Question

Assume the following premia: Strike $950 Call $120.405 93.809 84.470 71.802 51.873 Put $51.777 74.201 1000 1020 84.470 101.214 1050 1107 137.167 I 1) Suppose you invest in the S&P stock index for $1000, buy a 950-strike put, and sell a 1050- strike call. Draw a profit diagram for this position. What is the net option premium? 2) Here is a quote from an investment website about an investment strategy using options: One strategy investors apply is a "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. Suppose 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 pod times to expiration. a. What can you say about the strike price? b. What term best describes the position you have created? 3) Suppose you short the S&P index for $1000 and buy a 950-strike call. Construct payoff and profit diagrams for this position. Verify that you obtain the same payoff and profit diagram by borrowing $931.37 and buying a 950-strike put 4) Verify that you earn the same profit and payoff by (a) buying the S&R index for $1000, and (b) buying a 950-strike S&R call, selling a 950-strike S&R put, and lending $931.37 5) Suppose the stock price is $35 and the continuously compounded interest rate is 5 %. a. What is the 6-month forward price, assuming dividends are zero? b. If the 6-month forward price is $35.50, what is the annualized forward premium? 6) Describe the profit from the following portfolio: a long forward contract European put option on the asset with the same maturity as the forward contract and a strike price that is equal to the forward price of the asset at the time the portfolio is set up. on an asset and a long 7) Forwards and Puts (Hint: Compare Forward Contracts and Put Options) Suppose that USD-sterling spot and forward exchange rates are as follows: Spot 90-day forward 180-day forward 1.5580 1.5556 1.5518 What opportunities are open to an arbitrageur in the following situations? A 180-day European call option to buy £l for S1.52 costs 2 cents. (a) (b) 90-day European put option to sell £l for $1.59 costs 2 cents.

Answer 1

You have asked multiple unrelated questions in a single post. I will address first the question.

Please post the balance questions, one by one, separately.

Q - 1

Buy index, buy put of K1 = 950, sell call of K2 = 1,050

Net option premium = C - P = 71.802 - 51.777 = 20.025

Profit on expiration = max (K1 - S, 0) - max (S - K2, 0) + (S - 1,000) + net option premium = max (950 - S, 0) - max (S - 1,050, 0) + (S - 1,000) + 20.025

Please see the table below and then the graph:

Stock Price, S	Gain / (Loss) = max (950 - S, 0) - max (S - 1,050, 0) + (S - 1,000) + 20.025
0	-29.975
100	-29.975
200	-29.975
300	-29.975
400	-29.975
500	-29.975
600	-29.975
700	-29.975
800	-29.975
900	-29.975
1000	20.025
1100	70.025
1200	70.025
1300	70.025
1400	70.025

Gain (Loss) 80 60 40 20 Stock Price, S 0 200 400 600 800 1000 1200 1400 1600 1800 -20 40