Week 6

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Chapter Twenty

Options Markets: Introduction

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Options

• Derivatives are securities that get their value from the price of other securities.
• Can be powerful tools for hedging and speculation.
• Options are traded both on organized exchanges and OTC.

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The Option Contract: Calls

• A call option gives its holder the right to buy an asset:
• At the exercise or strike price
• On or before the expiration date
• Exercise the option to buy the underlying asset if market value > strike price.

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The Option Contract: Puts

• A put option gives its holder the right to sell an asset:
• At the exercise or strike price
• On or before the expiration date
• Exercise the option to sell the underlying asset if market value < strike price.

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The Option Contract

• The purchase price of the option is called the premium.
• Sellers (writers) of options receive premium income.
• If holder exercises the option, the option writer must make (call) or take (put) delivery of the underlying asset.

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Example 20.1 Profit and Loss on a Call

• A January 2010 call on IBM with an exercise price of $130 was selling on December 2, 2009, for $2.18.
• The option expires on the third Friday of the month, or January 15, 2010.
• If IBM remains below $130, the call will expire worthless.

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Example 20.1 Profit and Loss on a Call

• Suppose IBM sells for $197 on the expiration date.
• Option value = stock price-exercise price

$197- $195= $2

• Profit = Final value – Original investment

$2.00 - $3.65 = -$1.65

• Option will be exercised to offset loss of premium.
• Call will not be strictly profitable unless IBM’s price exceeds $198.65 (strike + premium) by expiration.

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Example 20.2 Profit and Loss on a Put

• Consider a February 2013 put on IBM with an exercise price of $195, selling on January 18, for $5.00.
• Option holder can sell a share of IBM for $195 at any time until February 15.
• If IBM goes above $195, the put is worthless.

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Example 20.2 Profit and Loss on a Put

• Suppose IBM’s price at expiration is $188.
• Value at expiration = exercise price – stock price:

$195 - $188 = $7

• Investor’s profit:

$7.00 - $5.00 = $2.00

• Holding period return = 40% over 28 days!

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Market and Exercise Price Relationships

In the Money - exercise of the option produces a positive cash flow

Call: exercise price < asset price

Put: exercise price > asset price

Out of the Money - exercise of the option would not be profitable

Call: asset price < exercise price.

Put: asset price > exercise price.

At the Money - exercise price and asset price are equal

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American vs. European Options

American - the option can be exercised at any time before expiration or maturity

European - the option can only be exercised on the expiration or maturity date

• In the U.S., most options are American style, except for currency and stock index options.

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Different Types of Options

• Stock Options
• Index Options
• Futures Options
• Foreign Currency Options
• Interest Rate Options

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Payoffs and Profits at Expiration - Calls

Notation

Stock Price = ST Exercise Price = X

Payoff to Call Holder

(ST - X) if ST >X

0 if ST < X

Profit to Call Holder

Payoff - Purchase Price

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Payoffs and Profits at Expiration - Calls

Payoff to Call Writer

- (ST - X) if ST >X

0 if ST < X

Profit to Call Writer

Payoff + Premium

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Figure 20.2 Payoff and Profit to Call Option at Expiration

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Figure 20.3 Payoff and Profit to Call Writers at Expiration

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Payoffs and Profits at Expiration - Puts

Payoffs to Put Holder

0 if ST > X

(X - ST) if ST < X

Profit to Put Holder

Payoff - Premium

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Payoffs and Profits at Expiration – Puts

Payoffs to Put Writer

0 if ST > X

-(X - ST) if ST < X

Profits to Put Writer

Payoff + Premium

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Figure 20.4 Payoff and Profit to Put Option at Expiration

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Option versus Stock Investments

• Could a call option strategy be preferable to a direct stock purchase?
• Suppose you think a stock, currently selling for $100, will appreciate.
• A 6-month call costs $10 (contract size is 100 shares).
• You have $10,000 to invest.

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Option versus Stock Investments

• Strategy A: Invest entirely in stock. Buy 100 shares, each selling for $100.
• Strategy B: Invest entirely in at-the-money call options. Buy 1,000 calls, each selling for $10. (This would require 10 contracts, each for 100 shares.)
• Strategy C: Purchase 100 call options for $1,000. Invest your remaining $9,000 in 6-month T-bills, to earn 3% interest. The bills will be worth $9,270 at expiration.

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Option versus Stock Investment

Investment Strategy Investment

Equity only Buy stock @ 100 100 shares $10,000

Options only Buy calls @ 10 1000 options $10,000

Leveraged Buy calls @ 10 100 options $1,000

equity Buy T-bills @ 3% $9,000

Yield

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Strategy Payoffs

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Figure 20.5 Rate of Return to Three Strategies

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Strategy Conclusions

• Figure 20.5 shows that the all-option portfolio, B, responds more than proportionately to changes in stock value; it is levered.
• Portfolio C, T-bills plus calls, shows the insurance value of options.
• C ‘s T-bill position cannot be worth less than $9270.
• Some return potential is sacrificed to limit downside risk.

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Protective Put Conclusions

• Puts can be used as insurance against stock price declines.
• Protective puts lock in a minimum portfolio value.
• The cost of the insurance is the put premium.
• Options can be used for risk management, not just for speculation.

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Covered Calls

• Purchase stock and write calls against it.
• Call writer gives up any stock value above X in return for the initial premium.
• If you planned to sell the stock when the price rises above X anyway, the call imposes “sell discipline.”

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Table 20.2 Value of a Covered Call Position at Expiration

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Figure 20.8 Value of a Covered Call Position at Expiration

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Straddle

• Long straddle: Buy call and put with same exercise price and maturity.
• The straddle is a bet on volatility.
• To make a profit, the change in stock price must exceed the cost of both options.
• You need a strong change in stock price in either direction.
• The writer of a straddle is betting the stock price will not change much.

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Table 20.3 Value of a Straddle Position at Option Expiration

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Figure 20.9 Value of a Straddle at Expiration

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Spreads

• A spread is a combination of two or more calls (or two or more puts) on the same stock with differing exercise prices or times to maturity.

• Some options are bought, whereas others are sold, or written.
• A bullish spread is a way to profit from stock price increases.

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Table 20.4 Value of a Bullish Spread Position at Expiration

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Figure 20.10 Value of a Bullish Spread Position at Expiration

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Collars

• A collar is an options strategy that brackets the value of a portfolio between two bounds.
• Limit downside risk by selling upside potential.
• Buy a protective put to limit downside risk of a position.
• Fund put purchase by writing a covered call.
• Net outlay for options is approximately zero.

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Put-Call Parity

• The call-plus-bond portfolio (on left) must cost the same as the stock-plus-put portfolio (on right):

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