{"categories":["Risk Management"],"contentHtml":"<h4>Lecture Notes</h4><h5>Options</h5><p>The straddle strategy is owning a call and put option with the same characteristics.</p><p>If I end up long a call option and short a put, it ends up being a forward contract.</p><p>I can cook with stocks and bonds to replicate a put option.</p><h5>paul wilmott</h5><p>Some famous trader who spoke about Black Scholes</p><p><a href=\"https://web.archive.org/web/20080724100130/http://www.wilmott.com/blogs/paul/index.cfm/2008/4/29/Science-in-Finance-IX-In-defence-of-Black-Scholes-and-Merton\" rel=\"noopener noreferrer\">https://web.archive.org/web/20080724100130/http://www.wilmott.com/blogs/paul/index.cfm/2008/4/29/Science-in-Finance-IX-In-defence-of-Black-Scholes-and-Merton</a></p><h5>Exam</h5><p>Replicate Black-Scholes model in Excel.</p><p>Simulate to verify.</p><p>Will be on exam!</p><p>Expect to be able to price a bond</p><p>discounted payoffs at each time step</p><p>Does this also have a closed-form solution? <strong>Open question:</strong> verify.</p><p>you might get coupons, which I can put in a savings account to accumulate interest</p><p>the bond can get more expensive if it has appetizers like this</p><p>it also reduces duration risk (look this up)</p><p>In futures hedging on equities, you can invest in treasury bonds in order to make your portfolio <math><mi>𝛽</mi></math>-neutral</p><p>And the same idea will lead you to having a bond portfolio duration neutral</p><p>Another item to check.</p><p>extraction of duration from real bond price data.</p><p>Process is in Exam II Review.</p><p>The Black Scholes model tells you what a</p><p>The intuition behind implied volatility:</p><p>black-scholes relies on historical volatility</p><p>but a risk manager might use forward looking information in the volatility</p><p>this comes from the implied volatility</p><h5>VIX</h5><p>VIX measures implied volatility in the market. It is <strong>the fear gauge</strong>.</p><p>Let’s look at calls and puts</p><p>If we graph their prices as a function of strike price, they form this interesting graph</p><math display=\"block\"><mspace width=\"-1em\"></mspace><mi>𝑔</mi><mi>𝑟</mi><mi>𝑎</mi><mi>𝑝</mi><mi>ℎ</mi></math><p>And then we get this area under the curve, and that is the typical calculation method for VIX.</p><p>But what happens when the market crashes</p><p>People are paying higher prices, insurance. Pushes the put price up which actually increases</p><p>start with the black-scholes model</p><p>Numerical exercise over the winter (<strong>Open question:</strong> complete it).</p>","contentSourceFormat":"typst","contentTypst":"=== Lecture Notes\n<lecture-notes>\n==== Options\n<options>\nThe straddle strategy is owning a call and put option with the same characteristics.\n\nIf I end up long a call option and short a put, it ends up being a forward contract.\n\nI can cook with stocks and bonds to replicate a put option.\n\n==== paul wilmott\n<paul-wilmott>\nSome famous trader who spoke about Black Scholes\n\n#link(\"https://web.archive.org/web/20080724100130/http://www.wilmott.com/blogs/paul/index.cfm/2008/4/29/Science-in-Finance-IX-In-defence-of-Black-Scholes-and-Merton\")\n\n==== Exam\n<exam>\nReplicate Black-Scholes model in Excel.\n\nSimulate to verify.\n\nWill be on exam!\n\nExpect to be able to price a bond\n\ndiscounted payoffs at each time step\n\nDoes this also have a closed-form solution? #strong[Open question:] verify.\n\nyou might get coupons, which I can put in a savings account to accumulate interest\n\nthe bond can get more expensive if it has appetizers like this\n\nit also reduces duration risk (look this up)\n\nIn futures hedging on equities, you can invest in treasury bonds in order to make your portfolio $beta$-neutral\n\nAnd the same idea will lead you to having a bond portfolio duration neutral\n\nAnother item to check.\n\nextraction of duration from real bond price data.\n\nProcess is in Exam II Review.\n\nThe Black Scholes model tells you what a\n\nThe intuition behind implied volatility:\n\nblack-scholes relies on historical volatility\n\nbut a risk manager might use forward looking information in the volatility\n\nthis comes from the implied volatility\n\n==== VIX\n<vix>\nVIX measures implied volatility in the market. It is #strong[the fear gauge].\n\nLet's look at calls and puts\n\nIf we graph their prices as a function of strike price, they form this interesting graph\n\n$ #h(-1em) g r a p h $\n\nAnd then we get this area under the curve, and that is the typical calculation method for VIX.\n\nBut what happens when the market crashes\n\nPeople are paying higher prices, insurance. Pushes the put price up which actually increases\n\nstart with the black-scholes model\n\nNumerical exercise over the winter (#strong[Open question:] complete it).","dataUrl":"https://sharifhsn.dev/api/posts/options-and-volatility.json","date":"2024-12-12","datePublished":"2024-12-12","description":"The straddle strategy is owning a call and put option with the same characteristics. If I end up long a call option and short a put, it ends up being a forward contract. I can…","site":"https://sharifhsn.dev","slug":"options-and-volatility","source":"FE-535 | Risk Management","sourceUrl":null,"tags":["Risk Management","Options","Volatility"],"title":"Options and Volatility","url":"https://sharifhsn.dev/blog/options-and-volatility/","version":"1","wordCount":313}