable Banks</li>
<li>Cash Flow Streams Categorization</li>
<li>Accounting Rules</li>
<li>Contra-Asset and Contra-Liability Accounting for Credit Risk</li>
<li>Contra-Asset and Contra-Liability Accounting for Funding</li>
<li>Accounting Cash Flow Setup Framework</li>
<li>Cash Flows related to VM Funding</li>
<li>Cash Flows at Counter-party Default</li>
<li>Cash Flows at Bank Default</li>
<li>CVA and DVA</li>
<li>FVA and FDA</li>
<li>FCA and FBA</li>
<li>CA and CL Adjustments</li>
<li>Own Credit Sensitivities</li>
<li>Triggers and Close-out Adjustments</li>
<li>Collateral Triggers and Close-outs</li>
<li>Incorporating ISDA 1992 Close-outs</li>
<li>VM Re-hypothecability across Funding Sets</li>
<li>Trade and Portfolio FTP Estimation</li>
<li>FTP for FCA/FBA Accounting</li>
<li>FTP for FVA/FDA Accounting</li>
<li>Exit Prices and Fair Valuation</li>
<li>FVA/FDA Accounting</li>
<li>FCA/FBA Accounting</li>
<li>Liquidity Spreads, Asset Liability Symmetry, and Alternative Allocations for Excess Collateral</li>
<li>Working Capital Management and Operations</li>
<li>Equity Gain and Debt Gain</li>
<li>Liquidity Based Analysis and Treatment</li>
<li>Problems with Gain Accounting</li>
<li>Albanese and Andersen (2014) Case Study</li>
<li>Case Study Setting and Purpose</li>
<li>Scenario Estimation of the XVA Metrics</li>
<li>Product and Scenario Threshold Type Scenarios</li>
<li>XVA Error Metrics and Incrementals</li>
<li>Estimation ofthe FCA/FBA - FVA/FDA Mismatch</li>
<li>Traditional Challenges with Derivative Accounting</li>
<li>Problems with FCA/FBA Accounting</li>
<li>FVA/FDA vs. FCA/FBA Enhancement</li>
<li>Trading Staff Point of View</li>
<li>Challenges with the XVA Metric Estimation</li>
<li>Shortfalls of the FVA/FDA Scheme</li>
<li>Alternate Specialized Value Metrics</li>
</ul>
<h3>
<a id="position-horizon-analyzer-library" class="anchor" href="#position-horizon-analyzer-library" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Position Horizon Analyzer Library</h3>
<h4>
<a id="convexity-corrections-associated-with-margining" class="anchor" href="#convexity-corrections-associated-with-margining" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Convexity Corrections Associated with Margining</h4>
<h4>
<a id="hedging-considerations" class="anchor" href="#hedging-considerations" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Hedging Considerations</h4>
<h4>
<a id="product-curve-effect-attribution" class="anchor" href="#product-curve-effect-attribution" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Product Curve Effect Attribution</h4>
<ul>
<li>Market Value Change Explain Components</li>
<li>Coupon Accrual Intrinsic</li>
<li>Market Parameters Intrinsic</li>
<li>Market Parameters Extrinsic</li>
<li>Market Value Change Effects Formulation</li>
</ul>
<h3>
<a id="statistical-curve-construction-library" class="anchor" href="#statistical-curve-construction-library" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Statistical Curve Construction Library</h3>
<h4>
<a id="inference-based-curve-construction" class="anchor" href="#inference-based-curve-construction" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Inference Based Curve Construction</h4>
<ul>
<li>Curve Smoothing in Finance</li>
<li>Bayesian Curve Calibration</li>
<li>Sequential Curve Estimation</li>
</ul>
<h3>
<a id="bond-rv-metrics-library" class="anchor" href="#bond-rv-metrics-library" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Bond RV Metrics Library</h3>
<ul>
<li>The Bond RV Measure Set</li>
<li>Asset Swap Spread</li>
<li>Bond Basis</li>
<li>Convexity</li>
<li>Credit Basis</li>
<li>Discount Margin</li>
<li>Duration</li>
<li>DV01</li>
<li>G Spread</li>
<li>I Spread</li>
