<!doctype html><htmllang=endir=ltrclass="blog-wrapper blog-post-page plugin-blog plugin-id-default"data-has-hydrated=false><metacharset=UTF-8><metaname=generatorcontent="Docusaurus v3.6.1"><titledata-rh=true>Autocallable Bonds | The Old Speice Guy</title><metadata-rh=truename=viewportcontent="width=device-width,initial-scale=1.0"><metadata-rh=truename=twitter:cardcontent=summary_large_image><metadata-rh=trueproperty=og:urlcontent=https://speice.io/2015/11/autocallable><metadata-rh=trueproperty=og:localecontent=en><metadata-rh=truename=docusaurus_localecontent=en><metadata-rh=truename=docusaurus_tagcontent=default><metadata-rh=truename=docsearch:languagecontent=en><metadata-rh=truename=docsearch:docusaurus_tagcontent=default><metadata-rh=trueproperty=og:titlecontent="Autocallable Bonds | The Old Speice Guy"><metadata-rh=truename=descriptioncontent="For a final project, my group was tasked with understanding three exotic derivatives: The Athena, Phoenix without memory, and Phoenix with memory autocallable products."><metadata-rh=trueproperty=og:descriptioncontent="For a final project, my group was tasked with understanding three exotic derivatives: The Athena, Phoenix without memory, and Phoenix with memory autocallable products."><metadata-rh=trueproperty=og:typecontent=article><metadata-rh=trueproperty=article:published_timecontent=2015-11-27T12:00:00.000Z><linkdata-rh=truerel=iconhref=/img/favicon.ico><linkdata-rh=truerel=canonicalhref=https://speice.io/2015/11/autocallable><linkdata-rh=truerel=alternatehref=https://speice.io/2015/11/autocallablehreflang=en><linkdata-rh=truerel=alternatehref=https://speice.io/2015/11/autocallablehreflang=x-default><scriptdata-rh=truetype=application/ld+json>{"@context":"https://schema.org","@id":"https://speice.io/2015/11/autocallable","@type":"BlogPosting","author":{"@type":"Person","name":"Bradlee Speice"},"dateModified":"2024-11-03T23:57:32.000Z","datePublished":"2015-11-27T12:00:00.000Z","description":"For a final project, my group was tasked with understanding three exotic derivatives: The Athena, Phoenix without memory, and Phoenix with memory autocallable products.","headline":"Autocallable Bonds","isPartOf":{"@id":"https://speice.io/","@type":"Blog","name":"Blog"},"keywords":[],"mainEntityOfPage":"https://speice.io/2015/11/autocallable","name":"Autocallable Bonds","url":"https://speice.io/2015/11/autocallable"}</script><linkrel=alternatetype=application/rss+xmlhref=/rss.xmltitle="The Old Speice Guy RSS Feed"><linkrel=alternatetype=application/atom+xmlhref=/atom.xmltitle="The Old Speice Guy Atom Feed"><linkrel=stylesheethref=/katex/katex.min.css><linkrel=stylesheethref=/assets/css/styles.16c3428d.css><scriptsrc=/assets/js/runtime~main.29a27dcf.jsdefer></script><scriptsrc=/assets/js/main.d461af80.jsdefer></script><bodyclass=navigation-with-keyboard><script>!function(){vart,e=function(){try{returnnewURLSearchParams(window.location.search).get("docusaurus-theme")}catch(t){}}()||function(){try{returnwindow.localStorage.getItem("theme")}catch(t){}}();t=null!==e?e:"light",document.documentElement.setAttribute("data-theme",t)}(),function(){try{for(var[t,e]ofnewURLSearchParams(window.location.search).entries())if(t.startsWith("docusaurus-data-")){vara=t.replace("docusaurus-data-","data-");document.documentElement.setAttribute(a,e)}}catch(t){}}()</script><divid=__docusaurus><divrole=regionaria-label="Skip to main content"><aclass=skipToContent_fXgnhref=#__docusaurus_skipToContent_fallback>Skip to main content</a></div><navaria-label=Mainclass="navbar navbar--fixed-top"><divclass=navbar__inner><divclass=navbar__items><buttonaria-label="Toggle navigation bar"aria-expanded=falseclass="navbar__toggle clean-btn"type=button><svgwidth=30height=30viewBox="0 0 30 30"aria-hidden=true><pathstroke=currentColorstroke-linecap=roundstroke-miterlimit=10stroke-width=2d="M4 7h22M4 15h22M4 23h22"/></svg></button><aclass=navbar__brandhref=/><divclass=navbar__logo><imgsrc=/img/logo.svgalt="Sierpi
<p>My only non-core class this semester has been in Structure Products. We've been surveying a wide variety of products, and the final project was to pick one to report on.
