fmshedge Wiki Rss Feedhttps://fmshedge.codeplex.com/fmshedge Wiki Rss DescriptionUpdated Wiki: Documentationhttps://fmshedge.codeplex.com/documentation?version=14<div class="wikidoc">See <a href="http://kalx.net/fms/rough/pp.html">http://kalx.net/fms/rough/pp.html</a> for probability preliminaries.<br /><br /><a href="https://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388285">This document</a> gives a careful derivation of the classic Black-Scholes/Merton partial differential equation. Instead of stopping at the necessary conditions for a self-financing hedge it also shows these conditions are sufficient.<br /><br /><a href="https://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=389612">This document</a> describes the discrete time multi-period model and proves the Fundamental Theorem of Asset Pricing for this model.<br />
<h2>Initial Hedge</h2>
Suppose you have to hedge a call option. You are paid upfront and have to reproduce the call option payoff at expiration using only the underlying and cash that you can borrow or invest at 0 interest rate.<br /><br />Take the money you get and borrow what you need to set up your initial delta hedge in the underlying. <br /><br />What value of the underlying at expriation would result in a perfect hedge?<br /><br />You need to take an active role and adjust your hedge over time, but you can't really change it continuously like the B-S/M theory assumes.<br />
<h2>First Rehedge</h2>
One approach is to place limit orders above and below the the current stock levels. Limit orders have a price and quantity. Fix the above and below prices. The quantity should be for the amount you need to change your initial delta hedge. Once you set the prices, all you need to know is when the limit order will be executed to compute the change in your hedge.<br /><br />As a first guess, calculate the delta at the above and below levels using the same time to expiration in order to determine the limit order quantities. Calculate <a href="https://fmshedge.codeplex.com/wikipage?title=C%28t%29%20-%20V%28t%29&referringTitle=Documentation">C(t) - V(t)</a>/t = <a href="https://fmshedge.codeplex.com/wikipage?title=C%28t%29%20-%20%28M%28t%29%20%2b%20N%28t%29%20S%28t%29%29&referringTitle=Documentation">C(t) - (M(t) + N(t) S(t))</a>/t when the underlying hits the above and below limit. What is the probablity the stock never hits either limit?<br /><br /><br /></div><div class="ClearBoth"></div>keithalewisTue, 14 May 2013 01:39:30 GMTUpdated Wiki: Documentation 20130514013930AUpdated Wiki: Documentationhttps://fmshedge.codeplex.com/documentation?version=13<div class="wikidoc">See <a href="http://kalx.net/fms/rough/pp.html">http://kalx.net/fms/rough/pp.html</a> for probability preliminaries.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388285">This document</a> gives a careful derivation of the classic Black-Scholes/Merton partial differential equation. Instead of stopping at the necessary conditions for a self-financing hedge it also shows these conditions are sufficient.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=389612">This document</a> describes the discrete time multi-period model and proves the Fundamental Theorem of Asset Pricing for this model.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388286">This document</a> derives the Kolmogorov parameterization for infinitely divisible distributions.<br />
<h2>Initial Hedge</h2>
Suppose you have to hedge a call option. You are paid upfront and have to reproduce the call option payoff at expiration using only the underlying and cash that you can borrow or invest at 0 interest rate.<br /><br />Take the money you get and borrow what you need to set up your initial delta hedge in the underlying. <br /><br />What value of the underlying at expriation would result in a perfect hedge?<br /><br />You need to take an active role and adjust your hedge over time, but you can't really change it continuously like the B-S/M theory assumes.<br />
<h2>First Rehedge</h2>
One approach is to place limit orders above and below the the current stock levels. Limit orders have a price and quantity. Fix the above and below prices. The quantity should be for the amount you need to change your initial delta hedge. Once you set the prices, all you need to know is when the limit order will be executed to compute the change in your hedge.<br /><br />As a first guess, calculate the delta at the above and below levels using the same time to expiration in order to determine the limit order quantities. Calculate <a href="https://fmshedge.codeplex.com/wikipage?title=C%28t%29%20-%20V%28t%29&referringTitle=Documentation">C(t) - V(t)</a>/t = <a href="https://fmshedge.codeplex.com/wikipage?title=C%28t%29%20-%20%28M%28t%29%20%2b%20N%28t%29%20S%28t%29%29&referringTitle=Documentation">C(t) - (M(t) + N(t) S(t))</a>/t when the underlying hits the above and below limit. What is the probablity the stock never hits either limit?