Options Markets: Introduction

Wong Wei Kang

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Outline •  Call & Put Options •  American vs. European Options •  Option versus Stock Investments •  Protective Put •  The Put-Call Parity Theorem

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Options •  Derivative securities or derivatives are securities that

get their value from the price of other securities •  Also called contingent claims because their payoffs

are contingent on the prices of other securities •  Powerful tools for hedging or speculation. •  Hedge –  To reduce risk by holding contracts or securities whose

payoffs are negatively correlated with some risk exposure

•  Speculate –  When investors use contracts or securities to place a bet on

the direction in which they believe the market is likely to move

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Options •  Options are traded both on organized exchanges

and OTC •  Chicago Board Options Exchange (CBOE) began

listing call options in 1973 –  Standardization of the terms of listed option contracts

increases market depth and lowers trading costs

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Call Option •  A call option gives its holder the right to buy

an asset: –  At the exercise price (X) or strike price (K) –  On or before the expiration date

•  It’s a right. Not an obligation. So exercise the option only if it is profitable to do so.

•  Exercise the option to buy the underlying asset if market value > strike price

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Put Option •  A put option gives its holder the right to sell an

asset: –  At the exercise price (X) or strike price (K) –  On or before the expiration date

•  It’s a right. Not an obligation. So exercise the option only if it is profitable to do so.

•  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. •  Option Writer: the seller of an option contract •  Sellers (writers) of options receive premium

income. •  If the option buyer (holder) exercises the

option, the option writer must make (for call) or take (for put) delivery of the underlying asset.

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Example 20.1 Profit and Loss on a Call •  A January 2010 expiration 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. •  Suppose IBM sells for $132 on the expiration date.

–  Option value = stock price – exercise price $132 – $130= $2

–  Profit = Final value – Original investment $2.00 – $2.18 = –$0.18

–  Option will be exercised to offset loss of premium. •  Call will not be strictly profitable unless IBM’s price exceeds

$132.18 (strike + premium) by expiration. 8

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. Might as well sell at the higher market price.

•  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! 9

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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Market and Exercise Price Relationships

•  Deep In-the-money – Describes an option that is in-the-money and for

which the strike price and the stock price are very far apart

•  Deep Out-of-the-money – Describes an option that is out-of–the-money and

for which the strike price and the stock price are very far apart

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Figure 20.1 Stock Options on IBM closing prices Open Interest = Number of Outstanding Contracts

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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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Stock Split and Dividend Payout •  To account for stock split, the exercise price is reduced by

a factor of the split, and the number of options held is increased by that factor.

•  A similar adjustment is made for stock dividends of more than 10%.

•  Cash dividends do not affect the terms of an option contract. –  Call option values are lower for high-dividend payout policies

because they slow the stock price increase –  Vice versa for put option

•  Anticipated dividend payments are factored into the option price.

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Different Types of Options •  Stock Options •  Index Options –  Options based on a stock market index such as the S&P

500 or NASDAQ100 •  Futures Options –  give holders the right to buy or sell a specified futures

contract •  Foreign Currency Options –  offer the right to buy or sell a quantity of one currency for a

specified amount of another currency •  Interest Rate Options –  Traded on Treasury notes and bonds, etc.

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Calls: Payoffs and Profits at Expiration

Payoff to Call Holder (ST - X) if ST >X 0 if ST < X

Profit to Call Holder Payoff – Premium

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Notation Stock Price = ST Exercise Price = X

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Figure 20.2 Payoff and Profit to Call Option at Expiration Exercise Price = $100; Premium = $14

Calls: Payoffs and Profits at Expiration

Payoff to Call Writer

- (ST - X) if ST >X 0 if ST < X

Profit to Call Writer

Payoff + Premium

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Figure 20.3 Payoff and Profit to Call Writers at Expiration Exercise Price = $100; Premium = $14

Puts: Payoffs and Profits at Expiration

Payoffs to Put Holder 0 if ST > X (X - ST) if ST < X

Profit to Put Holder

Payoff - Premium

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Figure 20.4 Payoff and Profit to Put Option at Expiration Exercise Price = $100

Puts: Payoffs and Profits at Expiration

Payoffs to Put Writer 0 if ST > X - (X - ST) if ST < X

Profits to Put Writer

Payoff + Premium

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Summary: Holder vs. Writer and Call vs. Put

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Bullish vs. Bearish Strategy

•  Bullish Strategy – Buying Calls – Writing Puts – Profits when stock prices increase

•  Bearish Strategy – Buying Puts – Writing Calls – Profits when stock prices fall

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Option vs. 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. •  You have $10,000 to invest.

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Option vs. 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.

•  Strategy C: Purchase 100 call options for $1,000. Invest your remaining $9,000 in 6-month T-bills, to earn 3% interest for 6 months. The bills will be worth $9,270 at expiration.

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Option vs. Stock Investment

Investment Strategy Investment Equity only Buy stock @$100 100 shares $10,000 Options only Buy calls @$10 1000 calls $10,000 Call plus Bills Buy calls @$10 100 calls $1,000

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

Strategy Conclusions •  Figure 20.5 shows that the all-option portfolio, B,

responds more than proportionately to changes in stock value; it is levered. –  Options can be used by speculators as effectively leveraged

stock positions

•  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. – The absolute limitation on downside risk is a novel and

attractive feature of this strategy 30

Protective Put •  Protective Put = Stock + Put •  Invest in stock and buy a put option on the stock •  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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Table 20.1 Value of a Protective Put Position at Expiration

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Figure 20.6 Value of a Protective Put

Position at Expiration

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Figure 20.7 Protective Put vs. Stock Investment (at-the-money option)

Put-Call Parity •  A protective put portfolio (stock-plus-put) provides a

payoff with a guaranteed minimum value, but with unlimited upside potential –  Table 20.1 –  Figure 20.6

•  But a call-plus-bills portfolio can also provide similar payoff –  Buy a call option and buy zero-coupon Treasury bills with

face value equal to the exercise price X of the call and with maturity date equal to the expiration date of the option

–  Next Table

–  Figure 20.5

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Value of a Call-plus-Bills Portfolio at Expiration

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The Put-Call Parity Theorem

•  Since both portfolios provide the same exact payoffs, the call-plus-bond portfolio (on left) must cost the same as the stock-plus-put portfolio (on right):

0(1 )Tf

XC S Pr

+ = ++

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Put-Call Parity Disequilibrium Example

Stock Price = 110 Call Price = 17 Put Price = 5 Risk Free = 5% Maturity = 1 yr X = 105

117 > 115 Since the protective put is less expensive, acquire the low cost alternative and sell the high cost alternative

0(1 )Tf

XC S Pr

+ = ++

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Table 20.5 Payoff to Arbitrage Strategy

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The Put-Call Parity Theorem

•  Extension for European call options on dividend-paying stocks

S0 + P = C + PV(X) + PV(dividends)

where PV(dividends) = Present value of the dividends that will be paid by the stock during the life of the option

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