03 Jun Question Barnard College Department of Economics
Question
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
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