Option Trading Blog

Introduction

With synthetic positions, we aim to make money not by trying to predict future movements, but by mis priced option prices. What does it mean to have a synthetic position?

Consider the following example: A trader who purchases a call that expires in one month with a strike price of 100 and writes a put with the same time of expiry and the same strike price of 100. His portfolio looks like this:

• long a one month 100 call

• short a 1 month 100 put

If at the end of the month, the underlying expires above 100, the put option expires worthless, and we will exercise our call option. If it expires below 100, we don’t exercise our long call, and we have to pay for the put option we have written. If you notice carefully, we managed to mimic the behaviour of the underlying. When you buy a stock for 100$, if at the end of 1 month it is above 100, you profit the difference, and if it below 100, you lose the difference. This is the essence of a synthetic position. This also works in the opposite way. Short selling a stock means buying a put and writing a call.

• synthetic long position = long call + short put

• synthetic short position = short call + long put

A note about the delta: Since the synthetic position mimics the underlying’s behaviour, we expect it to have a delta of approximately 100.

Suppose a stock is trading at 102$ and we want to take a long position (buying it). We have two choices: Buying it directly or buying the synthetic position, by buying a call and selling a put with the same expiry date. We will suppose the long call that expires in 1 month time, and has a strike of 100, costs 5$. The put with the same strike and expiry costs 3$. If we take the synthetic long, it’ll cost us 2$.

Consider that in 1 month time the stock now costs 110$. We have earned a total 10$-2$ = 8$. The same as we would have earned by just buying the stock. Now let us suppose the call option is traded at 4.90$ and the put at 3.05$. It’ll cost us now 1.85$ to take the long position, but we will profit 10$-1.85$ = 8.15$, which is better than just buying the stock. You can see that as long as the call option minus the put option is less than 2$, we are better off taking the long synthetic option. This difference is also called the synthetic market.

We can make the above more general:

• call price - put price = underlying price - exercise price

This is known as the put-call parity. From the above equation it is easy to show how to create a synthetic stock

• underlying price = call price - put price + exercise price

How To Profit

Knowing how to create a synthetic stock, we are faced with an opportunity of making a profit by a mis priced stock. If the stock is more expensive than the synthetic stock, we short sell the stock and buy the synthetic stock. If the stock is cheaper than the synthetic stock, we short sell the synthetic stock and buy the stock!

Suppose as before that the stock is traded at 102$. The 100 call is worth 5.10$, while the put is 2.85$. The synthetic difference is 2.25$. Since the stock and the synthetic stock are basically the same, a trader would want to buy the cheaper contract (the stock) and sell the expensive one (the synthetic stock).

Transaction Cash Flow

1. purchasing the stock -102
2. selling the call +5.1
3. purchasing the put -2.85
4. carry to expiration and exercise +100

total of : + .25

No matter what happens, he is guaranteed to receive .25$. At the beginning, he has a debit of 99.75$. If the stock goes up to 110$, the put expires worthless and he has to sell the stock for 100$.  Hence a profit of .25$. If the stock goes down to 90$, we sell the stock for 100$, and again we receive .25$.

All experienced traders are familiar with the synthetic price relationship, so such opportunities are short lived. In the next post I’ll explain in detail the risk involved in taking such positions in the market.