Fake Geometric Brownian Motion And Its Option Pricing - Xu, X (oxford university;mathematical institute, 2011)

(untitled)
In this thesis, we begin with introducing the notion of a fake geometric Brownian motion in analogy to the fake Brownian motion. Secondly we construct two discontinuous fake geometric Brownian motion processes via the solutions to the Skorokhod embedding problem. Finally we simulate European and path-dependent option pricings for stock prices following these processes, to see how different the results can be compared with the traditional Black & Scholes setting. Key words: fake Brownian motion, fake geometric Brownian motion, Skorokhod embedding problem, Azema-Yor solution, reversed Azema-Yor solution.