Options

Options Lecture 1: Option Basics

Learning Objectives

  • By the end of this lecture, you should be able to:

    • Define call and put options and understand the distinct roles of buyers (holders) and sellers (writers).

    • Explain key option terminology such as strike price, expiration date, and premium.

    • Discuss the main reasons why investors use options, including for flexibility, leverage, speculation, and hedging.

    • Calculate payoffs and profits for both buyers (long positions) and sellers (short positions) of call and put options.

    • Describe the two main methods of option settlement: cash settlement and physical settlement, and understand margin requirements.

    • Distinguish between in-the-money, at-the-money, and out-of-the-money options based on their intrinsic value.

What Are Options?

Definitions

  • Call Option: This grants the buyer the right (but not the obligation) to buy an underlying asset (like a stock) at a specified price, called the strike price, before or on a specific expiration date.

    • Why buy a call? Buyers typically purchase call options when they expect the price of the underlying asset to increase.

  • Put Option: This grants the buyer the right (but not the obligation) to sell an underlying asset at a specified price (the strike price) before or on a specific expiration date.

    • Why buy a put? Buyers typically purchase put options when they expect the price of the underlying asset to decrease.

  • Buyer (Holder): This is the party who purchases the option contract. They pay an upfront fee (the premium) and have the right to exercise the option, but they are not obligated to do so. Their maximum loss is limited to the premium paid.

  • Seller (Writer): This is the party who creates and sells the option contract. They receive the premium from the buyer and have the obligation to fulfill the terms of the contract if the buyer chooses to exercise it. Their potential losses can be significant.

  • Premium: This is the upfront fee or price paid by the buyer to the seller for the option contract. It's also known as the option price and represents the cost of acquiring the rights granted by the option.

Key Terminology

  • Strike Price (Exercise Price): Denoted as X or E, this is the fixed, pre-specified price at which the underlying asset can be bought (for a call option) or sold (for a put option) if the option is exercised.

  • Expiration Date (T): This is the last date on which the option contract can be exercised. After this date, the option expires and becomes worthless if not exercised.

  • European vs. American Options:

    • European Option: Can only be exercised on its expiration date (T). It's like a coupon you can only use on a specific final day.

    • American Option: Can be exercised any time between the purchase date and the expiration date, including on the expiration date itself. It offers more flexibility, like a coupon you can use any time before or on the final day.

  • Long-term Equity Anticipation Security (LEAPS): These are special types of options with much longer expiration periods, typically extending for several years into the future.

  • Premium (C for Call, P for Put): This is simply another reference to the price paid by the option buyer to the writer, as defined above.

  • Long Position: In options, a long position means you are the buyer of an option (either a call or a put). You own the right provided by the contract.

  • Short Position: In options, a short position means you are the seller or writer of an option. You have the obligation to fulfill the contract if exercised by the buyer.

Option Contracts

Characteristics

  • Most options trading takes place on organized exchanges, which provides a structured and efficient environment for buying and selling.

  • They are well-suited for a liquid secondary market because options contracts are standardized (e.g., fixed expiration dates, specific strike prices, and uniform contract sizes).

    • Standardization ensures buyers and sellers can easily find counter-parties and close their positions before expiration.

  • Options are standardized, meaning they have a limited and uniform set of underlying securities, expiration cycles, and strike prices, making them easier to trade.

  • The Option Clearing Corporation (OCC) acts as a guarantor for options contracts, arranging their exercise and ensuring that obligations between buyers and sellers are met.

  • Margin Requirement: This refers to the collateral (a certain amount of money) that must be posted by an option seller (writer). This margin ensures that the writer has sufficient funds to cover their potential obligations if the option is exercised against them, as writers face potentially unlimited losses for short calls and significant losses for short puts.

  • Contract Size: This represents the quantity of the underlying asset controlled by one option contract. Typically, one option contract represents 100 shares of the underlying stock. The exercise price and premium are always quoted per unit (e.g., per share), so you multiply by the contract size to get the total value.

Why Options?

Investment Flexibility

  • Flexibility: Options significantly expand the range of strategies available to investors. They allows you to create highly customized payoff profiles that might not be possible with just buying or selling the underlying asset directly.

    • Example: You can profit from a stock going up, down, or even staying flat, and you can also use them to bet on how volatile a stock will be.

  • Leverage: Options offer substantial leverage. For a relatively small upfront investment (the premium), you can control a much larger value of the underlying asset. This amplifies both potential gains and potential losses as a small movement in the underlying asset's price can lead to a large percentage change in the option's value.

  • Speculation: Investors use options to express their views on the future direction of an underlying asset's price (e.g., they believe it will go up or down) or their expectations about its future volatility. This is often done using leverage to magnify potential returns.