<li>Macaulay Duration</li>
<li>Modified Duration</li>
<li>Option Adjusted Spread</li>
<li>Par Asset Swap Spread</li>
<li>Par Spread</li>
<li>Par Equivalent CDS Spread (PECS)</li>
<li>Price</li>
<li>Spread Over Treasury Benchmark</li>
<li>Yield</li>
<li>Yield Basis</li>
<li>Yield Spread</li>
<li>Yield01</li>
<li>Zero Discount Margin (ZDM)</li>
<li>Z Spread</li>
<li>Relative Value Cross-Metric Grid</li>
<li>Basic Measures</li>
</ul>
<h3>
<a id="stochastic-evolution-and-option-pricing-library" class="anchor" href="#stochastic-evolution-and-option-pricing-library" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Stochastic Evolution and Option Pricing Library</h3>
<h4>
<a id="stochastic-calculus" class="anchor" href="#stochastic-calculus" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Stochastic Calculus</h4>
<ul>
<li>Single-Factor Stochastic Calculus</li>
<li>Multi-Factor Stochastic Calculus</li>
<li>Risk Neutral Pricing Framework</li>
</ul>
<h4>
<a id="black-scholes-methodology" class="anchor" href="#black-scholes-methodology" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Black Scholes Methodology</h4>
<ul>
<li>The Replication Technique</li>
<li>Capital Asset Pricing Model</li>
<li>Multi-numeraire Formulation</li>
<li>First Order Log-normal Black Scholes Greeks</li>
<li>Second Order Log-normal Black Scholes Greeks</li>
<li>Third Order Log-normal Black Scholes Greeks</li>
<li>Time-Dependent Black Scholes</li>
<li>Local Volatility Models</li>
<li>Black Normal Model Specification and Dynamics</li>
<li>Options on Forward</li>
<li>The Black76 Model</li>
</ul>
<h4>
<a id="stochastic-volatility-models-the-heston-model" class="anchor" href="#stochastic-volatility-models-the-heston-model" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Stochastic Volatility Models: The Heston Model</h4>
<ul>
<li>Model Specification and Dynamics</li>
<li>Price Estimation Through Characteristic Functions</li>
<li>Fourier Inversion in Characteristic Function</li>
</ul>
<h4>
<a id="dynamical-latent-state-calibration" class="anchor" href="#dynamical-latent-state-calibration" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Dynamical Latent State Calibration</h4>
<ul>
<li>Fokker-Planck Equations</li>
<li>Volatility Observations vs. Calibrations</li>
</ul>
<h3>
<a id="interest-rate-dynamics-and-option-pricing-library" class="anchor" href="#interest-rate-dynamics-and-option-pricing-library" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Interest Rate Dynamics and Option Pricing Library</h3>
<h4>
<a id="hjm-model" class="anchor" href="#hjm-model" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>HJM Model</h4>
<ul>
<li>Formulation</li>
<li>Hull-White from HJM</li>
<li>G2++ - A 2-Factor HJM Model</li>
<li>HJM to LMM</li>
<li>HJM PCA</li>
</ul>
<h4>
<a id="hull-white-model" class="anchor" href="#hull-white-model" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Hull-White Model</h4>
<ul>
<li>Short-Rate Formulation</li>
<li>Hull-White Trinomial Tree</li>
<li>Construction of the Symmetric Trinomial Tree</li>
<li>Displacing the Nodes of the Trinomial Tree</li>
</ul>
<h4>
<a id="market-model-fo-interest-rate-dynamics" class="anchor" href="#market-model-fo-interest-rate-dynamics" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Market Model fo Interest Rate Dynamics</h4>
<ul>
<li>Nomenclature and Notation</li>
<li>The BGM Model</li>
<li>LIBOR Rate Dynamics</li>
<li>Relation to the HJM Dynamics</li>
<li>Existence, Uniqueness, and Regularity of the LIBOR Dynamics Solution</li>
<li>Upper/Lower Bounds for the LIBOR Rate</li>
<li>Invariant Measure for the LIBOR Rate</li>
<li>BGM Cap/Floor Pricing</li>
<li>Payer Swap Option Pricing</li>
<li>Payer Swap Option Pricing Simplification</li>
