{"categories":["Computational Methods"],"contentHtml":"<p>I’m out on vacation this week, so I watched the recording</p><h3>Textbook</h3><h4>Stochastic Processes</h4><p>A stochastic processes is merely a collection of indexed random variables. The indexing of these variables confers a structure onto the rvs which gives them some properties.</p><p>The indexing structure can be a set or an interval, which would imply a discrete or continuous stochastic process, respectively.</p><h3>Syllabus</h3><p>Late assignments are not accepted under any circumstances, at least 24 hours in advance must be warned.</p><p>Attendance is mandatory for in-person, not for online.</p><p>Old book with pseudocode with formula.</p><p>which is a lot more</p><p>Main things we cover:</p><p>Monte carlo approximation</p><p>Finite difference</p><p>Trees</p><p>Black-Scholes PDE solution we study in 610</p><p>Most models do not have a formula though</p><p>So how do we estimate the value then? That’s what this class is about</p><p>There are two fundamental ways</p><p>Approximate the process. Let’s say I know the path for sure. I can calculate the value by using the payoff formula.</p><p>I can generate millions of paths and then average them. That is very slow.</p><p>Or I could look at the probability of each path, and then average them? That’s trees.</p><p>Or you could solve the PDE. You can get complicated PDEs, but they always have a very similar structure.</p>","contentSourceFormat":"typst","contentTypst":"I'm out on vacation this week, so I watched the recording\n\n== Textbook\n<textbook>\n=== Stochastic Processes\n<stochastic-processes>\nA stochastic processes is merely a collection of indexed random variables. The indexing of these variables confers a structure onto the rvs which gives them some properties.\n\nThe indexing structure can be a set or an interval, which would imply a discrete or continuous stochastic process, respectively.\n\n== Syllabus\n<syllabus>\nLate assignments are not accepted under any circumstances, at least 24 hours in advance must be warned.\n\nAttendance is mandatory for in-person, not for online.\n\nOld book with pseudocode with formula.\n\nwhich is a lot more\n\nMain things we cover:\n\nMonte carlo approximation\n\nFinite difference\n\nTrees\n\nBlack-Scholes PDE solution we study in 610\n\nMost models do not have a formula though\n\nSo how do we estimate the value then? That's what this class is about\n\nThere are two fundamental ways\n\nApproximate the process. Let's say I know the path for sure. I can calculate the value by using the payoff formula.\n\nI can generate millions of paths and then average them. That is very slow.\n\nOr I could look at the probability of each path, and then average them? That's trees.\n\nOr you could solve the PDE. You can get complicated PDEs, but they always have a very similar structure.","dataUrl":"https://sharifhsn.dev/api/posts/computational-methods-week-01.json","date":"2025-01-28","datePublished":"2025-01-28","description":"I’m out on vacation this week, so I watched the recording A stochastic processes is merely a collection of indexed random variables. The indexing of these variables confers a…","site":"https://sharifhsn.dev","slug":"computational-methods-week-01","source":"Computational Methods in Quantitative Finance","sourceUrl":null,"tags":["Computational Methods","Stochastic Processes","Numerical Methods","Option Pricing"],"title":"Stochastic Processes and Computational Pricing","url":"https://sharifhsn.dev/blog/computational-methods-week-01/","version":"1","wordCount":212}