Introduction to Options

• A financial option is a right to buy or sell a financial security.

  • A call option is the right to buy an asset at a pre-specified price.

  • A put option is the right to sell an asset at a pre-specified price.

  • The pre-specified price is called the exercise price or strike price.

• For concreteness, consider an option on a stock.

• You pay upfront to acquire an option.
  • The amount you pay is called the option premium.
    
  • It is not part of the contract but instead is determined in the market (like a stock price).
• You buy options to hedge or to speculate. You sell options for income.
• Sellers of options need to have sufficient equity in their accounts (margin). A buyer needs enough cash to pay the premium but no more (like buying a stock).

• If you’ve bought an option, you are “long.”” If you’ve sold an option, you are “short.”
• After a trade occurs, the option clearinghouse steps in the middle and becomes the counterparty to both sides.
  • The long party has an option to buy from or sell to the clearinghouse at the strike.
  • The short party has an obligation to sell to or buy from the clearinghouse at the strike.

• Borrowing language from horse racing, we say a call is
  • in the money if the stock price is above the strike,
  • at the money if the stock price equals the strike
  • out of the money if the stock price is below the strike
• The reverse for puts

Value of a call at maturity

• At maturity (the expiration date), the value of a call is

With strike = 50,

Value of a put at maturity

• At maturity, the value of a put is

With strike = 50,

European and American

• An option is valid for a specified period of time, after which it expires.
  • Most financial options can be exercised at any time the owner wishes, prior to expiration. Such options are called American.
  • There are some options that can only be exercised on the expiration date. They are called European. Both types are traded on both continents.

Open Interest and Trading out of Positions

• Usually buyers sell to close their position rather than exercising.
• And sellers buy to close their positions rather than being obliged to buy/sell.
• Open interest rises when a contract first begins to trade, then eventually declines as people trade to close their positions.

Open Interest Example

• When a contract is first opened for trading, open interest is zero.
• Suppose Andy buys a contract from Chloe, and Brooke buys a contract from David.
  • Longs = Andy and Brooke
  • Shorts = Chloe and David
  • Open interest = 2

• Suppose Andy then sells a contract to David.
  • Andy: long + short = no position
  • David: short + long = no position
  • Longs = Brooke
  • Shorts = Chloe
  • Open interest = 1