During the last decades the valuation of an option has attracted considerable interest, which is one of the most important and popular financial derivatives in the financial market. Due to its simplicity and clarity in obtaining the price of the option, the classical Black–Scholes (B-S) (or Black–Scholes–Merton) options pricing model was proposed.
However, the classical Black–Scholes model was established under some strict assumptions, such as frictionless, price changing smoothly and option be exercised at maturity. Specially, some empirical evidence has shown that one of the significant shortcomings of the classical B–S model is that Gaussian shocks underestimate the probability that stock prices exhibit significant movements or jumps over small time steps in a financial market.
To overcome this problem, the Lévy processes are introduced to replace the standard Brownian motions. Fractional derivatives are quasi-differential operators, which provide useful tools for a description of memory and hereditary properties and are closely related to Lévy processes.
Therefore, the complex fractional dynamical systems have been introduced more and more into the financial field.This proposal aims to carry out innovative and novel research to solve the following highly related problems on computational models of complex fractional dynamical systems and application to finance. The results will be also used for other fractional models in the financial marke.
Activities will include:
- conducting a thorough preliminary literature review
- undertaking coursework where needed
- attending School Seminars and fractional group meeting
- developing a rigorous theoretical analysis of fractional models.
- deriving, designing and implementing numerical methods for solving fractional differential equations
- PhD: write 4-6 Q1 journal papers
- Honours or Master of Philosophy: write 1-2 Q1 journal papers
Skills and experience
You should have skills and experience in computational mathematics, MATLAB or FORTRAN.
You may be able to apply for a research scholarship in our annual scholarship round.
Contact the supervisor for more information.