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ECON V3025 Fall 2014 questions

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Question;Barnard College;Department of Economics;Financial Economics;ECON V3025 Fall 2014;Rajiv Sethi 2 Lehman;Phone: (212) 854 5140 rs328@columbia.edu;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

 

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