CPT206 Java Programming for Financial Mathematics:

Coursework 2 Task Specification

Thomas Selig

Due date: Sunday, 9 May, 2021, 10pm

        This is the specification task sheet for the Coursework 2 assessment component of your CPT206 module. This is worth 15% of your final grade for this module. The submission deadline for this assignment is Sunday, 9 May, 2021, at 10pm. Detailed submission instructions are provided in Section 3.

1 Task specification (60 marks)

The aim of this coursework is to implement the Hull-White model, which is a model of future interest rates. First described by John Hull and Alan White in 1990, this model is one of the historically most important interest rate models, and is still often used for risk-management purposes in the market today. As part of this task, you will also produce a report documenting your design choices, detailed in Section 2.

1.1 Model dynamics

The model is a short-rate model, whose dynamics are given by the following equation:

dr(t) = (θ(t) − ar(t)) dt + σdW(t).

In Equation (1), a and σ are positive constants, the function θ(t) is chosen so as to exactly fit the initial yield curve observed in the market, and W(t) is a standard Brownian motion. This means that the differential dW(t) has normal distribution with mean 0 and variance dt.

1.2 Task description (40 marks)

You will write a Java program that simulates the Hull-White model over a given time period. Your Java program should be written in a single Main class. It should take the following input parameters:

• The constants a, σ, and the function θ(t) which drive the model’s behaviour. These should be chosen by yourself (e.g. as class variables/constants), and the values selected will be documented in the report (see Section 2).

• An initial rate r0 > 0.

• A time period T > 0 and a positive integer n indicating the number of increment intervals.

        The idea is to break down the time period [0, T] into n increment intervals of length , and apply the Euler method to Equation (1) to simulate the model over that time period. In other words, we should have: r(t = 0) = r0, and for any given time for some k ∈ {0, . . . , n − 1}, r(t + dt) = r(t) + dr(t), where the increment dr(t) is given by Equation (1).

        Your program should display the values of the rate function r(t) over the chosen time period (i.e. should show the values of r(t) for all t of the form as above). It should also calculate the minimum, maximum and average values of the rate function, and display them. For the minimum and maximum, it should also display the point t at which these are reached.

1.3 Code quality (20 marks)

The remaining marks (20) for the coding part will be awarded for general code quality as seen in the course materials to date. Here is some guidance.

• Keep your code neat and tidy; make sure it is properly indented throughout.

• Choose suitable names for variables and methods.

• Comment your code as needed.

• Split your code into separate methods as appropriate; code in the main method should be kept to a minimum; methods overall should not be too long.

2 Report (40 marks)

You will write a report providing some details on how you designed and implemented your program, as described in Section 1. Your report will consist of three main parts.

2.1 Input parameter choices (15 marks) 

In this part, you should explain the choices you make for the parameters a, σ and the function θ(t) which drive the behaviour of your system. For this, you will need to do some short researches on the Hull-White model and choose suitable values for these. Include links to any references used in your report. This part should be no more than 1 page in length.

2.2 Program design choices (15 marks)

In this part, you should explain the design choices you made for your Java program. You should consider the following questions.

• What are the different members (class variables or methods) of your Java class? What is their purpose?

• How did you proceed in implementing the model’s dynamics as described by Equation 1? How did you calculate minimum, maximum and average values of the rate function?

This part should be no more than 1 page in length.

2.3 Testing description (10 marks)

In your report, you should include a description of the testing you undertake of your system. State clearly which functionalities you are testing, what test you are carrying out, and why. You may include screenshots (of code, the output console, etc.) for clarity. This part should be no more than 1 page in length, screenshots excluded.

3 Submission instructions

In the dedicated “Coursework 3 submission” Assignment activity on the Learning Mall Online, you will need to submit the following two (2) documents.

• A plaintext .txt file, into which you have copied the source code of your Java class. This file should be named “CPT206 CW2 Code studentId.txt”.

• Your report from Section 2, typed into for instance a Word document, and converted into a PDF file. This file should be named “CPT206 CW2 Report studentId.pdf”.

The submission deadline is: Sunday, 9 May, 2021, 10pm.

        This assignment is individual work. Plagiarism (e.g. copying materials from other sources without proper acknowledgement) is a serious academic offence. Plagiarism and collusion will not be tolerated and will be dealt with in accordance with the University Code of Practice on Academic Integrity. Submitting work created by others, whether paid for or not, is a serious offence, and will be prosecuted vigorously. Individual students may be invited to explain parts of their code in person during a dedicated BBB session, and if they fail to demonstrate an understanding of the code, no credit will be given for that part of the code.

        Late submissions. The standard University policy on late submissions will apply: 5% of the total marks available for the component shall be deducted from the assessment mark for each working day after the submission date, up to a maximum of five working days, so long as this does not reduce the mark below the pass mark (40%); submissions more than five working days late will not be accepted.

        Good luck!