Because these are all very similar, we decided to demonstrate all 3 products at once.</p>
<p>What follows below is a notebook demonstrating the usage of <ahref=http://julialang.comtarget=_blankrel="noopener noreferrer">Julia</a> for Monte-Carlo simulation of some exotic products.</p>
<h2class="anchor anchorWithStickyNavbar_LWe7"id=underlying-simulation>Underlying simulation<ahref=#underlying-simulationclass=hash-linkaria-label="Direct link to Underlying simulation"title="Direct link to Underlying simulation"></a></h2>
<p>In order to price the autocallable bonds, we need to simulate the underlying assets. Let's go ahead and set up the simulation first, as this lays the foundation for what we're trying to do. We're going to use <ahref="http://finance.yahoo.com/q?s=jnj"target=_blankrel="noopener noreferrer">JNJ</a> as the basis for our simulation. This implies the following parameters:</p>
<ul>
<li><spanclass=katex><spanclass=katex-mathml><math><semantics><mrow><msub><mi>S</mi><mn>0</mn></msub></mrow><annotationencoding=application/x-tex>S_0</annotation></semantics></math></span><spanclass=katex-htmlaria-hidden=true><spanclass=base><spanclass=strutstyle=height:0.8333em;vertical-align:-0.15em></span><spanclass=mord><spanclass="mord mathnormal"style=margin-right:0.05764em>S</span><spanclass=msupsub><spanclass="vlist-t vlist-t2"><spanclass=vlist-r><spanclass=vliststyle=height:0.3011em><spanstyle=top:-2.55em;margin-left:-0.0576em;margin-right:0.05em><spanclass=pstrutstyle=height:2.7em></span><spanclass="sizing reset-size6 size3 mtight"><spanclass="mord mtight">0</span></span></span></span><spanclass=vlist-s></span></span><spanclass=vlist-r><spanclass=vliststyle=height:0.15em><span></span></span></span></span></span></span></span></span></span> = $102.2 (as of time of writing)</li>
<li><spanclass=katex><spanclass=katex-mathml><math><semantics><mrow><mi>r</mi></mrow><annotationencoding=application/x-tex>r</annotation></semantics></math></span><spanclass=katex-htmlaria-hidden=true><spanclass=base><spanclass=strutstyle=height:0.4306em></span><spanclass="mord mathnormal"style=margin-right:0.02778em>r</span></span></span></span> = [.49, .9, 1.21, 1.45, 1.69] (term structure as of time of writing, linear interpolation)</li>
<li><spanclass=katex><spanclass=katex-mathml><math><semantics><mrow><mi>μ</mi></mrow><annotationencoding=application/x-tex>\mu</annotation></semantics></math></span><spanclass=katex-htmlaria-hidden=true><spanclass=base><spanclass=strutstyle=height:0.625em;vertical-align:-0.1944em></span><spanclass="mord mathnormal">μ</span></span></span></span> = <spanclass=katex><spanclass=katex-mathml><math><semantics><mrow><mi>r</mi><mo>−</mo><mi>q</mi></mrow><annotationencoding=application/x-tex>r - q</annotation></semantics></math></span><spanclass=katex-htmlaria-hidden=true><spanclass=base><spanclass=strutstyle=height:0.6667em;vertical-align:-0.0833em></span><spanclass="mord mathnormal"style=margin-right:0.02778em>r</span><spanclass=mspacestyle=margin-right:0.2222em></span><spanclass=mbin>−</span><spanclass=mspacestyle=margin-right:0.2222em></span></span><spanclass=base><spanclass=strutstyle=height:0.625em;vertical-align:-0.1944em></span><spanclass="mord mathnormal"style=margin-right:0.03588em>q</span></span></span></span> (note that this implies a negative drift because of current low rates)</li>
<h3class="anchor anchorWithStickyNavbar_LWe7"id=defining-the-simulation>Defining the simulation<ahref=#defining-the-simulationclass=hash-linkaria-label="Direct link to Defining the simulation"title="Direct link to Defining the simulation"></a></h3>
<p>To make things simpler, we simulate a single year at a time. This allows us to easily add in a dividend policy without too much difficulty, and update the simulation every year to match the term structure. The underlying uses GBM for simulation between years.</p>
<h3class="anchor anchorWithStickyNavbar_LWe7"id=example-simulation>Example simulation<ahref=#example-simulationclass=hash-linkaria-label="Direct link to Example simulation"title="Direct link to Example simulation"></a></h3>
<p>Let's go ahead and run a sample simulation to see what the functions got us!</p>
<h3class="anchor anchorWithStickyNavbar_LWe7"id=computing-the-term-structure>Computing the term structure<ahref=#computing-the-term-structureclass=hash-linkaria-label="Direct link to Computing the term structure"title="Direct link to Computing the term structure"></a></h3>
<p>Now that we've got the basic motion set up, let's start making things a bit more sophisticated for the model. We're going to assume that the drift of the stock is the difference between the implied forward rate and the quarterly dividend rate.</p>
