Put Call Question.........................?

Question

Applying the put-call parity equation, can anyone describe the steps in creating a synthetic stock.

Answer 1

ZMan is almost right -- you would also have to buy a bond.

Put-Call Parity is:

S+P=PV(K)+C

where:

S is the stock

P is the price of a European put with strike price K

C is the price of a European call with strike price K

PV(K) is the present value of K that matures on the expiration date of the two options.

A little algebra shows that:

S = PV(K)+C-P

So, you need to go long a K dollar zero coupon bond, long a call option and short a put option.

Answer 2

A synthetic long stock position is created by selling puts and buying an equal number of calls with the same expiration and strike price.

A synthetic short stock position is created by buying puts and selling an equal number of calls with the same expiration and strike price.

Addendum

While I agree with Taranto that you have to consider the interest rate on cash, I do not agree that you have to buy a bond. For example, if you had an account with $100,000 in stocks in it but no cash, you would have to pay interest on a margin debt if you purchased the stock on margin. If you open a synthetic long stock position for a credit, you will not pay interest on a margin debt. The interest you do not pay resolves the carrying cost factor in the put-call parity formula without buying a bond.