Options Markets - FIN3710

Option Contracts

• Premium: The purchase price of an option.

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

• Call Option: The right, but not the obligation, to buy an asset at a specified exercise price on or before a specified expiration date.

• Put Option: The right, but not the obligation, to sell an asset at a specified exercise price on or before a specified expiration date.

Moneyness

• Out of the Money: An option that would generate negative cash flow if exercised immediately.

  • Call option: S_T < X

    Put option: S_T > X

• At the Money: An option where the exercise price equals the asset price. $S_T = X$

• In the Money: An option that would generate positive cash flow if exercised immediately.

  • Call option: S_T > X

  • Put option: S_T < X

Option Trading

• Most option trading occurs on organized exchanges, providing:

  • Ease of trading.

  • A liquid secondary market.

  • Standardized contracts with allowable expiration dates and exercise prices.

  • A limited, uniform set of securities.

  • More competitive market.

Option Types

• European Option: Can be exercised only at expiration.

• American Option: Can be exercised on or before expiration.

Option Clearing Corporation (OCC)

• Jointly owned by exchanges.

• Arranges for exercised options through member firms.

• Requires option writers to post margin to ensure fulfillment of their obligations.

Other Listed Options

• Index Options: Call or put options based on a stock market index like the S&P 500.

• Futures Options: Give the holder the right to buy or sell a futures contract at a specified exercise price, which serves as the futures price.

• Foreign Currency Options: Offer the right to buy or sell a foreign currency for a specified amount of domestic currency.

• Interest Rate Options: Options on Treasury notes, bonds, bills, and other countries’ government bonds, allowing investors to speculate on or hedge interest rate movements.

Values of Options at Expiration

Call Options

• Payoff to call holder at expiration:

  • $S<em>T - X$ if ST > X

  • $0$ if $S_T ≤ X$

• Payoff to call writer at expiration:

  • $-(S<em>T - X)$ if ST > X

  • $0$ if $S_T ≤ X$

Put Options

• Payoff to put holder at expiration:

  • $X - S<em>T$ if ST < X

  • $0$ if $S_T ≥ X$

• Payoff to put writer at expiration:

  • $-(X - S<em>T)$ if ST < X

  • $0$ if $S_T ≥ X$

Options versus Stock Investment

• Strategies:

  • Invest entirely in stock (e.g., 100 shares at $90 each).

  • Invest entirely in at-the-money options (e.g., buy 900 calls at $10 each).

  • Buy 100 call options (e.g., for $1,000) and invest the remaining capital (e.g., $8,000) in risk-free assets like T-bills.

Rate of Return (RoR)

The rate of return varies significantly based on the stock price and the chosen investment strategy.

• Portfolio A: 100 shares of stock

  • RoR ranges from -5.56% to 22.22% depending on the stock price.

• Portfolio B: 900 call options

  • RoR ranges from -100% to 100% depending on the stock price, demonstrating high leverage.

• Portfolio C: 100 calls plus $8,000 in T-bills

  • RoR ranges from -9.33% to 12.89%, providing a more conservative approach.

Option Strategies

• Protective Put: Buying an asset and a put option on that asset to guarantee minimum proceeds equal to the put's exercise price; used for risk management.

• Covered Call: Writing a call option on an asset you already own; generates income but limits upside potential.

• Straddle: Buying both a call and a put option with the same exercise price and expiration date; profits from significant price movements in either direction.

• Spread: Combination of two or more call options or put options on the same asset with differing exercise prices or times to expiration; used to fine-tune risk and reward.

• Collar: An options strategy that brackets the value of a portfolio between two bounds, limiting both gains and losses.

Protective Put Strategy

The protective put strategy provides a guaranteed minimum payoff equal to the strike price $X$.

Covered Call Strategy

The covered call strategy generates income from the option premium but caps the potential upside at the strike price $X$.

Straddle Strategy

The straddle strategy profits from significant price movements in either direction, with losses limited to the combined premiums paid for the call and put options.

Bullish Spread Strategy

A bullish spread profits if the asset price increases, with the maximum profit limited to the difference between the two strike prices, $X<em>2 - X</em>1$.

Optionlike Securities

• Callable Bonds: Bonds that the issuer can redeem at a specified price before maturity; issuers retain a call option.

  • Issued with a coupon rate higher than on straight debt to compensate investors for the embedded call option.

  • Usually includes a call protection period during which the bond cannot be called.

• Convertible Securities: Securities that give the holder the right to exchange them for common stock, regardless of the market price.

• Collateralized Loans: Loans secured by collateral, where the lender has recourse only to the collateral in case of default.

  • Nonrecourse loan: No recourse beyond the right to the collateral.

• Warrants: Options issued by a firm to purchase shares of the firm’s stock.

• Leveraged Equity and Risky Debt: When a corporation borrows money, the maximum possible collateral for the loan is the total of the firm’s assets.

Collateralized Loans as Optionlike Securities

• Implicit call option to the borrower:

  • The borrower can turn the collateral over to the lender and retain the right to reclaim it by paying off the loan.

  • The borrower will repay $L$ dollars and can sell the collateral to the lender for $L$ dollars, even if $S_T$ is less than $L$.