<p>We're given the yearly term structure, and need to calculate the quarterly forward rate to match this structure. The term structure is assumed to follow:</p>
<divclass="language-julia codeBlockContainer_Ckt0 theme-code-block"style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><divclass=codeBlockContent_biex><pretabindex=0class="prism-code language-julia codeBlock_bY9V thin-scrollbar"style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><codeclass=codeBlockLines_e6Vv><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain">forward_term </span><spanclass="token operator"style="color:hsl(221, 87%, 60%)">=</span><spanclass="token plain"></span><spanclass="token keyword"style="color:hsl(301, 63%, 40%)">function</span><spanclass="token punctuation"style="color:hsl(119, 34%, 47%)">(</span><spanclass="token plain">yearly_term</span><spanclass="token punctuation"style="color:hsl(119, 34%, 47%)">)</span><spanclass="token plain"></span><br></span><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"></span><spanclass="token comment"style="color:hsl(230, 4%, 64%)"># It is assumed that we have a yearly term structure passed in, and starts at year 0</span><spanclass="token plain"></span><br></span><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"></span><spanclass="token comment"style="color:hsl(230, 4%, 64%)"># This implies a nominal rate above 0 for the first year!</span><spanclass="token plain"></span><br></span><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"> years </span><spanclass="token operator"style="color:hsl(221, 87%, 60%)">=</span><spanclass="token plain"> length</span><spanclass="token punctuation"style="color:hsl(119, 34%, 47%)">(</span><spanclass="token plain">term</span><spanclass="token punctuation"style="color:hsl(119, 34%, 47%)">)</span><spanclass="token operator"style="color:hsl(221, 87%, 60%)">-</span><spanclass="token number"style="color:hsl(35, 99%, 36%)">1</span><spanclass="token plain"></span><spanclass="token comment"style="color:hsl(230, 4%, 64%)"># because we start at 0</span><spanclass="token plain"></span><br></span><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"> structure </span><spanclass="token operator"style="color:hsl(221, 87%, 60%)">=</span><spanclass="token plain"></span><spanclass="token punctuation"style="color:hsl(119, 34%, 47%)">[</span><spanclass="token punctuation"style="color:hsl(119, 34%, 47%)">(</span><spanclass="token plain">term</span><spanclass="token punctuation"style="color:hsl(119, 34%, 47%)">[</span><spanclass="token plain">i</span><spanclass="token operator"style="color:hsl(221, 87%, 60%)">+</span><spanclass="token number"style="color:hsl(35, 99%, 36%)">1</span><spanclass="token punctuation"style="color:hsl(119, 34%, 47%)">]</span><spanclass="token plain"></span><spanclass="token operator"style="color:hsl(221, 87%, 60%)">/</span><spanclass="token plain"> term</span><spanclass="token punctuation"style="color:hsl(119, 34%, 47%)">[</span><spanclass="token plain">i</span><spanclass="token punctuation"style="color:hsl(119, 34%, 47%)">]</span><spanclass="token punctuation"style="color:hsl(119, 34%, 47%)">)</span><spanclass="token plain"></span><spanclass="token keyword"style="color:hsl(301, 63%, 40%)">for</span><spanclass="token plain"> i</span><spanclass="token operator"style="color:hsl(221, 87%, 60%)">=</span><spanclass="token number"style="color:hsl(35, 99%, 36%)">1</span><spanclass="token punctuation"style="color:hsl(119, 34%, 47%)">:</span><spanclass="token plain">years</span><spanclass="token punctuation"style="color:hsl(119, 34%, 47%)">]</span><spanclass="token plain"></span><br></span><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"></span><spanclass="token keyword"style="color:hsl(301, 63%, 40%)">end</span><spanclass="token punctuation"style="color:hsl(119, 34%, 47%)">;</span><br></span></code></pre><divclass=buttonGroup__atx><buttontype=buttonaria-label="Copy code to clipboard"title=Copyclass=clean-btn>
<h3class="anchor anchorWithStickyNavbar_LWe7"id=illustrating-the-term-structure>Illustrating the term structure<ahref=#illustrating-the-term-structureclass=hash-linkaria-label="Direct link to Illustrating the term structure"title="Direct link to Illustrating the term structure"></a></h3>
<p>Now that we've got our term structure, let's validate that we're getting the correct results! If we've done this correctly, then:</p>
<h3class="anchor anchorWithStickyNavbar_LWe7"id=the-full-underlying-simulation>The full underlying simulation<ahref=#the-full-underlying-simulationclass=hash-linkaria-label="Direct link to The full underlying simulation"title="Direct link to The full underlying simulation"></a></h3>
