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1 line
39 KiB
JavaScript
1 line
39 KiB
JavaScript
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"use strict";(self.webpackChunkspeice_io=self.webpackChunkspeice_io||[]).push([["3241"],{11859:function(e,n,s){s.r(n),s.d(n,{assets:function(){return o},contentTitle:function(){return l},default:function(){return h},frontMatter:function(){return r},metadata:function(){return a},toc:function(){return m}});var a=s(48279),i=s(85893),t=s(50065);let r={slug:"2015/11/autocallable",title:"Autocallable Bonds",date:new Date("2015-11-27T12:00:00.000Z"),authors:["bspeice"],tags:[]},l=void 0,o={authorsImageUrls:[void 0]},m=[{value:"Underlying simulation",id:"underlying-simulation",level:2},{value:"Defining the simulation",id:"defining-the-simulation",level:3},{value:"Example simulation",id:"example-simulation",level:3},{value:"Computing the term structure",id:"computing-the-term-structure",level:3},{value:"Illustrating the term structure",id:"illustrating-the-term-structure",level:3},{value:"The full underlying simulation",id:"the-full-underlying-simulation",level:3},{value:"Final simulation",id:"final-simulation",level:3},{value:"Athena Simulation",id:"athena-simulation",level:2},{value:"Phoenix without Memory Simulation",id:"phoenix-without-memory-simulation",level:2},{value:"Phoenix with Memory Simulation",id:"phoenix-with-memory-simulation",level:2}];function c(e){let n={a:"a",annotation:"annotation",code:"code",h1:"h1",h2:"h2",h3:"h3",hr:"hr",img:"img",li:"li",math:"math",mi:"mi",mn:"mn",mo:"mo",mrow:"mrow",msub:"msub",p:"p",pre:"pre",semantics:"semantics",span:"span",strong:"strong",ul:"ul",...(0,t.a)(),...e.components};return(0,i.jsxs)(i.Fragment,{children:[(0,i.jsx)(n.p,{children:"For a final project, my group was tasked with understanding three exotic derivatives: The Athena, Phoenix without memory, and Phoenix with memory autocallable products."}),"\n",(0,i.jsx)(n.p,{children:"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.\nBecause these are all very similar, we decided to demonstrate all 3 products at once."}),"\n",(0,i.jsxs)(n.p,{children:["What follows below is a notebook demonstrating the usage of ",(0,i.jsx)(n.a,{href:"http://julialang.com",children:"Julia"})," for Monte-Carlo simulation of some exotic products."]}),"\n",(0,i.jsx)(n.hr,{}),"\n",(0,i.jsx)(n.pre,{children:(0,i.jsx)(n.code,{className:"language-julia",children:"using Gadfly\n"})}),"\n",(0,i.jsx)(n.h1,{id:"athenaphoenix-simulation",children:"Athena/Phoenix Simulation"}),"\n",(0,i.jsx)(n.h2,{id:"underlying-simulation",children:"Underlying simulation"}),"\n",(0,i.jsxs)(n.p,{children:["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 ",(0,i.jsx)(n.a,{href:"http://finance.yahoo.com/q?s=jnj",children:"JNJ"})," as the basis for our simulation. This implies the following parameters:"]}),"\n",(0,i.jsxs)(n.ul,{children:["\n",(0,i.jsxs)(n.li,{children:[(0,i.jsxs)(n.span,{className:"katex",children:[(0,i.jsx)(n.span,{className:"katex-mathml",children:(0,i.jsx)(n.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,i.jsxs)(n.semantics,{children:[(0,i.jsx)(n.mrow,{children:(0,i.jsxs)(n.msub,{children:[(0,i.jsx)(n.mi,{children:"S"}),(0,i.jsx)(n.mn,{children:"0"})]})}),(0,i.jsx)(n.annotation,{encoding:"application/x-tex",children:"S_0"})]})})}),(0,i.jsx)(n.span,{className:"katex-html","aria-hidden":"true",children:(0,i.jsxs)(n.span,{className:"base",children:[(0,i.jsx)(n.span,{className:"strut",style:{height:"0.8333em",verticalAlign:"-0.15em"}}),(0,i.jsxs)(n.span,{className:"mord",children:[(0,i.jsx)(n.span,{className:"mord mathnormal",style:{marginRight:"0.05764em"},children:"S"}),(0,i.jsx)(n.span,{className:"msupsub",children:(0,i.jsxs)(n.span,{className:"vlist-t vlist-t2",children:[(0,i.jsxs)(n.span,{className:"vlist-r",children:[(0,i.jsx)(n.span,{className:"vlist",style:{height:"0.3011em"},children:(0,i.jsxs)(n.span,{style:{top:"-2.55em",marginLeft:"-0.0576em",marginRight:"0.05em"
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