What this dissertation aims to do is to use Levy process to price European option in the FTSE 100 market.
Research Question:
• What role does the Levy process play in explaining the option pricing market?
• How is Digital Option price using Levy Processes determined?
• How accurate are Levy Processes compared to the Black-Scholes when pricing Options?
Time Plan towards Achieving the goal of my dissertation:
I intend to complete this dissertation by the 18th of August 2017.
Timeline:
Chapter 1 The introduction should have been completed by the 30th of June
Suggested Methodology:
Chapter 2 and 3 The Literature review of this dissertation must have been completed by me by the 16th of July 2017. The reason is because I would need relevant papers and more so recent papers that describe my topic accurately which is a bit difficult to find but it is possible.
Chapter 4&5 Chapter 4 is proposed to be done by the 10th of August 2017. This is because of the high level of learning that I would need to learn this work. I would have to build the algorithm I will use for the project on MATLAB which can take a bit of time.
Chapter 6: Chapter 6 should take like three days to be done. The work will then be read from the start for a proper perusal for errors and spell checks. Also to see if it is well understood by reader because of the high mathematical content.
The suggested research methodology that would be used in this dissertation would be the Black- Scholes, Nominal Inverse Gaussian Process and the Variance Gamma process for pure jumps should be used. Barndorff- Nielson (1995,1998), Ryberg (1997,1999), Albrecher and Predota (2004) and Benth et al (2006) have been able ot discuss the validity of the NIG levy process. The reasons the parameters that I will
use to estimate the models will be the Method of Moments and Maximum Likelihood Estimation.
The method that would be use to price the model will be the Monte Carlo Method. The Monte Carlo Method will be used here because it is a valid tool when it comes to complicated pricing. However, on main drawback of the monte Carlo Simulation is that they have a slow computational speed. Other closed form of estimation exists such as the Partial Intergo-differential equation and also the Fourier Transformation Method, I would like to use the Monte Carlo Simulation due to its reliability and accuracy in price estimation.
Information and Data Requirement:
The data that would be required for this dissertation is European digital call option on the FTSE 100 index for a period of 6 years. This data is available on Data Stream. (I am not in the university yet and do not have access to DataStream). However, I am certain that there is numerous data that is available on the FTSE 100 index option.
Relevant Articles:
Wim Schoutens. Levy Processes in Finance. Wiley, 2003. 10, 12 (This is a textbook that I have already placed an order for that will bw available to me by the end of the month). This textbook will be next to indispensable for the completion of this project.
Please find attached the other articles that will be relevant to my methodologies to the email.
—————————————————————————————————–
In the dissertation I just wanted you to know that I am trying to price Digital Options Using Levy processes. I attached a file that explains the work I wanted to best essay. The methodology I provided would be required to help price the digital options. I also attached a research paper that talks well about Levy processes and the estimation. Also I provided some research questions which would also serve as a guide.
In the introduction I was expecting to see things on the Black- Scholes, Geometric Brownian motion to show reasons why the Levy process are better. And also the Levy processes I am going to be using which are NIG and Variance Gamma under the real Jumps. Also I am trying to price Digital Option, it’s not called PDO ( Pricing Digital Options) it’s just DO ( Digital Options). Thank you for your effort. Regards, Taiwo.