<p>Now that we have the term structure set up, we can actually start doing some real simulation! Let's construct some paths through the full 5-year time frame. In order to do this, we will simulate 1 year at a time, and use the forward rates at those times to compute the drift. Thus, there will be 5 total simulations batched together.</p>
<h3class="anchor anchorWithStickyNavbar_LWe7"id=final-simulation>Final simulation<ahref=#final-simulationclass=hash-linkaria-label="Direct link to Final simulation"title="Direct link to Final simulation"></a></h3>
<p>We're now going to actually build out the full motion that we'll use for computing the pricing of our autocallable products. It will be largely the same, but we will use far more sample paths for the simulation.</p>
<h2class="anchor anchorWithStickyNavbar_LWe7"id=athena-simulation>Athena Simulation<ahref=#athena-simulationclass=hash-linkaria-label="Direct link to Athena Simulation"title="Direct link to Athena Simulation"></a></h2>
<p>Now that we've defined our underlying simulation, let's actually try and price an Athena note. Athena has the following characteristics:</p>
<ul>
<li>Automatically called if the underlying is above the <strong>call barrier</strong> at observation</li>
<li>Accelerated coupon paid if the underlying is above the <strong>call barrier</strong> at observation<!---->
<ul>
<li>The coupon paid is <spanclass=katex><spanclass=katex-mathml><math><semantics><mrow><mi>c</mi><mo>⋅</mo><mi>i</mi></mrow><annotationencoding=application/x-tex>c \cdot i</annotation></semantics></math></span><spanclass=katex-htmlaria-hidden=true><spanclass=base><spanclass=strutstyle=height:0.4445em></span><spanclass="mord mathnormal">c</span><spanclass=mspacestyle=margin-right:0.2222em></span><spanclass=mbin>⋅</span><spanclass=mspacestyle=margin-right:0.2222em></span></span><spanclass=base><spanclass=strutstyle=height:0.6595em></span><spanclass="mord mathnormal">i</span></span></span></span> with <spanclass=katex><spanclass=katex-mathml><math><semantics><mrow><mi>i</mi></mrow><annotationencoding=application/x-tex>i</annotation></semantics></math></span><spanclass=katex-htmlaria-hidden=true><spanclass=base><spanclass=strutstyle=height:0.6595em></span><spanclass="mord mathnormal">i</span></span></span></span> as the current year, and <spanclass=katex><spanclass=katex-mathml><math><semantics><mrow><mi>c</mi></mrow><annotationencoding=application/x-tex>c</annotation></semantics></math></span><spanclass=katex-htmlaria-hidden=true><spanclass=base><spanclass=strutstyle=height:0.4306em></span><spanclass="mord mathnormal">c</span></span></span></span> the coupon rate</li>
</ul>
</li>
<li>Principle protection up until a <strong>protection barrier</strong> at observation; All principle at risk if this barrier not met</li>
<divclass="codeBlockContainer_Ckt0 theme-code-block"style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><divclass=codeBlockContent_biex><pretabindex=0class="prism-code language-text codeBlock_bY9V thin-scrollbar"style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><codeclass=codeBlockLines_e6Vv><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"> Mean of simulation 1: $103.2805; Simulation time: 5.59s</span><br></span><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"> Mean of simulation 2: $103.3796; Simulation time: 5.05s</span><br></span><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"> Mean of simulation 3: $103.4752; Simulation time: 5.18s</span><br></span><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"> Mean of simulation 4: $103.4099; Simulation time: 5.37s</span><br></span><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"> Mean of simulation 5: $103.3260; Simulation time: 5.32s</span><br></span><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"> Mean over 5 simulations: 103.37421610015554</span><br></span><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"> Present value of Athena note: $95.00, notional: $100.00</span><br></span></code></pre><divclass=buttonGroup__atx><buttontype=buttonaria-label="Copy code to clipboard"title=Copyclass=clean-btn><spanclass=copyButtonIcons_eSgAaria-hidden=true><svgviewBox="0 0 24 24"class=copyButtonIcon_y97N><pathfill=currentColord="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svgviewBox="0 0 24 24"class=copyButtonSuccessIcon_LjdS><pathfill=currentColord=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z/></svg></span></button></div></div></div>
