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© 2007 Thomson South-Western

Chapter 18Options Basics

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Economic Benefits Provided by OptionsDerivative securities are instruments that derive their value from the value of other

assets.Derivatives include options, futures, and

swaps. Options and other derivative securities have several

important economic functions:

– Help bring about more efficient allocation of risk – Save transactions costs…sometimes it is cheaper to trade a

derivative than its underlying asset.– Permit investments strategies that would not otherwise be possible

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Options Basics

Options: contracts that grant the buyer the right to buy or sell stock at a fixed price.

Options provide real economic benefit to society.

Put-call parity establishes a link between market prices of calls, puts, shares, and

bonds.Factors that affect option prices: underlying

price, time to maturity, strike price, interest rate and volatility.

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Options Vocabulary

Long position

• The buyer of an option has a long position, and has the ability to exercise the option.

Short position

• The seller (or writer) of an option has a short position, and must fulfill the contract if the buyer exercises.

• As compensation, the seller receives the option premium.

Options trade on an exchange (such as CBOE) or in the over-the-counter market.

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Options Vocabulary

Call option • Gives the holder the right to

purchase an asset at a specified price on or before a certain date

Put option • Gives the holder the right to sell as

asset at a specified price on or before a certain date

Strike price or exercise price: the price specified for purchase or sale in an option contract

American or European

option

• American options allow holders to exercise at any point prior to expiration.

• European options allow holders to exercise only on the expiration date.

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Option Price

Call PutS>X In-the-money Out-of-the-

moneyS=X At-the-money At-the-moneyS<X Out-of-the-

moneyIn-the-money

S = current stock price

X = strike price

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Option Quotations

50504545

Strike

6.503.50June46.315.251.50March46.313.885.88June46.312.384.00March46.31

PutCallExpires

General Electric

In-the-money callsOut-of-the-money puts

In-the-money putsOut-of-the-money calls

• Option quotations specify the per share price for an option contract, which is a contract to buy or sell 100 shares of the underlying stock

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Intrinsic and Time Value of Options

Intrinsic value

• For in the money options: the difference between the current price of the underlying asset and the strike price

• For out of the money options: the intrinsic value is zero

Time value • The difference between the option’s intrinsic value and its market price (premium)

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Payoff Diagrams

Show the value of an option, or the value at expiration

Y-axis plots exercise value or “intrinsic value.”

X-axis plots price of underlying asset.

Use payoff diagrams for:

Long and short positions

Gross and net positions (the net positions subtract the option

premium)

Payoff: the price of the option at expiration date

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Long Call Option Payoffs

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Short Call Option Payoffs

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Long Put Option Payoffs

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Short Put Option Payoffs

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Naked Option PositionsNaked call option position - occurs

when an investor buys or sells an option on a stock without already owning the underlying stock

Naked put option positions – occurs when a trader buys or sells a put option without owning the underlying stock

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Portfolios of OptionsLook at payoff diagrams for combinations of options

rather than just one.

Diagrams show the range of potential strategies made possible by options.

Some positions, in combination with other positions, can be a form of portfolio insurance.

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Straddle PositionsLong straddle - a portfolio consisting

of long positions in calls and puts on the same stock with the same strike price and expiration date

Short straddle - a portfolio consisting of short positions in calls and puts on the same stock with the same strike price and expiration date

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Long Straddle

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Short Straddle

Call x = 60, premium = $5, Put x = 60, premium = $4

60

+9

51 69

Net payoff

Gross payoff

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Payoff Diagrams for Stocks and Bonds

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Covered Call StrategyWriting covered calls –common

trading strategy that mixes stock and call options An investor who owns a share of stock

sells a call option on that stock. The investor receives the option

premium immediately. The trade-off is that if the stock price

rises the holder of the call option will exercise

the right to purchase it at the strike pricethe investor will lose the opportunity to

benefit from the appreciation in the stock.

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Payoff Diagram for Covered Call Strategy

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Payoff of a Put Option and a Share of Stock – a Protective Put

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Payoff of a Call Option and a Zero-Coupon Bond

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Put-Call ParityFollowing conditions must be met:

1. The call and put options must be on the same underlying stock.

2. The call and put options must have the same exercise price.

3. The call and put options must share the same expiration date.

4. The underlying stock must not pay a dividend during the life of the options.

5. The call and put options must be European options.

6. The bond must be a risk-free, zero-coupon bond with a face value equal to the strike price of the options and with a maturity date identical to the options’ expiration date.

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Synthetic Put OptionTraders can create a synthetic put

option by purchasing a bond and a call option while simultaneously short-selling the stock.

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Put-Call Parity Arbitrage

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Using Put-Call Parity to Create Synthetic Positions

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Factors Affecting Option Values

Price of underlying

asset

• Asset price and call price are positively related.

• Asset price and put price are negatively related.

Time to expiration

• More time usually makes options more valuable.

Strike price

• Higher X means higher put price; lower X means higher call price.

Interest rate

• Calls: higher “r” means higher call value

• Puts: higher “r” reduces put value

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Factors Affecting Option Values

Holding other factors constant, call and put option prices increase as the time to expiration increases.

Call prices decrease and put prices increase when the difference between the underlying stock price and the exercise price (S − X) decreases.

Call and put option prices increase as the volatility of the underlying stock increases.

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Calculating Option PricesThe binomial options model

recognizes that investors can combine options (either calls or puts) with shares of the underlying asset to construct a portfolio with a risk-free payoff.

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Binomial Option Pricing

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Binomial Option PricingData needed:

The current price of the underlying stock

The amount of time remaining before the option expires

The strike price of the optionThe risk-free rateThe possible values of the underlying

stock in the future

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Multistage Binomial Trees

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Multistage Binomial Trees

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Risk-Neutral MethodIf a combination of stock and options is

risk-free, it must sell for the same price as a risk-free bond.

If an asset promises a risk-free payoff, risk-averse and risk-neutral investors agree on how it should be valued.

Whether investors are risk averse or risk neutral, the binomial model’s calculations are the same.

We can assume investors are risk neutral, which gives us a new way to value options.