ECON V3025 Fall 2014 questions

Barnard College
Department of Economics
Financial Economics
ECON V3025 Fall 2014
Rajiv Sethi 2 Lehman
Phone: (212) 854 5140 [email protected]
Problem Set 6
Due Date: Monday, December 8
1. A stock is currently trading for $50. An investor
constructs a portfolio composed of
options on this stock as follows: (i) buy one at-the-money
put, (ii) buy one at-themoney
call, (iii) write one put with strike price $60, and (iv)
sell one call with strike
price $40. All options have the same time to expiration T.
Express the payoff from
this strategy in terms of the share price ST on the
expiration date, using a table and a
graph. What are the highest and lowest values that the
payoff could take? Assuming
that investors can borrow at the risk free rate, and that
this rate is positive, which of
the two at-the-money options will have the higher premium?
Explain your answer. [4]
2. Consider a stock with current price S0. Call options on
this stock with strike price X
and expiry after time T currently cost C, while put options
with the same strike price
and expiration date cost P. The stock is expected to pay a
dividend D at time T, and
the risk-free rate of interest is rf . Determine the payoffs
at time T from each of the
following strategies: (i) a protective put, and (ii) a
call-plus-bills portfolio, where the
bills have face value X + D. Use your findings to obtain a
put-call parity theorem for
dividend-paying stocks. [4]
3. Suppose that the current price of an asset is $400. After
six months, there are two
possible values for the asset price, and after one year
there are three, as follows:
t = 0 t =
1
2
t = 1
S
++ = 484
%
S
+ = 440
% &
S0 = 400 S
+? = 418
& %
S
? = 380
&
S
?? = 361
The annual risk-free rate of interest is 5%. If there is no
arbitrage opportunity, find
the price of an at-the-money call option on this asset, with
expiration date one year
from today. [4]4. In each of the following cases, determine
whether or not there is an arbitrage opportunity
and, where possible, describe the steps you would take in
order to construct
an arbitrage portfolio. Provide as much detail about current
and future cash flows as
possible. Assume that borrowing at the risk-free rate is
possible, and any asset can be
sold short.
(a) The annual dividend yield on the S&P 500 index is below
the interest rate on one
year Treasury bills, and the futures price for delivery of
the index after one year
is below the current value of the index.
(b) The annual risk-free rate of interest is greater in the
UK than in Switzerland, and
the forward exchange rate, in British pounds per Swiss
Franc, is above the spot
exchange rate.
(c) Call options with strike price 110 and expiration after
one year have a premium
of $4, while the underlying share has price $100, and the
risk-free rate of interest
is 10%. Assume that the underlying share pays no dividends.
[4]
5. Obtain the prices for the E-mini S&P 500 futures
contracts with expiration in March
and September 2015 from the Chicago Mercantile Exchange.
Make a note of the date
and time at which the quotes you are using were last
updated. Which of the two
contracts has the higher price? Find estimates of the
current S&P dividend yield, and
current risk-free interest rates over the relevant horizon
(cite your sources). Use this
information to compare the futures prices to the predictions
of the Spot-Futures Parity
Theorem. [4]
2