Question

Use the following option prices for options on a stock index that pays no dividends to answer question. The options have three months to expiration, and the index value is currently 1,000.

STRIKE (K)	CALL PRICE	PUT PRICE
975	77.716	43.015
1000	64.595	X
1025	53.115	67.916

a. In order to create a synthetic long forward with a price of 975, what options need 
to be bought or sold? What is the total price of those trades? 


b. An investor buys the index and buys a 975 put. What is the name of this position 
and what are the minimum and maximum profits (or losses) on the position? 


(Please answer with all the steps and formula. No excel please)

Answer 1

a. In order to create a Synthetic Long forward position, the investor buys a call option and sells a put option of the same strike price at the same time.
Here, in order to create the synthetic long forward with a price of 975, the investors buys 975 call and sells 975 put.

Total Price of Trade = Premium Received from Put - Premium Paid for Call = 43.015 - 77.716 = -34.701

There is a net cash outflow of 34.701.

b. Since the investor buys the put option and also the stock, he is insuring himself from the downside of the stock movements. The Strategy is Protective Put.
Here the upside is unlimited as the put option will expire worthless, if the stock continues to move up.
However, the maximum loss is (1000 - 975) + Put Premium = 25 + 43.015 = 68.015