# EXAMINATION FOR THE DEGREE OF MASTER OF SCIENCE (FINANCE) AND OTHER DEGREES DERIVATIVES

FIN9007

Exam Time Table Code FIN9007

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EXAMINATION FOR THE DEGREE OF

MASTER OF SCIENCE (FINANCE) AND OTHER DEGREES

DERIVATIVES

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

• (a) With reference to the Black Scholes model explain the concept of risk (30%) neutral valuation. Outline the Monte Carlo valuation procedures.
• Demonstrate the manner in which the Black-Scholes model is adapted to (40%) accommodate European futures options, i.e. the Black’s model for futures

• Explain the exponentially weighted moving average (EWMA) model for (30%)

estimating volatility from historical data. Explain how to apply the GARCH methodology to derive and forecast an asset’s volatility.

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

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

• “Time series momentum”, by Moskowitz, T., Ooi, Y. H. and Pedersen, L. H. (2012), Journal of Financial Economics 104, 228250.

• (a) Stock A has a daily volatility of 1.2% and stock B has a daily volatility of (50%)

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?

1. What is the 99%, 5-day VaR for 1 million dollar investment in stock B?
• What is the 99%, 5-day VaR for 1 million dollar investment in stock A and 1 million dollar investment in stock B?
1. What is the benefit of diversification for the 99% VaR?

• Explain why the futures price Ft of a stock (without paying dividend) with (50%) price St satisfies F Set t r T t( ), 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 St follows a Geometric Brownian Motion, what is the process followed by the futures price Ft ? Interpret your result.

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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 NewtonRaphson 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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