Why does martingale pricing work?

By on May 4th, 2015

Martingale methods are a staple in financial mathematics and it allows us to deal with a much broader set of cash flows than the PDE-approach, which I covered in an earlier post. Here I try as best as possible to give a simple walkthrough of the concepts and ideas behind it. First of all a […]

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Pricing Financial Derivatives Using Partial Differential Equations: A Step-by-Step Solution of the Black-Scholes Equation

By on April 27th, 2015

In this post I will try to give a quick overview of the pricing of options using PDEs. Using partial differential equation was the method first employed by Fischer Black and Myron Scholes in order to estimate the value of a European option and it has had a strong position as an elementary strategy for […]

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How to Solve Stochastic Differential Equations: the Integrating Factor Technique

By on April 16th, 2015

In this blog post I will present a quite simple technique for finding the solution to an SDE. This method will unfortunately not solve any SDE you are likely to come across, and it is not able to solve systems of stochastic processes, but the solution to many common equations that have something in common […]

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Solving the Geometric Brownian Motion

By on April 7th, 2015

The most common Stochastic Differential Equation (SDE) in finance is the traditional Geometric Brownian Motion (GMB), used by Black, Scholes and Merton to find the closed-form solution to European Options. Solving the SDE might be a simple exercise for many, but I chose to include it and give it its own blog post since some […]

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Solving First Order ODEs in Finance, Part 2

By on January 9th, 2015

Continuing from the first part of this blog “series”, which can be found here, I will move on to a more general form of ODEs, which are structured as: Note here that we cannot separate the function as was possible before, instead we are stuck with a function which multiplies y. The first step in […]

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Solving First Order ODEs in Finance, Part 1

By on December 27th, 2014

Traditional ODEs are a topic that is rarely covered more than briefly (if at all) in quant-finance courses and most often it is assumed you already know it. However, for us who are not from an engineering, maths or physics background, ODEs are not necessarily such a common occurrence. At the same time, first order […]

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