Investments - Options Markets

Options

A right to buy or sell an asset at a predetermined future date and price.

Futures

An obligation to buy or sell an asset at a predetermined future date and price.

The buyer must purchase (seller must sell) the underlying asset at the predetermined price, regardless of the current market price at the expiration date.

Agricultural and physical commodities, financial assets, hedging and speculations, traded on futures and exchanges (CME).

Call Option

Right to buy asset at specified exercise price on or before specified expiration date

Put Option

Right to sell asset at specified exercise price on or before specified expiration date

Underlying Asset

Stock, index, commodity, currency…

Exercise Style

European or American

Strike Price (exercise price)

Price set for calling / putting asset

Expiration Date

Options have a finite lifespan. The expiration date is the last day the option can be exercised.

Moneyness

In the money: exercise would generate positive cash flow

At the money: exercise price equals asset price

Out of the money: exercise would generate negative cash flow

Options Trading

Most trading occurs on organized exchanges

• CBOE (Chicago Board Option Exchange)

• ISE (International Securities Exchange)

• AMEX (American Stock Exchange)

Ease of trading

Liquid secondary market

Standardized by allowable expiration date and exercise price

• Limited, uniform set of securities

• Results in more competitive market

American Option

Can be exercised on or before expiration

Stock options

European Option

Can be exercised only at expiration

Foreign currency options

Majority of stock index options

Stock Options

American style: settled by delivery of the underlying stock.

1 contract for 100 shares of the underlying.

Settled by delivery of the underlying stock.

Index Options

Based on the stock market index

Specified the multiplier, for example SPX has the multiplier $100 (each point of the S&P 500 Index is worth $100 per contract)

Always cash-settled

Usually European style

Futures Options

Give holders the right to buy/sell futures contracts using exercise price as the futures price

Foreign Currency Options

Offers right to buy/sell foreign currency for specified amount of domestic currency

Allow investors to hedge currency risk or to speculate on currency moves.

Interest Rate Options

Options on Treasury notes / bonds / bills and other countries’ government bonds

Allow investors to hedge or speculate on the directional moves in interest rates

Call Options

Payoff to call holder at expiration

• S_T - X if S_T > X

• 0 if S_T < X

Payoff to call writer

• -(S_T - X) if S_T > X

  • 0 if S_T < X

Put Options

Payoff to put holder

• 0 if S_T > X

• X - S_T if S_T < X

Payoff to call Writer

• 0 if S_T > X

• -(X - S_T) if S_T < X

Protective Put

Asset combined with put option that guarantees minimum proceeds equal to put’s exercise price.

Risk management to limit risk of portfolio

Covered Call

Writing call on asset together with buying asset

Straddle

Combination of call and put, each with same exercise price and expiration date

Spread

Combination of two or more call options / put options on the same asset with differing exercise prices / times to expiration

Payoff to Straddle

Buying a call and put with the same strike price and expiration date.

If the tock price is close to the strike price at expiration of the options, the straddle leads to a loss.

If there is a sufficiently large move in either direction, a significant profit will result.

A straddle is used when an investor is expecting a large move in a stock price but does not know in which direction the move will be.

Payoff to Bullish Spread

An optimistic options strategy used when the investor expects a moderate rise in the price of the underlying asset.

Strategy designed to profit from a moderate rise in the price of the underlying security.

Callable Bonds

Issued with coupon rate higher than on straight debt

Investor’s compensation for call option retained by issuer

Usually includes call protection period

Convertible Securities

Convey options to holder rather than issuer

Typically give holder right to exchange for common stock, regardless of market price

They have imbedded call option

Warrants

Option issued by firm to purchase shares of firm’s stock

Collateralized Loans

Right to collateral

Asian Options

Options with payoffs that depend on average price of underlying asset during portion of option life

Currency-Translated Options

Have either asset or exercise price denominated in foreign currency

Binary Options

An all or nothing payout structure

Based on the value of stocks, currencies, level of CPI or GDP, or outcomes of events

Black-Scholes Model

Mathematical model for pricing European style options (closed form solution)

Can be used for American options with some adjustment

Binomial Tree

A numerical method using a “tree” to price the option.

A lot of iterations (500) → can take a lot of computational time.

Can be used for the valuation of any kind of options:

• American

• European

• Exotic,…

Put Call Parity

Connects valuation among all the asset classes

Equilibrium must exist, otherwise there would be an arbitrage opportunity