L25: Options intro

Options are a type of financial asset called derivative securities. The derivative means that the value of these assets depends on the value of a different asset (often called the “underlying” asset).

Call options

A call option is a financial asset (a contract really) that gives you the right (but not the obligation) to

  • buy a particular stock (called the underlying stock)
  • at a particular price (called the strike price)
  • on or before a particular date (called the expiration date)
    • the “or before” only applies to American options
    • for European options you are not allowed to exercise your option before the expiration date
      • you can assume that all the options we talk about in this class are American options

The price you have to pay to buy an option is called the premium of that option.

When/if you choose to buy the underlying asset, we say that you are exercising your option. It only makes sense to do so when the stock is trading at a price higher than the strike price of the option.

Example 1:

On Oct 14, 2014, a call option on Facebook (FB), expiring on Nov 14, 2014 with strike price of $75 sold for $5. The price of FB on Oct 14 was $76.

Q1: For this call option, what is the:

  • Underlying asset
  • Strike price
  • Expiration date
  • Premium

Q2: What is your profit if you exercise this option immediately after you buy it?

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Q3: Suppose on Oct 21, 2014, FB is trading at $74 a share. Would you exercise the option?

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Q4: Suppose right before the call option expires (on Nov-14, 2014), FB is trading at $76 a share. Would you exercise the option?

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Call option payoff and profit

The payoff (revenue) of a call option that you own is the difference between the underlying stock price (let’s call it S) and the option’s strike price (let’s call it X) when \(S > X\) and 0 otherwise (since you wouldn’t exercise it when \(S < X\)).

\[Payoff = max(S - X, 0)\]

The profit from the call option equals its payoff minus it premium (i.e. the price you paid to buy the option).

\[Profit = max(S - X, 0) - Premium\]

Example 2:

You buy a call option on stock A for a premium of $14. The strike price is $80 and the option expires in a month.

Q1: What is the payoff from this call option if the price of stock A is $60? How about $70? $80? $90? $100?

Q2: What is the profit from the call option in each of those scenarios?

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Q3: Draw a graph that shows your payoff (revenue) and your profit as a function of the price of stock A.

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Selling (writing) call options

If you sell (aka “write”) a call option, you are in the opposite position from the person who buys it: you give them the option (but not the obligation) to buy the underlying asset from you at a given strike price. If they decide to exercise that option, you (as the seller of the option) are obligated to sell them the underlying stock at the strike price (even though it might be trading at a higher price on the market).

The payoff (revenue) of a call option that you sell is the negative of the payoff to the person that bought it:

\[Payoff = - max(S - X, 0)\]

The profit from selling a call option equals the negative of the profit to the person that bought it:

\[Profit = - max(S - X, 0) + Premium\]

Example 3:

You sell a call option on stock A for a premium of $10. The strike price is $50 and the option expires in a month.

Q1: What is your payoff from this call option if the price of stock A is $40? How about $50? $60? $70?

Q2: What is your profit from the call option in each of those scenarios?

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Q3: Draw a graph that shows your payoff (revenue) and your profit as a function of the price of stock A.

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Put options

A put option is a financial asset that gives you the right (but not the obligation) to

  • sell a particular stock (called the underlying stock)
  • at a particular price (called the strike price)
  • on or before a particular date (called the expiration date)

It only makes sense to exercise a put option when the stock is trading at a price lower than the strike price of the option.

Example 4:

On Oct 14, 2014, you buy a put option on Facebook (FB) for $5. The option expires on Nov 14, 2014 and has a strike price of $75. The price of FB on Oct 14 was $74.

Q1: For this put option, what is the:

  • Underlying asset
  • Strike price
  • Expiration date
  • Premium

Q2: What is your profit if you exercise this option immediately after you buy it?

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Q3: Suppose on Oct 21, 2014, FB is trading at $76 a share. Would you exercise the option?

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Q4: Suppose right before the put option expires (on Nov-14, 2014), FB is trading at $74 a share. Would you exercise the option?

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Put option payoff and profit

The payoff (revenue) of a put option that you own is the difference between the option’s strike price (let’s put it X) and the underlying stock price (let’s put it S) when \(X > S\) and 0 otherwise (since you wouldn’t exercise it when \(X < S\)).

\[Payoff = max(X - S, 0)\]

The profit from the put option equals its payoff minus it premium (i.e. the price you paid to buy the option).

\[Profit = max(X - S, 0) - Premium\]

Example 5:

You buy a put option on stock A for a premium of $10. The strike price is $40 and the option expires in a month.

Q1: What is the payoff from this put option if the price of stock A is $60? How about $40? $20? $0?

Q2: What is the profit from the put option in each of those scenarios?

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Q3: Draw a graph that shows your payoff (revenue) and your profit as a function of the price of stock A.

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Selling (writing) put options

If you sell (aka “write”) a put option, you are in the opposite position from the person who buys it: you give them the option (but not the obligation) to sell the underlying asset to you at a given strike price. If they decide to exercise that option, you (as the seller of the option) are obligated to buy the underlying stock from them at the strike price (even though it might be trading at a lower price on the market).

The payoff (revenue) of a put option that you sell is the negative of the payoff to the person that bought it:

\[Payoff = - max(X - S, 0)\]

The profit from selling a put option equals the negative of the profit to the person that bought it:

\[Profit = - max(X - S, 0) + Premium\]

Example 6:

You sell a put option on stock A for a premium of $10. The strike price is $60 and the option expires in a month.

Q1: What is your payoff from this put option if the price of stock A is $1? How about $50? $60? $70? 80?

Q2: What is your profit from the put option in each of those scenarios?

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Q3: Draw a graph that shows your payoff (revenue) and your profit as a function of the price of stock A.

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