Project Title: Testing the Biased Geometric Brownian Motion
Student: Thepdanai Danswasvong
Course: MSc Computational Finance
Abstract:
This dissertation proposes a new stock price model "The biased
geometric Brownian motion". In short, the biased geometric
Brownian motion is a normal geometric Brownian motion with a newly
introduced "biased factor". The forecasting performance of the
biased geometric Brownian motion was tested in order to evaluate
whether the efficient portfolio which is constructed from prediction
of share prices from this new model will outperforms an optimal
portfolio created from the current or past information. The formulation
of the biased factor employs the fundamental and principle knowledge
on fuzzy logic and fuzzy set theory. Factors which are closely relate
to the recent performance of the stock such as the daily rate of
return and price movement are described by linguistic variables which
are characterised by fuzzy sets. The defuzzification of these variables
is the process to calculate the value of the biased factor. In addition
to the biased factor, the genetic algorithm was constructed in order to
solve the portfolio optimisation problem. The genetic algorithm is used
to determine the optimal portfolio in the performance test of the biased
geometric Brownian motion. Several tests were conducted in order to
verify the performance of the biased geometric Brownian motion and the
genetic algorithm. In the end, it turns out that both the original and
the biased geometric Brownian motion are unsuitable for the prediction
of share price in the current economic recession. On the other hand,
the performance of the genetic algorithm in solving the portfolio
selection problem was marvellous.