<br /><br /><br /></div><div class="ClearBoth"></div>keithalewisSun, 17 Jun 2012 16:35:45 GMTUpdated Wiki: Documentation 20120617043545PUpdated Wiki: Documentationhttps://fmshedge.codeplex.com/documentation?version=12<div class="wikidoc">See <a href="http://kalx.net/fms/rough/pp.html">http://kalx.net/fms/rough/pp.html</a> for probability preliminaries.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388285">This document</a> gives a careful derivation of the classic Black-Scholes/Merton partial differential equation. Instead of stopping at the necessary conditions for a self-financing hedge it also shows these conditions are sufficient.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=389612">This document</a> describes the discrete time multi-period model and proves the Fundamental Theorem of Asset Pricing for this model.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388286">This document</a> derives the Kolmogorov parameterization for infinitely divisible distributions.<br />
<h2>Initial Hedge</h2>
Suppose you have to hedge a call option. You are paid upfront and have to reproduce the call option payoff at expiration using only the underlying and cash that you can borrow or invest at 0 interest rate.<br /><br />Take the money you get and borrow what you need to set up your initial delta hedge in the underlying. <br /><br />What value of the underlying at expriation would result in a perfect hedge?<br /><br />You need to take an active role and adjust your hedge over time, but you can't really change it continuously like the B-S/M theory assumes.<br />
<h2>First Rehedge</h2>
One approach is to place limit orders above and below the the current stock levels. Limit orders have a price and quantity. Fix the above and below prices. The quantity should be for the amount you need to change your initial delta hedge. Once you set the prices, all you need to know is when the limit order will be executed to compute the change in your hedge.<br /><br />As a first guess, calculate the delta at the above and below levels using the same time to expiration in order to determine the limit order quantities. Calculate C(t) - V(t) = C(t) - (M(t) + N(t) S(t)) when the underlying hits the above and below limit. What is the probablity the stock never hits either limit?<br /><br /><br /></div><div class="ClearBoth"></div>keithalewisSun, 17 Jun 2012 15:57:27 GMTUpdated Wiki: Documentation 20120617035727PUpdated Wiki: Documentationhttps://fmshedge.codeplex.com/documentation?version=11<div class="wikidoc">See <a href="http://kalx.net/fms/rough/pp.html">http://kalx.net/fms/rough/pp.html</a> for probability preliminaries.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388285">This document</a> gives a careful derivation of the classic Black-Scholes/Merton partial differential equation. Instead of stopping at the necessary conditions for a self-financing hedge it also shows these conditions are sufficient.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=389612">This document</a> describes the discrete time multi-period model and proves the Fundamental Theorem of Asset Pricing for this model.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388286">This document</a> derives the Kolmogorov parameterization for infinitely divisible distributions.<br /><br />Suppose you have to hedge a call option. You are paid upfront and have to reproduce the call option payoff at expiration using only the underlying and cash that you can borrow or invest at 0 interest rate.<br /><br />Take the money you get and borrow what you need to set up your initial delta hedge in the underlying. <br /><br />What value of the underlying at expriation would result in a perfect hedge?<br /><br />You need to take an active role and adjust your hedge over time, but you can't really change it continuously like the B-S/M theory assumes.<br />
<h2>Initial Rehedge</h2>
One approach is to place limit orders above and below the the current stock levels. Limit orders have a price and quantity. Fix the above and below prices. The quantity should be for the amount you need to change your initial delta hedge. Once you set the prices, all you need to know is when the limit order will be executed to compute the change in your hedge.<br /><br />As a first guess, calculate the delta at the above and below levels using the same time to expiration in order to determine the limit order quantities. Calculate C(t) - V(t) = C(t) - (M(t) + N(t) S(t)) when the underlying hits the above and below limit. What is the probablity the stock never hits either limit?<br /><br /><br /></div><div class="ClearBoth"></div>keithalewisSun, 17 Jun 2012 15:56:35 GMTUpdated Wiki: Documentation 20120617035635PUpdated Wiki: Documentationhttps://fmshedge.codeplex.com/documentation?version=10<div class="wikidoc">See <a href="http://kalx.net/fms/rough/pp.html">http://kalx.net/fms/rough/pp.html</a> for probability preliminaries.