No. of Pages:
No. of Questions:
3
7
EC3070
MIDSUMMER EXAMINATIONS 2009
Subject
ECONOMICS
Title of Paper
EC3070 FINANCIAL DERIVATIVES
Time Allowed
ONE AND A HALF HOURS
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Instructions to candidates
Answer ONE question from SECTION A
and ONE question from SECTION B
(The answers carry equal weight)
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CONTINUED …
EC3070
Section A
1. Consider a long position in a European call option with a strike price K1 .
(a) Graph the profit from this investment as a function of the spot price
at maturity, and explain the graph.
(b) Carefully explain the consequences on the initial investment and the
profit profile of adding to this portfolio a short position in a call option
with the same underlying asset, maturity date and with strike price
K2 with (i) K2 < K1 and (ii) K2 > K1 .
(c) Explain the differences between a strip, a strap and a straddle. Under
which circumstances would you recommend each of them as a trading
strategy?
2. Establish the formula for the present value of a stream of n annual payments of £a, which begin in one year’s time, when the risk-free rate of
interest r is used in forming the discount factor.
For an investment of £1,000, option A offers you annual payments of £50
in perpetuity. Option B offers you ten annual installments of £45 and the
return of the £1,000 together with the final installment.
Evaluate these two options and declare which of them you would prefer, if
you do not regard them as equal. (Hint. you may assume that there is a
risk-free annual rate of interest of 5%.)
3. A stock price is currently S0 = 50. At the end of the month, it will be
either S1u = 60 or S1d = 40. The risk-free rate of continuously compounded
interest is 6% per annum. What is the value c1|0 of a one-month European
call option with a strike price of $45? Give a detailed explanation of your
reasoning.
CONTINUED
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EC3070
Section B
4. Describe and explain the financial circumstances affecting any two of the
following events:
(a) The run on Northern Rock and the demise of Lehman Brothers,
(b) The crash of the Wall Street stock market in 1929,
(c) The bail-out of Long Term Capital Management in 1998,
(d) The collapse of the AIG insurance empire,
(e) The acquisition, by trading in financial markets, of a controlling
interest in the Volkswagen company by the Porsche company.
5. Describe the provisions for the financial protection of farmers and traders
in agricultural commodities that are offered by the Chicago Board of Trade.
Are the activities of the Board of Trade in protecting the interests of these
parties helped or hindered by the presence of market speculators?
6. Give the mathematical definitions of the following stochastic processes:
(a) A standardised Wiener process,
(b) Arithmetic Brownian motion,
(c) Geometric Brownian motion.
Let the equation describing the evolution of the spot price S of a financial
asset be
dS = Sµdt + Sσdw(t),
where dw(t) denotes a standardised Wiener process. With reference to
Ito’s lemma, derive the expression for the logarithm of the process.
What effect does the level of volatility have upon the rate of drift?
What features of our experience of the real world are missing from the
equation?
7. Derive the one-step binomial formula for the premium of a European call
option written at time t = 0 and with a date of expiry at time t = τ .
Generalise the formula to the case of an n-step binomial model and indicate
how this converges on the Black–Scholes option pricing formula as n → ∞.
Give an account of the properties of the Black–Scholes formula in terms
of the ceteribus paribus variations of its several arguments and comment
on the realism of the assumptions that underlie the model from which it
is derived.
END OF PAPER
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