In this video/ movie clip, I will introduce the concept of put options. Please refer to the post “Introduction to Call Options” if you are not familiar with the terminologies. Transcript is shown below.

As in call option, put option is also a contract. You buy put option because you expect the underlying asset will depreciate. A put option allows you to sell the underlying asset at a particular price. Again, you have the right to exercise the option but you don’t the obligation to do so. On the other hand, the seller of the put option has the obligation if buyer chooses to do so.

Let’s look into an example. Assume there is a put option with $4 premium (P). And the exercise price X of the option is $20. What will be the value of the put option as the stock price changes? Let’s say the stock price is $20 on the expiration day, then if you exercise the option, you can buy the stock at the market price (S=$20) and the option allows you to sell the stock at the exercise price (X=$20). So, you will gain nothing. However, you already paid $4 premium. That means you lose $4. And thus the value of the option is -$4. Now what if the stock drops to $16? Now you are can buy stock at market price (S=$16) and you can sell the stock at the exercise price (X=$20). So you will gain $4. Again, you already paid $4 for premium. So you don’t lose and you don’t gain. So the value of the option is $0 when the S = $16. So you can see that the breakeven point of the put option is when S = X-P. As the stock price further reduces, your gain will increase because you can buy stock at lower market price but still sell it at X. What if the stock price is higher than the exercise price? Since you can only buy stock at a higher price than at which you can sell (X), you will not choose to exercise the contract. So the loss is capped at the premium again, i.e. -$4.

Similar to the call option, the seller has a value curve being the mirror image of the buyer about the zero. So, this is again, a zero sum game. Also, the seller’s curve is called “short put” while the buyer curve is called “long put”. So for options, “short” or “long” are determined by “buy” or  “sell”, regardless of the nature of the option (call or put).

What’s the difference between the call option and put option? You notice that the gain of the buyer is capped at X-P and the loss of the seller is capped at X-P in put option. Because the price of the stock cannot drop below zero. While for call option, they are unlimited.