Derivative Securities: Pricing, Hedging and Trading (ICM211)
Answer any THREE questions
Q1 Write a report for a client detailing the risks and benefits of holding
an equity options portfolio. Your report should focus on the
appropriate volatility spreads for a sample of different market
conditions and the risk management of the associated Greek
exposures. (100%)
Q2. a) Explain why a bullish vertical spread has very low, or zero,
Gamma, Theta and Vega exposure. (25%)
b) In what respect is a put ratio vertical spread different from a short
put? Also explain why the put ratio vertical spread might not always
be long Delta. (25%)
c) Explain why shorter dated options are better than longer dated
ones for trading actual volatility. (25%)
d) In what sense can the implied volatility of an option be regarded
as the price (premium) of that option? (25%)
Q3 The following questions are based on the Chicago Mercantile
Exchange Strategy Guide. For each initial position and new position
resulting from the follow-up trade, you must give a brief explanation
of the risks associated with the Greek exposures which you have
listed.
a) i) You are bullish and want to be net long volatility but want to
do the trade for a net credit. What is your initial position and
its associated Greek exposures?
ii) You want to remain long volatility but now have no directional
view. What is your follow-up trade and new position and its
associated Greek exposures? (20%)
b) i) You want to be net short volatility but also believe that the
market has very mild downside potential. What is your initial
position and its associated Greek exposures?
ii) You want to remain short volatility but now have no
directional view. What is your follow-up trade and new
position and its associated Greek exposures? (20%)
c) i) You are mildly bearish and have no view of volatility. What is
your initial position and its associated Greek exposures?
ii) You remain mildly bearish but now believe that volatility will
fall. What is your follow-up trade and new position and its
associated Greek exposures? (20%)
d) i) You want to be net short volatility but also believe that the
market has very mild upside potential. What is your initial
position and its associated Greek exposures?
ii) You are now bearish on fundamentals but believe that
volatility is rising. What is your follow-up trade and new
position and its associated Greek exposures? (20%)
e) i) You want to be net long volatility but do want upside or
downside directional risk. What is your initial position and its
associated Greek exposures?
ii) You want to remain long volatility but are now bullish on the
market. What is your follow-up trade and new position and its
associated Greek exposures? (20%)
Q4. Using diagrams, explain in detail the riskless hedge principle behind
option pricing and show how it can be used to price options.
(100%)
Q5. a) In what critical way does a call ratio backspread differ from
holding just long calls? Explain exactly why this is the case. (25%)
b) In option theory we can keep a short option delta neutral without
losing money. Explain why this is not the case in practice. (25%)
c) Are short butterflies always long Gamma, long Vega and short
Theta? Explain why this might not be the case. (25%)
d) Explain under what conditions it might be possible to keep a short
Gamma position Delta neutral without losing money. (25%)
Q6. a) Outline the benefits and risks of holding a short time spread,
explaining why the Greek exposures are what they are. (25%)
(b) Explain how and why Gamma changes through time. (25%)
(c) A market maker has a position with a 52% Delta and a 6%
Gamma. What information does the 6% Gamma give the market
maker and how can he take advantage of it, if at all? (25%)
(d) Explain why the Rho of long calls is positive and that of long puts
negative. Also explain why the opposite is true for short calls and
short puts. (25%)
(End of Question Paper)
