Chapter 19

Options

Define options and discuss why they are used.

Describe how options work and give some basic strategies.

Explain the valuation of options. Identify types of options other than puts and

calls.

Learning Objectives

Call (Put): Buyer has the right, but not the obligation, to purchase (sell) a fixed quantity from (to) the seller at a fixed price before a certain date Exercise (strike) price: “fixed price” Expiration (maturity) date: “certain date”

Option premium or price: paid by buyer to the seller to get the “right”

Options

Financial derivative securities: derive all or part of their value from another (underlying) security

Options are created by investors, sold to other investors

Why trade these indirect claims? Expand investment opportunities, lower cost,

increase leverage

Why Options Markets?

Exercise (Strike) price: the per-share price at which the common stock may be purchased or sold

Expiration date: last date at which an option can be exercised

Option premium: the price paid by the option buyer to the writer of the option, whether put or call

Option Terminology

Options exchanges Chicago Board Options Exchange (CBOE) Montreal Exchange (ME)

Standardized exercise dates, exercise prices, and quantities Facilitate offsetting positions through a clearing

corporationClearing corporation is guarantor, handles

deliveries

Options Trading

In-the-money options have a positive cash flow if exercised immediately Call options: S > E Put options: S < E

Out-of-the-money options should not be exercised immediately Call options: S < E Put options: S > E

If S = E, an option is at the money

Options Characteristics

Intrinsic value is the value realized from immediate exercise Call options: maximum (S0-E, 0)

Put options: maximum (E-S0, 0)

Prior to option maturity, option premiums exceed intrinsic value

Time Value = Option Price - Intrinsic Value

Options Characteristics

25 27 29

4

0

-4

Stock Priceat Expiration

Profit perOption ($)

How does buying a stock comparewith buying a call option?

Buyer

Seller

Payoff Diagram for a Call Option

23 25 27

4

0

-4

Stock Priceat Expiration

Profit perOption ($)

How does selling a stock comparewith buying a put option?

Buyer

Seller

Payoff Diagram for a Put Option

23 25 27 29

4

0

-4

Stock Priceat Expiration

Profit ($)Purchased share

Written call

Combined

Covered Call Writing

23 25 27 29

4

0

-4

Stock Priceat Expiration

Profit ($)

Combined

Purchased put

Purchased share

Protective Put Buying

Hedging strategy that provides a minimum return on the portfolio while keeping upside potential

Buy protective put that provides the minimum return Put exercise price greater or less than the

current portfolio value?

Problems in matching risk with contracts

Portfolio Insurance

23 25 27 29

2

0

-2

Stock Priceat Expiration

Profit ($)

Combined

Purchased put

Purchased share

Portfolio Insurance

Exercise prior to maturity implies the option owner receives intrinsic value only, not time value For call options, buy stock at below market

price Would more be earned by selling option?

For put options, receive cash from selling stock at above market price

Could cash be reinvested for a higher return?

Should Options be Exercised Early?

At maturity, option prices are equal to their intrinsic values Intrinsic value is minimum price prior to maturity

Maximum option prices prior to maturity Call options: price of stock, S0

Put options: exercise price, E

Option Price Boundaries

Stock Prices

CallPrices

E

PutPrices

Stock Prices

E

E

C =S

Option Price Boundaries

Five variables needed to value a European call option on a non-dividend paying stock

The Black-Scholes pricing formula is:

tdd t

t)5.r()EPCMPln(d

)d(Ne

EP)d(NCMPCP

12

2

1

2rt1

tdd t

t)5.r()EPCMPln(d

)d(Ne

EP)d(NCMPCP

12

2

1

2rt1

Black-Scholes Model

Black-Scholes valuation is for call options Put-call parity shows relationship between

call and put options so that riskless arbitrage is not possible

Price of put = E/(ert) - S +C Put replicated by riskless lending, short

sale of stock, purchased call

Put-Call Parity

Variable Call Put Stock Price + - Exercise Price - + Time to maturity + + Stock volatility + + Interest rates + - Cash dividends - +

Variable Call Put Stock Price + - Exercise Price - + Time to maturity + + Stock volatility + + Interest rates + - Cash dividends - +

Factors Affecting Prices

Options can be used to control the riskiness of common stocks If stock owned, sell calls or buy puts

Call or put option prices do not usually change the same dollar amount as the stock being hedged Shares purchased per call written = N(d1)

Shares purchased per put purchased = N(d1) - 1

Hedge Ratios

Stock-Index Options: option contracts on a stock market index

Interest Rate Options: option contracts on fixed income securities

Currency Options: Option contracts whose value is based on the value of an underlying currency

Other Types of Options

Options available on S&P/TSE 60 Index, S&P 500 Index, NYSE Index, etc.

Bullish on capital markets implies buying calls or writing puts

Bearish on capital markets implies buying puts or writing calls

At maturity or upon exercise, cash settlement of position

Basics of Stock-Index Options

Speculation opportunities similar to options on individual stocks

Hedging opportunities permit the management of market risk Well-diversified portfolio of stocks hedged by

writing calls or buying puts on stock index What return can investor expect?

Strategies with Stock-Index Options

Appendix 19-A Combinations of Options Straddle – A combination of a put and a call

on the same stock with the same exercise date and exercise price A purchaser believes that the underlying stock

price is highly volatile and may go either up or down

A seller believes that the underlying stock price will exhibit small volatility but could go up or down

Strip – A combination of two puts and a call on the same security, same exercise date and price

Strap – combines two calls with a put

The purchase and sale of an equivalent option varying in only one respect

Two basic spreads: Money spread involves the purchase of a call

option at one exercise price and the sale of the same maturity option, but with a different exercise price

Time spread involves the purchase and sale of options are identical except for expiration dates

Appendix 19-A Spreads of Options

Appendix 19-BRights and Warrants

Right – to purchase a stated number of common shares at a specified price with a specified time (often several months)

Warrant – to purchase a stated number or common shares at a specified price with a specified time (often several years)

Appendix 19-C Put-Call Parity

No-Arbitrage Argument Example:

Payoff at TPortfolio Action S(T) <E S(T) >EA Buy 1 call 0 S(T) – E

Invest PV(E) in T-bills

E E

Total Payoff E S(T)B Buy 1 share S(T) S(T)

Buy 1 put E – S(T) 0Total payoff E S(T)