FIN9007
Exam Time Table Code FIN9007
Approved calculators only permitted
EXAMINATION FOR THE DEGREE OF
MASTER OF SCIENCE (FINANCE) AND OTHER DEGREES
DERIVATIVES
Wednesday, 9th August 2017 2:30 PM - 4:30 PM
Examiners: Professor Gerhard Kling
and the internal examiners
Write on both sides of the answer paper
Answer any THREE questions
All questions carry equal marks
Allocation of marks within questions is shown in brackets
You have TWO HOURS to complete the paper
FIN9007/AUG2017

Answer any THREE questions

1 (a) With reference to the Black Scholes model explain the concept of risk
neutral valuation. Outline the Monte Carlo valuation procedures.
(30%)

(b) Demonstrate the manner in which the Black-Scholes model is adapted to
accommodate European futures options, i.e. the Black’s model for futures
options.
(40%)

(c) Explain the exponentially weighted moving average (EWMA) model for
estimating volatility from historical data. Explain how to apply the GARCH
methodology to derive and forecast an asset’s volatility.
(30%)

2 Consider ONE of the following articles. Briefly document the key elements
of the paper, the methodology used in the investigation, and provide a
commentary on the ramifications of the main findings highlighted in the
article.
(100%)

(i) “Understanding VIX”, by Whaley R. (2009), Journal of Portfolio
Management, 35, 98–105.

(ii) “Time series momentum”, by Moskowitz, T., Ooi, Y. H. and
Pedersen, L. H. (2012), Journal of Financial Economics 104, 228-
250.

3 (a) Stock A has a daily volatility of 1.2% and stock B has a daily volatility of
1.8%. The correlation between the two stock price returns is 0.2.
I. What is the 99%, 5-day VaR for 1 million dollar investment in
stock A?
II. What is the 99%, 5-day VaR for 1 million dollar investment in
stock B?
III. What is the 99%, 5-day VaR for 1 million dollar investment in
stock A and 1 million dollar investment in stock B?
IV. What is the benefit of diversification for the 99% VaR?

(50%)
(b) Explain why the futures price tF of a stock (without paying dividend) with
price tS satisfies
( ) ,r T tt tF S e
 where r is the risk-free rate, and T is
the maturing date. Can you use the same arguments to price all other
types of futures contracts? Furthermore, if the stock price tS follows a
Geometric Brownian Motion, what is the process followed by the futures
price ?tF Interpret your result.

(50%)

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FIN9007/AUG2017

4 (a) Outline the mean-variance approach to hedge ratio construction. What
are the speculative demand and the hedging demand? Interpret them
economically.
(50%)

(b) What is the implied volatility? Explain how the Bisection OR the Newton-
Raphson procedure is utilized to calculate the implied volatility of options
priced according to the Black-Scholes model.
(50%)

5 (a) Detail the basic concepts of Value at Risk (VaR); explain how to use
historical simulation to estimate VaR. Comment on the advantages and
disadvantages of this method.

(40%)

(b) What are volatility smiles, describe the key features of volatility smiles,
and why do you think they exist?
(30%)

(c) What is credit risk? Explain the risk-neutral and real-world default
probabilities and the difference between them. Which should be used for
(i) valuation and (ii) scenario analysis? How are recovery rates usually
defined and how is the recovery rate used to approximately calculate
default probability?
(30%)

END OF EXAMINATION
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