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388285">This document</a> gives a careful derivation of the classic Black-Scholes/Merton partial differential equation. Instead of stopping at the necessary conditions for a self-financing hedge it also shows these conditions are sufficient.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=389612">This document</a> describes the discrete time multi-period model and proves the Fundamental Theorem of Asset Pricing for this model.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388286">This document</a> derives the Kolmogorov parameterization for infinitely divisible distributions.<br /><br />Suppose you have to hedge a call option. You are paid upfront and have to reproduce the call option payoff at expiration using only the underlying and cash that you can borrow or invest at 0 interest rate.<br /><br />Take the money you get and borrow what you need to set up your initial delta hedge in the underlying. <br /><br />What value of the underlying at expriation would result in a perfect hedge?<br /><br />You need to take an active role and adjust your delta hedge, but you can't really change it continuously like the B-S/M theory assumes.<br />
<h2>Initial Hedge</h2>
One approach is to place limit orders above and below the the current stock levels. Limit orders have a price and quantity. Fix the above and below prices. The quantity should be for the amount you need to change your initial delta hedge. This is called gamma. Once you set the prices, all you need to know is when the limit order will be executed to compute the change in your hedge.<br /><br />But you don't know that.<br /><br /><br /><br /></div><div class="ClearBoth"></div>keithalewisSun, 17 Jun 2012 15:34:56 GMTUpdated Wiki: Documentation 20120617033456PUpdated Wiki: Documentationhttps://fmshedge.codeplex.com/documentation?version=9<div class="wikidoc">See <a href="http://kalx.net/fms/rough/pp.html">http://kalx.net/fms/rough/pp.html</a> for probability preliminaries.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388285">This document</a> gives a careful derivation of the classic Black-Scholes/Merton partial differential equation. Instead of stopping at the necessary conditions for a self-financing hedge it also shows these conditions are sufficient.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=389612">This document</a> describes the discrete time multi-period model and proves the Fundamental Theorem of Asset Pricing for this model.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388286">This document</a> derives the Kolmogorov parameterization for infinitely divisible distributions.<br /><br />Suppose you have to hedge a call option. You are paid upfront and have to reproduce the call option payoff at expiration using only the underlying. <br /><br />Take the money you get for that to set up your initial delta hedge in the underlying. <br /><br />What happens if you do nothing after that?<br /><br />That could be a perfect hedge, but only if delta*S = max{S - k} at expiration.<br /><br />You need to take an active role and adjust your delta hedge, but you can't really change it continuously like the B-S/M theory assumes.<br /><br />One approach is to place limit orders above and below the the current stock levels. Limit orders have a price and quantity. Fix the above and below prices. The quantity should be for the amount you need to change your initial delta hedge. This is called gamma. Once you set the prices, all you need to know is when the limit order will be executed to compute the gamma.<br /><br />But you don't know that.<br /><br /><br /><br /></div><div class="ClearBoth"></div>keithalewisSun, 17 Jun 2012 00:56:41 GMTUpdated Wiki: Documentation 20120617125641AUpdated Wiki: Documentationhttps://fmshedge.codeplex.com/documentation?version=8<div class="wikidoc">See <a href="http://kalx.net/fms/rough/pp.html">http://kalx.net/fms/rough/pp.html</a> for probability preliminaries.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388285">This document</a> gives a careful derivation of the classic Black-Scholes/Merton partial differential equation. Instead of stopping at the necessary conditions for a self-financing hedge it also shows these conditions are sufficient.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=389612">This document</a> describes the discrete time multi-period model and proves the Fundamental Theorem of Asset Pricing for this model.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388286">This document</a> derives the Kolmogorov parameterization for infinitely divisible distributions.<br /></div><div class="ClearBoth"></div>keithalewisThu, 14 Jun 2012 01:10:02 GMTUpdated Wiki: Documentation 20120614011002AUpdated Wiki: Documentationhttps://fmshedge.codeplex.com/documentation?version=7<div class="wikidoc">See <a href="http://kalx.net/fms/rough/pp.html">http://kalx.net/fms/rough/pp.html</a> for probability preliminaries.