<li>Mismatched Periods Cap/Swaption Pricing</li>
<li>Approximate vs. Full Simulation Comparisons</li>
<li>Typical Model Calibration Results</li>
</ul>
<h4>
<a id="the-sabr-model" class="anchor" href="#the-sabr-model" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>The SABR Model</h4>
<ul>
<li>Parameter Estimation</li>
</ul>
<h3>
<a id="lmm-extensions-calibration-and-greeks-library" class="anchor" href="#lmm-extensions-calibration-and-greeks-library" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>LMM Extensions, Calibration, and Greeks Library</h3>
<h4>
<a id="lmm-calibration-and-greeks-overview" class="anchor" href="#lmm-calibration-and-greeks-overview" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>LMM Calibration and Greeks Overview</h4>
<ul>
<li>Robust LMM Calibration Approaches Overview</li>
<li>Cross-Currency LIBOR Market Model</li>
<li>LMM Based Greeks Calculation Approaches</li>
<li>Major Extensions to LMM</li>
<li>Hedging the Derivatives Cash Flow</li>
<li>LMM Skew and its Calibration</li>
<li>LMM Smile and its Calibration</li>
<li>Cross-Currency Extensions to LMM</li>
<li>LMM Monte-Carlo Methods and Greeks</li>
<li>Numerical Methods for LMM Calibration</li>
</ul>
<h3>
<a id="algorithmic-differentiation-library" class="anchor" href="#algorithmic-differentiation-library" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Algorithmic Differentiation Library</h3>
<ul>
<li>Algorithmic Differentiation in Finance</li>
<li>Program Sequence Construction Modes</li>
<li>Canonicalization - Program Statements Simplification by Decomposition</li>
<li>Challenges of Automating the Differentiation</li>
<li>Wengert Representation and Optimal Program Structure Synthesis</li>
<li>Optimization using Pre-accumulation and Check-Pointing</li>
<li>Algorithmic Differentiation Financial Application Space Customization</li>
<li>Sensitivity Generation During Curve Construction</li>
<li>Curve Jacobian</li>
<li>Stochastic Entity Evolution - Sensitivity Formulation</li>
<li>Sensitivities to Stochastic State Variates and Dynamical Parameters</li>
<li>State Variate Evolution Constrained by Splines</li>
<li>Formulation of the Evolution of the Stochastic Variate Self-Jacbian</li>
<li>Correlated Stochastic Variates Evolution</li>
<li>LMM Forward Rate Evolution</li>
<li>Formulation of the Pay-off Function Stochastic Evolution</li>
<li>Path Greeks</li>
<li>Pay-off Sensitivity to the Correlation Matrix</li>
<li>Algorithmic Differentiation in Pay-off Sensitivities Calculation</li>
<li>Bermudan Swap Option Sensitivities Formulation</li>
<li>Bermudan Swap Option Sensitivites Greek Estimation</li>
<li>LSM Methodology</li>
<li>NTD Basket Sensitivities Product Formulation</li>
<li>Basket Options</li>
</ul>
<h3>
<a id="asset-backed-model-library" class="anchor" href="#asset-backed-model-library" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Asset Backed Model Library</h3>
<ul>
<li>Overview of the Credit Model Methodology</li>
<li>Scope of the Model</li>
<li>Data Model Construction Rules</li>
<li>Loan Data Quality Rules</li>
<li>Lending Club Loan Level Data</li>
<li>Loan Credit Model Implementation</li>
<li>Credit Model Selection Methodology</li>
<li>Regressor Contribution Weights</li>
<li>Empirical Analysis of Seasoning Effects</li>
<li>Analysis of the Vintage/Cohort Effects</li>
<li>Analysis of the Empirical Seasonality Effects</li>
<li>CPR and CDR Curve Estimation</li>
<li>Credit Model Enhancements</li>
</ul>
<h2>
<a id="contact" class="anchor" href="#contact" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Contact</h2>
<p><a href="mailto:[email protected]">[email protected]</a></p>
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