I need my MSc Financial Math Dissertation to be done. My course is purely Math based and we will also have to write codes using computer languages such as Matlab, C++. It needs to be around 20,000 words. I have provided topic choices and guidelines below. I need the topic confirmation by tomorrow and full paper by April 30th. Please let me know if you can help me and what would be the price. Awaiting your reply ASAP.
Below are the choice of topics:
TOPIC 1
Dynamic programming for portfolio optimization: in the Markovian setting one can associate to a portfolio optimization problem a partial differential equation that the value function is expected to solve, in a suitable sense. One may investigate existence, uniqueness and regularity of solutions to such PDEs. Prerequisites: some familiarity with PDEs would be desirable.
Hedging and optimization in incomplete markets: in this very vast field, one can thoroughly study one of the many problems, and try to consider an original case.
Affine processes in the modeling of the term structure of interest rates.
Option pricing by Fourier transform techniques. Prerequisites: elementary knowledge of (undergraduate) Fourier analysis would be desirable.
Enlargement and shrinking of filtrations and applications (e.g. to models of insider trading). Prerequisites: previous exposure to (at least) measure-theoretic probability is essential.
Backward stochastic differential equations and applications to pricing and hedging. Prerequisites: see above.
Properties of CIR equations: existence, positivity, and connection with Bessel process.
TOPIC 2
CME-LCH Basis
In recent years, regulators have encouraged banks to use clearing houses as a means of diluting counterparty exposure and to improve market transparency for financial derivatives. During 2015 a difference opened up between the prices of interest rate swaps cleared on the London Clearing House (LCH) and the Chicago Mercantile Exchange (CME), two of the world's major clearing houses. Apparently an arbitrage, this difference has persisted into 2016 at levels multiple times the size of the bid-offer for these products.
What has caused this 'arbitrage', and why have arbitrageurs not intervened to remove it?
Which financial derivatives are affected by the CME-LCH basis, and how?
Develop a computationally inexpensive model for the CME-LCH basis, calibrated to the basis for on-market interest rate swaps, and demonstrate the impact of the model on the valuations of off-market swaps and European swaptions.
TOPIC 3
This project is on credit migration. The credit migration model introduced by (amongst others) Jarrow, Lando and Turnbull in the late 1990s seeks to explain the credit spread dynamics of a particular issuer via credit rating transitions, which are encapsulated in a Markov chain transition matrix. I want to analyse and model the time variability of this matrix, through a stochastic time change in which during periods of stress -time speeds up- and higher densities of rating transition are observed, including transition to default. The stochastic time change could arise through an integrated CIR process or Levy process. The annual S&P ratings report contains enough data (1981-2015) that are necessary to do some useful work on this. We may also extend the model to take into account market spread levels, thereby having an extended model that combines historical and market-implied or -risk-neutral- probabilities.
The project will involve some programming, including optimisation, and data analysis.
TOPIC 4
Hedging of Out-of-the-Money Interest Rate Options
Prior to 2008, long term interest rates in developed markets have tended to be about 5% or higher, whereas they have since hovered around historical lows of about 2%. As it is common for interest rate products to be done at the prevailing interest rate environment, many European and Bermudan swaptions were done based on a strike around 5%. Given these tend to be very long-dated (say 30y), we currently still have a lot of legacy high strike swaptions in the inventory of financial institutions, with a long time to maturity (say over 20y).
Traditionally, risk of options are managed via delta and vega hedging. How would the hedging of these high strike options have performed over the past history since 2008? What implications are there for us if rates stay low for much longer?
TOPIC 5
Sensitivity of operational risk capital allocation on the model threshold

The Basel committee which regulates the banking industry promotes prudent risk management practices and requires banks to carry out their own models on internal data sets to evaluate amounts of capital necessary to face operational risks (ex-AMA, ICAAP, CCaR, etc.). The banks are given a freedom (to certain extend) to set the threshold as the minimum value of operational losses to be included in the capital calculation. This threshold is often referred to as the model threshold.
The standard method for the operational risk capital calculation is to use the risk measure Value at Risk (VaR). However, the model threshold on the risk data strongly influences the value of the risk measure VaR, in turn the capital calculation.
This project aims at analysing the sensitivity of the operational risk capital value on the model threshold.

