Options Markets

Options Markets Overview

15.1 Option Contracts

  • Definition of Option Contract: A financial derivative that provides the buyer the right, but not the obligation, to purchase or sell an asset at a specified price within a predetermined period.

Call Option

  • Definition: Grants the holder the right to buy an asset at a specified exercise price on or before a specified expiration date.

  • Key Terms:

    • Strike Price: The price at which the asset can be bought (call) or sold (put).

    • Premium: The cost of purchasing the option.

Put Option

  • Definition: Grants the holder the right to sell an asset at a specified exercise price on or before a specified expiration date.

Moneyness of Options

  • In the Money (ITM): An option is considered in the money if it would generate positive cash flow if exercised.

  • Out of the Money (OTM): An option is out of the money if it would generate negative cash flow if exercised.

  • At the Money (ATM): An option where the exercise price equals the current asset price.

Example Case - IBM (IBM) Options (as of August 24, 2011)

  • Underlying Stock Price: $166.76

  • Options Listing:

    • Strike Prices & Premiums for September 2011, October 2011, January 2012, and April 2012 for both calls and puts are provided, showing:

    • Prices for exercise alongside volume and open interest, indicating market activity.

Options Trading

  • Most trading of options occurs on organized exchanges due to:

    • Ease of Trading: Facilitated processes for participants.

    • Liquid Secondary Market: Ability to quickly buy and sell options.

    • Standardization: Options are standardized by expiration date and exercise price, resulting in a limited, uniform set of securities which enhances competition in the market.

Types of Options

  • American Option: Can be exercised at any time before or on the expiration date.

  • European Option: Can only be exercised on the expiration date itself.

15.2 Values of Options at Expiration

  • Call Options Payoff:

    • Calculation of Payoff at Expiration:

    • For the call holder: If stock price at expiration ($ST$) exceeds strike price ($X$): Payoff = $ST - X$; else Payoff = $0.

    • For the call writer: If $ST > X$: Payoff = $-(ST - X)$; else Payoff = $0.

  • Put Options Payoff:

    • Calculation of Payoff:

    • For the put holder: If $ST < X$: Payoff = $X - ST$; else Payoff = $0.

Figures Illustrating Payoff at Expiration

  • Figure 15.2: Payoff and Profit for Call Option at Expiration

    • Visualizing the relationship between stock price at expiration ($S_T$) and options value.

  • Figure 15.3: Payoff and Profit for Call Writers at Expiration

  • Figure 15.4: Payoff, Profit for Put Option at Expiration

Comparison of Investment Strategies

  • Investment Options:

    • A: Invest in 100 shares of stock at $90 each.

    • B: Invest entirely in at-the-money options (900 calls at $10).

    • C: Buy 100 call options ($1,000) and invest remaining $8,000 in 6-month Treasury bills at 2% interest.

Rate of Return (RoR) Analysis

  • Portfolio Value Comparison:

    • A (100 shares):

    • Value at various stock prices ($85, $90, $95, $100, $105, $110$).

    • B (900 call options):

    • Payoffs at different stock prices.

    • C (100 calls and Treasury bills):

    • Portfolio values considering rate of return from T-bills with initial investment.

Figures for RoR Visualization

  • Figure 15.5: Rate of Return (%) for three strategies as stock price changes.

Option Strategies

  • Protective Put: Combining an asset with a put option to guarantee minimum proceeds equal to the put’s exercise price.

  • Covered Call: Writing a call option while holding the same asset.

  • Straddle: A strategy combining a call option and a put option, both having the same exercise price and expiration date.

  • Spread: A strategy that involves multiple call or put options on the same asset, differing by exercise prices or expiration times.