Forwards and Options

Respond to each of the following questions (notice that there are main questions and sub-questions below some of the main questions - don't miss any!)

1. Suppose you enter into a long 6-month forward position at a forward price of $60. What is the payoff in 6 months for prices of $50, $55, $60, $65, and $70?

2. Suppose that instead you buy a 6-month call option with a strike price of $60. What is the payoff in 6 months at the same prices for the underlying asset?

3. Comparing the payoffs of parts (a) and (b), which contract should be more expensive (i.e., the long call or long forward)? Why is this so?

4. Suppose you enter into a short 6-month forward position at a forward price of $60. What is the payoff in 6 months for prices of $50, $55, $60, $65, and $70?

5. Suppose you buy a 6-month put option with a strike price of $60. What is the payoff in 6 months at the same prices for the underlying asset?

6. Comparing the payoffs of parts (a) and (b), which contract should be more expensive (i.e., the long put or short forward)? Why is this so?

7. Use the following premiums for S&P options with 6 months to expiration:

Strike                     Call                          Put

$950                       $120.405               $51.777

1000                       93.809                  74.201

1020                       84.470                  84.470

1050                       71.802                  101.214

1107                       51.873                  137.167

Assume you buy a 1,000-strike S&P call, sell a 1050-strike S&P call, sell a 1,000-strike S&P put, and buy a 1050-strike S&P put.
a. Using a table, verify that there is no S&P price risk in this transaction.
b. What is the initial cost of the position?
c. What is the value of the position after 6 months?
d. What is the implicit interest rate in these cash ?ows over 6 months?

8. Here is a quote from an investment website about an investment strategy using options:

One strategy investors are applying to the XYZ options is using "synthetic stock." A synthetic stock is created when an investor simultaneously purchases a call option and sells a put option on the same stock. The end result is that the synthetic stock has the same value, in terms of capital gain potential, as the underlying stock itself. Provided the premiums on the options are the same, they cancel each other out so the transaction fees are a wash.(as cited in McDonald, 2013, question 3.19)

Suppose, to be concrete that the premium on the call you buy is the same as the premium on the put you sell, and both have the same strikes and times to expiration.

a. What can you say about the strike price?

b. What term best describes the position you have created? What is the shape of the profit diagram?

c. Suppose the options have a bid-ask spread. If you are creating a synthetic purchased stock and the net premium is zero inclusive of the bid-ask spread, where will the strike price be relative to the forward price?

d. If you create a synthetic short stock with zero premium inclusive of the bid-ask spread, where will the strike price be relative to the forward price?

e. Do you consider the "transaction fees" to really be "a wash"? Why or why not?

Complete your response in 2-4 pages using Microsoft Word or Excel. For calculations, you must show work to receive credit.