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EC566 Quantitative Methods in Finance
Term Assignment
This assignment is 100 marks and is worth 40% of your overall grade for this module.
The deadline for submission of this term assignment is 5pm Tuesday, 31st March
2020. Late submissions will not be accepted. Typed assignments must be submitted
on Blackboard in PDF format on or before this date along with two .py files (one for
Question 1 labelled ‘firstname surname Q1.py’ and another for Question 2 labelled ‘firstname
surname Q2.py’). Please also include the related Python output in the assignment
document (graphs etc.). This is an individual assignment and you must submit your
own version of the assignment. Marks breakdown in [ ].
1. Select three financial assets of your choice. For each asset, obtain daily price data for
five years up until 29/02/2020 and use this data to conduct a quantitative analysis of
these assets to answer the following questions. Assume the risk-free rate, r is currently
4%.
(a) How far does each asset reflect the features of financial market data discussed in [10]
class i.e. stationarity, log-returns, random walks (graphs are required).
(b) Use the CAPM model to estimate the expected return and the systematic risk [15]
for each asset and discuss the implications of the αs and βs for each asset (graphs
are required).
(c) Use Modern Portfolio Theory to construct an efficient frontier for these assets [15]
and to choose the optimal portfolio and the minimum variance portfolio of the
three assets. Explain your steps in detail and discuss the diversification strategy
(graphs are required).
(d) Use the CAPM model to estimate the expected return and the systematic risk for [15]
the optimal portfolio and the minimum variance portfolio above and discuss the
implications of the α and β for these portfolios. Comment on the diversification
strategy.
(e) Use Value at Risk to measure how risky each asset is and how risky the optimal [15]
portfolio and the minimum variance portfolio are and comment on the diversifi-
cation strategy (graphs are required).
1
2. (a) Define a function in Python that prices a call option using Black-Scholes. The [10]
output from the function should read in three lines:
The value of d1 is:
The value of d2 is:
The call option price using Black-Scholes is:
Hint: N(d1) is equivalent to stats.norm.cdf(d1) in Python where scipy.stats is
imported as stats
(b) Define a function in Python that prices a put option using Black-Scholes. The [10]
output from the function should read in three lines:
The value of d1 is:
The value of d2 is:
The put option price using Black-Scholes is:
Hint: N(d1) is equivalent to stats.norm.cdf(d1) in Python where scipy.stats is
imported as stats
(c) Use the above two functions to price a call option and a put option at t = 0 [10]
where the relevant parameters are as follows:
S0 = 100 underlying stock price at t = 0
X = 100 exercise/strike price
T = 1 expiry in 1 year
r = 0.04 risk-free rate
σ = 0.2 volatility of underlying stock
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