Posted on Fri 02 March 2018 in Finance • Tagged with finance, binomial-model
In the previous post introducing the Binomial Options Pricing Model, we discussed a very simple model for the movement of stock prices. In that model, we assumed that at the end of a certain period of time, the value of a stock could take on one of two possible values …
Posted on Thu 01 March 2018 in Thesis • Tagged with thesis, quaternions
In our last post we laid the foundation necessary to understand the quaternions, a 4-dimensional number system with some interesting properties that are applicable in higher-dimensional geometry. We didn't actually define or discuss the quaternions in that post, but instead discussed the real and complex numbers. It might be helpful …
Posted on Thu 22 February 2018 in Thesis • Tagged with thesis, quaternions, complex numbers
In the introductory post to this series of posts explaining my thesis, we first heard about "quaternion-Kähler manifolds," a type of geometric object with special curvature properties. These special geometric properties are related to the algebraic properties of the quaternions, a 4-dimensional number system that generalizes the somewhat more familiar …
Posted on Fri 16 February 2018 in Finance • Tagged with finance, binomial-model
A lot of work in mathematical finance is related to the pricing of financial derivatives, that is, financial assets that have values that depend on (that is, values that are derived from) the value of another asset. Some of the simplest derivatives are European call and put options. In this …
Posted on Thu 08 February 2018 in Thesis
When you're a mathematics PhD student, your work is likely to be totally inscrutable to just about anyone you meet, even many fellow mathematicians. This is probably true for advanced research work in nearly any field, but I think the problem is especially bad in pure mathematics, largely for two …