Hedging

  • Hedging: Options are powerful tools for managing and reducing risk. By purchasing an option, a buyer can define their maximum potential loss in advance, effectively creating a defined risk profile where they know their maximum potential loss upfront, regardless of how much the underlying asset's price moves adversely.

Option Quote Example

  • Mini-SPX is an option on 1/10 of the S&P500 index.

  • Multiplier (Contract Size): 100

  • Sample Quotes:

    • At 1:01 PM EDT: 133.63, 1.24 (0.92%)

    • Options with different strikes and their corresponding values (e.g., Call options expiring December 20, 2013, including the following):

    • Symbol: XSP131221C00080000; Last: 48.81; Bid: 51.55; Ask: 54.05; Volume: 0; Open Interest: 2

    • Pay attention to strike prices ranging from 80.00 to 150.00 and corresponding call and put option symbols.

Mini-SPX Example

Details of a European Call Option

  • Option Characteristics:

    • Expiration: December 2013

    • Exercise Price (E or X): 140

    • Current Index Value (S): 133.63

    • Premium (C): 11.80

    • Contract Size: 100 multiplier

  • Open Interest: 10 contracts - the total number of outstanding option contracts that have not yet been exercised or closed.

  • Notes: Options can be bought or sold multiple times before expiry.

Payoff and P/L Calculation

  • If the stock trades at S_T = 160:

    • The writer's payout: (160 - 140) \times 100 = 2000

    • Profit for the long position net of initial cost is calculated as:

    • \text{Payoff} - \text{Premium} = (20 - 11.80) \times 100 = 820

    • Percentage Return: \frac{8.20}{11.80} = 69.49 \text{%}

    • Leverage Effect: A small move in the underlying asset can cause a large percentage gain.

  • If S_T = 130 (option expires worthless):

    • Loss = Premium paid = 1,180

    • Percentage Return: -$100$%

Option Settlement

Types of Settlement

  • Cash Settlement: No delivery of the underlying asset occurs. The financial difference between the market price and the strike price is settled in cash.

    • Call Option Settlement Formula: S_T - X

    • Put Option Settlement Formula: X - S_T

  • Physical Settlement: Involves the actual delivery of the underlying asset.

    • Call Option: The seller delivers the underlying asset, and the buyer pays the strike price for it.

    • Put Option: The buyer delivers the underlying asset, and the seller pays the strike price for it.

  • Closing Positions: Most option positions are typically closed by offsetting trades (buying back an option you sold, or selling an option you bought) rather than waiting for physical delivery or cash settlement at expiration.

  • Margin Requirements: Required only for option writers (sellers) to ensure they can meet potential obligations; no margin is required for buyers, who pay the premium upfront.

Call Payoff and Profit

  • Payoff for a long call option at expiry (T):

    • Formula: \text{Payoff} = \text{Max}(S_T - X, 0)

    • Profit at expiry: \text{Profit} = \text{Max}(S_T - X, 0) - C

    • This describes the limited downside (maximum loss is the premium paid) and unlimited upside of buying (going long) a call option.

  • For the writer (short call position), the opposite is true:

    • \text{Payoff} = - \text{Max}(S_T - X, 0)

    • \text{Profit} = C - \text{Max}(S_T - X, 0)

Put Payoff and Profit

  • For the put buyer (long put position):

    • Payoff at expiry: \text{Max}(X - S_T, 0)

    • Profit: \text{Max}(X - S_T, 0) - P

    • Gains occur when the underlying price falls below the strike price. Your value increases as the stock price decreases.

    • Max Payoff: X (when S_T reaches 0), Maximum profit: X - P

    • Maximum loss: -P (the premium paid, if the option expires worthless).

  • For the writer (short put position):

    • \text{Payoff} = - \text{Max}(X - S_T, 0)

    • \text{Profit} = P - \text{Max}(X - S_T, 0)

Moneyness of an Option

Definitions

  • In the Money: An option is "in the money" if it has a positive intrinsic value, meaning it would generate a profit (before considering premium) if exercised immediately.

    • For calls, this means the current underlying asset price (St) is above the strike price (X): St > X

    • For puts, this means the current underlying asset price (St) is below the strike price (X): X > St

    • Intrinsic value is calculated as:

    • S_t - X \text{ for a call}

    • X - S_t \text{ for a put}

  • At the Money: An option is "at the money" if the current underlying asset price (S_t) is approximately equal to the strike price (X).

    • For both calls and puts, S_t \approx X

    • The intrinsic value is approximately zero.

  • Out of the Money: An option is "out of the money" if it has no intrinsic value and would expire worthless if exercised immediately.

    • For calls, this means the current underlying asset price (St) is below the strike price (X): St < X

    • For puts, this means the current underlying asset price (St) is above the strike price (X): X < St

    • The intrinsic value is zero.