AFE7501-B Quantitative Methods in Finance Assignment

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Reference no: EM132768732

AFE7501-B Quantitative Methods in Finance - University of Bradford

Question 1 [Regression]

The data in Table 1 below links the stopping distance (in metres) of a car y to the speed of a car x (speed measured in mph).

Speed (mph) x Stopping distance (metres) Y

20	12
30	23
40	36
50	53
60	73
70	96

Table 1: Data for Question 1
(a) Enter this data into R and list the commands used

(b) Fit a suitable regression model to this data

(d) For the estimates in part (c) use R to construct a 95% prediction interval for each of these four speeds: 10, 80, 90 and 100mph. What is the interpretation of the prediction intervals in this case?

(e) How is the process of choosing a regression model in part (b) different to other regression examples you might see in accounting and finance?

Question 2 Probability regression

(a) List the assumptions underpinning the classical regression model.

The data in Table 2 below link the probability Y that a sales voucher is redeemed compared to the size of the discount X offered.

Discount XSample size Number of redeemed			coupons Probability of redemption Y
5	500	100	0.2
7	500	122	0.224
9	500	147	0.294
11	500	176	0.352
13	500	211	0.422
15	500	244	0.488
17	500	277	0.554
19	500	310	0.620
21	500	343	0.686
23	500	372	0.744
25	500	391	0.782

Table 2: Data for Question 2

(b) Enter the data in Table 2 into R and list the commands used.

(d) What is the regression model in part (c) called?

(e) Show that the linear regression model in part (c) cannot satisfy the classical linear regression assumptions listed in part (a).

(f) If X is equal to 31.63 estimate the probability that a voucher is redeemed in each case.

(g) Suggest a better model than the model in part (c). Use this model to re-estimate the probability in part (f).

Question 3 [Financial price data]

(a) Download price data for a financial asset of your choice. [Hint: possibilities here include stock price data from yahoo finance or cryptocurrency data].

European Union Countries

Non-European Union Countries

25, 33.99, 10, 20, 12.5, 19, 23.5, 20, 20, 30.175, 26, 10, 12.5, 27.5, 15, 15, 28.59, 20, 27, 19, 12.5, 16, 15, 17, 30, 22, 21

33.3,

35,

10,

24, 10, 15, 20, 12.5, 10, 9, 20,

15,

25,

20,

Explain why the asset or index you have chosen is interesting and give the precise dates for which you have collected the data.

(b) Download the data into R and calculate the log-returns.

List the R commands used.

(c) Fit an ARCH(1) model to the log-returns in part (b) and test for the presence of an ARCH effect within this data. List the R commands and R packages used.

(c) Fit a GARCH(1, 1) model to the log-returns in part (b) and test for the presence of ARCH and GARCH effects within this data. List the R commands and R packages used.

(e) List the stylised empirical facts of financial time series.

(f) [Independent research required]. Explain how more advanced family GARCH models can be fitted to the data in part (b) using R.

Question 4 [Basic hypothesis tests]

The data in Table 3 below lists the corporation tax rates for selected EU and non-EU countries.

Table 3: Data on Corporation Tax rates for Question 4
(a) Read this data into R and list the R commands used.

(b) Test for a difference in the mean corporation tax rate between EU and non-EU countries.

(d) Based on the findings in part (c-d) what are the implications of Brexit upon the rate of UK corporation tax?

(e) What implications might the current coronavirus pandemic have upon the data in Table 3?

Reference no: EM132768732

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