代写MA3071编程、代做MATLAB程序设计

日期：2024-10-13 10:21

MA3071 Financial Mathematics - DLI

Year 2024-2025

Coursework 1

INSTRUCTIONS AND DEADLINE:

Please electronically submit one piece of typed work per person as a single PDF file via

Blackboard by November 04, 2024, at 12:00 (UK) / 20:00 (China).

MARKING CRITERIA:

>> Coursework is marked out of 100 points, with the number of marks for each main

question indicated at the beginning of each.

>> Clearly justify and explain your answers. You are expected to use MATLAB for calculations.

A printout without full explanations of the formulas and reasoning will result

in a deduction of marks.

>> You are required to submit a single PDF file containing the computational results,

justifications, explanations, and the programming code for each question. Ensure that

your MATLAB code is properly commented.

>> You need to copy your MATLAB code into the PDF file. Your code should be in text

format and must be copyable. Do not insert your code as images or screenshots, and

do not submit separate code files.

>> To ensure you are able to consolidate your knowledge, understanding and skills, generative

AI tools must not be used at any point during the assessment.

>> You can submit your answers up to 3 attempts when submitting via Blackboard. Only

the last attempt of your submission will be assessed. Email submissions won’t be

accepted.

Please note: Any numerical results should be rounded to four decimal places.

LATE SUBMISSION:

In cases where there are no accepted mitigating circumstances, late submission of coursework

will lead automatically to the imposition of a penalty. Your mark will be reduced in

line with the University’s penalties scheme for late submission of coursework. The University’s

regulations about the late submission of coursework are found in Senate Regulation 7:

governing the Assessment of Taught Programmes. Refer specifically to 7.94 for details on

penalties for late submission.

1Question [100 marks]

The spreadsheet “BARC.L.xlsx” lists historical data for the monthly adjusted closing prices

1

of Barclays Bank (BARC.L) stock from 31/May/2014 to 31/May/2024 (a total of 121

months).

Assume that the price (St) of BARC.L follows a log-normal distribution, such that

where ρ is the risk-free interest rate and σ is the volatility of the stock.

Suppose that today is 01/Jun/2024, and S0 is equal to the closing price of last month.

The future price of BARC.L over the next 12 months is modelled by a 20-period binomial

tree, such that

St = St−1Yt

where Yt

, t = 1, 2, . . . , 20 are i.i.d random variables with the following distributions

P(Yt = u) + P(Yt = d) = 1, t = 1, · · · , 20

Consider a European put option on the BARC.L stock with a fixed strike price of K = £210

and a maturity date of 31/May/2025. In the UK market, the interest rate set by the Bank

of England is 5% per annum2

. Answer the following questions:

a) [20 marks] Estimate the monthly volatility of the BARC.L stock, as well as the u and

d factors of the binomial tree.

b) [40 marks] Calculate today’s arbitrage-free option price of the European put option.

c) [40 marks] Determine the hedging portfolio for the European put option.

1The effect of dividends on stock prices has been excluded from the adjusted closing prices.

2For official annual bank rate in the UK, see https://www.bankofengland.co.uk/monetary-policy/

the-interest-rate-bank-rate

2