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388285">This document</a> gives a careful derivation of the classic Black-Scholes/Merton partial differential equation. Instead of stopping at the necessary conditions for a self-financing hedge it also shows these conditions are sufficient.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=389612">This document</a> describes the discrete time multi-period model and proves the Fundamental Theorem of Asset Pricing for this model.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388286">This document</a> derives the Kolmogorov parameterization for infinitely divisible distributions.<br /></div><div class="ClearBoth"></div>keithalewisThu, 14 Jun 2012 01:08:34 GMTUpdated Wiki: Documentation 20120614010834AUpdated Wiki: Documentationhttps://fmshedge.codeplex.com/documentation?version=6<div class="wikidoc"><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388285">This document</a> gives a careful derivation of the classic Black-Scholes/Merton partial differential equation. Instead of stopping at the necessary conditions for a self-financing hedge it also shows these conditions are sufficient.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=389612">This document</a> describes the discrete time multi-period model and proves the Fundamental Theorem of Asset Pricing for this model.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388286">This document</a> derives the Kolmogorov parameterization for infinitely divisible distributions.<br /></div><div class="ClearBoth"></div>keithalewisWed, 13 Jun 2012 12:23:41 GMTUpdated Wiki: Documentation 20120613122341PUpdated Wiki: Documentationhttps://fmshedge.codeplex.com/documentation?version=5<div class="wikidoc"><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388285">This document</a> gives a careful derivation of the classic Black-Scholes/Merton partial differential equation. Instead of stopping at the necessary conditions for a self-financing hedge it also shows these conditions are sufficient.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388286">This document</a> derives the Kolmogorov parameterization for infinitely divisible distributions.<br /></div><div class="ClearBoth"></div>keithalewisSat, 09 Jun 2012 12:58:42 GMTUpdated Wiki: Documentation 20120609125842PUpdated Wiki: Documentationhttps://fmshedge.codeplex.com/documentation?version=4<div class="wikidoc"><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388285">This document</a> gives a careful derivation of the classic Black-Scholes/Merton PDE. Instead of stopping at the necessary conditions for a self-financing hedge it also shows these conditions are sufficient.<br /><br /><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388286">This document</a> derives the Kolmogorov parameterization for infinitely divisible distributions.<br /><br /></div><div class="ClearBoth"></div>keithalewisSat, 09 Jun 2012 12:53:25 GMTUpdated Wiki: Documentation 20120609125325PUpdated Wiki: Documentationhttps://fmshedge.codeplex.com/documentation?version=3<div class="wikidoc"><a href="http://www.codeplex.com/Download?ProjectName=fmshedge&DownloadId=388285">This document</a> gives a careful derivation of the classic Black-Scholes/Merton PDE. Instead of stopping at the necessary conditions for a self-financing hedge it also shows these conditions are sufficient.<br /><br /><span class="unresolved">Cannot resolve file macro, invalid file name or id.</span> derives the Kolmogorov parameterization for infinitely divisible distributions.<br /><br /></div><div class="ClearBoth"></div>keithalewisSat, 09 Jun 2012 12:52:56 GMTUpdated Wiki: Documentation 20120609125256PUpdated Wiki: Documentationhttps://fmshedge.codeplex.com/documentation?version=2<div class="wikidoc">This document gives a careful derivation of the classic Black-Scholes/Merton PDE. Instead of stopping at the necessary conditions for a self-financing hedge it also shows these conditions are sufficient.<br /><br />This document derives the Kolmogorov parameterization for infinitely divisible distributions.<br /><br /></div><div class="ClearBoth"></div>keithalewisSat, 09 Jun 2012 12:51:19 GMTUpdated Wiki: Documentation 20120609125119PUpdated Wiki: Documentationhttps://fmshedge.codeplex.com/documentation?version=1<div class="wikidoc">Black-Scholes/Merton hedging</div><div class="ClearBoth"></div>keithalewisSat, 09 Jun 2012 12:49:25 GMTUpdated Wiki: Documentation 20120609124925PUpdated Wiki: Black-Scholes/Merton hedginghttps://fmshedge.codeplex.com/wikipage?title=Black-Scholes/Merton hedging&version=1<div class="wikidoc">
<p>This document derives the B-S/M partial differential equation. </p>
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