Background knowledge:
· Basic knowledge on operational risk, terminology and concepts
· Knowledge on VaR;

Software and Packages:
· We will run the codes in R, so prior experience in R would be helpful.
TOPIC 6
Title: The exponent expansion and the Inhomogeneous Geometric Brownian motion with time dependent coefficients

The aim of the project is to apply a semi-analytical approximation known as exponent expansion [1,2] to the calculation Arrow-Debreu prices of the so-called inhomogeneous geometric Brownian motion with time dependent coefficients.
You will develop the semi-analytical calculation of zero coupon bonds and interest rate swaptions and compare the results with those obtained by means of hand coded Partial Differential equations.
2) Title: Pricing of high-dimensional American options by neural networks

The aim of the project is to compare the performance of standard least square regression methods [1,2] and artificial neural networks [3] for the approximation of the exercise boundary of American and Bermudan options in Monte Carlo.
You will develop the required Monte Carlo algorithms and compare the performance on several examples of financial relevance.
TOPIC 7
Investigating mechanisms leading to volatility clustering using agent-based models
While volatility clustering is considered to be a classical stylised fact observed in financial asset price time-series, no consensus has been reached about the behavioural mechanisms of market participants that may give rise to such observations.

This project will consist of:

i) A Critical evaluation of key literature concerning agent-based models.
ii) Developing an understanding of “multifractality” in financial time-series.
iii) Develop/extend an agent based model, and a comparison of the “model output” with that of classical statistical models.

Prerequisite: A basic background of statistical/probabilistic methods, and a familiarity with basic programming that will be used to develop an agent-based model.
TOPIC 8
Evolution of decisions on choice
The project work will use nonlinear ordinary differential equations to model the evolution of decisions on choice, e.g. where to trade, where to migrate to, where to invest when several options are available. This is constrained by resources or government limits, which act as nonlinear feedback to determine the growth or decay of the individual choices and also the winning choice. The effects of gradual or sudden changes in resources or policy are of interest, as are the influences of the modelling parameters and the numbers of choices available. Data on the web and comparisons with alternative approaches will be sought as time allows.
TOPIC 9
Importance sampling methods applied to stochastic Lagrangian models of transport
Transport in the atmospheric boundary layer can be modelled by a set of stochastic differential equations. Sometimes, the problem of interest is to calculate the expected transport between two localised regions (in space in time). The project will explore importance sampling methods (Milstein's method, Go-with-the-winners) with the aim of improving the efficiency of the calculation.
Below are the guidelines:
MSc Project Guidelines and Information
The FM MSc project MATHG099 contributes for 1/3 to the overall MSc mark, with the 8 taught components adding up to the remaining 2/3. Please see Passing the Course section of FM Booklet for more information regarding the overall MSc mark and types of degree.
General Project Guidelines
The MSc project can range from an extensive survey and critique of existing research to the development of a new model or an extension of an existing one. Each project will be assessed taking into account where the main focus of effort lies. A component of original research is not a requirement of the project, but will be given due credit if present. A student should discuss these details with their supervisor.
Whatever the student decides with their supervisor, there are some parts that all projects should include:
An introduction outlining the project and giving a clear statement of the objectives of the project.
Details of mathematical calculations that can be checked. Where it makes the text more readable, an appendix could be used for some of the calculations.
Clear referencing of all material sourced, whether from books, published journals, the internet, personal communication, etc. Essentially, if it is not the student’s idea or work, it needs to be referenced. Failure to reference material may be construed as plagiarism. The college takes a firm stance on plagiarism. If in doubt the student should ask the advice of their supervisor.
Conclusions, including a summary of the project findings, and, where new research was carried out, a discussion of the strengths and weaknesses of the model/method, and possible improvements.
Style and Presentation
It is expected that the MSc thesis be written with the free LaTex typesetting software. Some marks will be awarded for the quality of the written work, including its readability, clarity of argument and overall presentation. There is no word limit for the dissertation.
Supervision
It is expected that the students work independently. The supervisor is available for guidance and research advice.
Marking
The pass mark for the project is 50%. The project will be assessed according to the following marking scheme:
Presentation, style and elegance (max. 20 points)
Diligence, care and thoroughness (max. 20 points)
Selection of sources and references, and the scope and depth of literature review (max. 20 points)
Elements of originality, critical thought and analysis, and mathematical sophistication (max. 40 points)