<h2class="anchor anchorWithStickyNavbar_LWe7"id=phoenix-without-memory-simulation>Phoenix without Memory Simulation<ahref=#phoenix-without-memory-simulationclass=hash-linkaria-label="Direct link to Phoenix without Memory Simulation"title="Direct link to Phoenix without Memory Simulation"></a></h2>
<p>Let's move into pricing a Phoenix without memory. It's very similar to the Athena production, with the exception that we introduce a coupon barrier so coupons are paid even when the underlying is below the initial price.</p>
<p>The Phoenix product has the following characteristics (example <ahref=https://www.rbccm.com/usstructurednotes/file-780079.pdftarget=_blankrel="noopener noreferrer">here</a>):</p>
<ul>
<li>Automatically called if the underlying is above the <strong>call barrier</strong> at observation</li>
<li>Coupon paid if the underlying is above a <strong>coupon barrier</strong> at observation</li>
<li>Principle protection up until a <strong>protection barrier</strong> at observation; All principle at risk if this barrier not met</li>
<li>Observed yearly</li>
</ul>
<p>Some example paths (all assume that a call barrier of the current price, and coupon barrier some level below that):</p>
<ul>
<li>At the end of year 1, the stock is above the call barrier; the note is called and you receive the value of the stock plus the coupon being paid.</li>
<li>At the end of year 1, the stock is above the coupon barrier, but not the call barrier; you receive the coupon. At the end of year 2, the stock is below the coupon barrier; you receive nothing. At the end of year 3, the stock is above the call barrier; the note is called and you receive the value of the stock plus a coupon for year 3.</li>
</ul>
<p>We're going to re-use the same simulation, with the following parameters:</p>
<ul>
<li>Call barrier: 100%</li>
<li>Coupon barrier: 70%</li>
<li>Coupon: 6%</li>
<li>Capital protection until 70% (at maturity)</li>
<divclass="codeBlockContainer_Ckt0 theme-code-block"style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><divclass=codeBlockContent_biex><pretabindex=0class="prism-code language-text codeBlock_bY9V thin-scrollbar"style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><codeclass=codeBlockLines_e6Vv><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"> Mean of simulation 1: $106.0562; Simulation time: 5.72s</span><br></span><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"> Mean of simulation 2: $106.0071; Simulation time: 5.85s</span><br></span><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"> Mean of simulation 3: $105.9959; Simulation time: 5.87s</span><br></span><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"> Mean of simulation 4: $106.0665; Simulation time: 5.93s</span><br></span><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"> Mean of simulation 5: $106.0168; Simulation time: 5.81s</span><br></span><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"> Mean over 5 simulations: 106.02850857209883</span><br></span><spanclass=token-linestyle="color:hsl(230, 8%, 24%)"><spanclass="token plain"> Present value of Phoenix without memory note: $97.44</span><br></span></code></pre><divclass=buttonGroup__atx><buttontype=buttonaria-label="Copy code to clipboard"title=Copyclass=clean-btn><spanclass=copyButtonIcons_eSgAaria-hidden=true><svgviewBox="0 0 24 24"class=copyButtonIcon_y97N><pathfill=currentColord="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svgviewBox="0 0 24 24"class=copyButtonSuccessIcon_LjdS><pathfill=currentColord=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z/></svg></span></button></div></div></div>
<h2class="anchor anchorWithStickyNavbar_LWe7"id=phoenix-with-memory-simulation>Phoenix with Memory Simulation<ahref=#phoenix-with-memory-simulationclass=hash-linkaria-label="Direct link to Phoenix with Memory Simulation"title="Direct link to Phoenix with Memory Simulation"></a></h2>
<p>The Phoenix with Memory structure is very similar to the Phoenix, but as the name implies, has a special "memory" property: <strong>It remembers any coupons that haven't been paid at prior observation times, and pays them all if the underlying crosses the coupon barrier</strong>. For example:</p>
<ul>
<li>Note issued with 100% call barrier, 70% coupon barrier. At year 1, the underlying is at 50%, so no coupons are paid. At year 2, the underlying is at 80%, so coupons for both year 1 and 2 are paid, resulting in a double coupon.</li>
</ul>
<p>You can also find an example <ahref=https://www.rbccm.com/usstructurednotes/file-781232.pdftarget=_blankrel="noopener noreferrer">here</a>.</p>
<p>Let's go ahead and set up the simulation! The parameters will be the same, but we can expect that the value will go up because of the memory attribute</p>
