Option Market Basics

An Introduction to Project 2 Richard Cangelosi February 27, 2003

What Will be Discussed

• • • • •

The Language of options Payoff diagrams Put-call parity Option pricing

•

Basic assumptions

•

Simple model Requirements for Preliminary Report

Objective

To Price a European Call Option Using Excel-Based Simulations and Bootstrapping methods

Markets and Instruments

•

Money Markets

•

Capital Markets

 Longer-term fixed income markets  Equity markets  Option markets  Futures markets

Equity Markets

• • • • • Common stock, also known as equity securities or equities, represent ownership shares in a corporation One share – one vote Residual claim Limited liability Primary versus Secondary Markets

Derivative Markets

These instruments provide payoffs that depend on the values of other assets such as commodity prices, bond and stock prices, or market index values.

Why Buy Stock?

• What is the opportunity?

• What is the risk?

• If you buy a stock for $100 today and sell it one year later for $100, did you break even?

• Is there a way to change the risk/reward profile of buying stocks?

Stock and T-bill Payoffs

Some Options Strategy Payoffs

What Are Options?

• • • •

Options are:

• Contracts Giving the buyer the right to buy or sell An underlying asset (e.g., 100 shares of specified common stock) At a fixed price (the strike price) On or before a given date

Terminology

• • Holder:

Buyer

(has a “long” position) Option buyers have

rights

 Long Calls: the right to buy  Long Puts: the right to sell Writer:

Seller

(has a “short” position) Option writers have

obligations

 Short Calls: the obligation to sell  Short Puts: the obligation to buy

Important Terminology

•

Underlying

Typically 100 shares of the stock on which the right or obligation exists.

Example:

XYZ

December 80 Call @ 5.50

100 shares of XYZ stock is the

“underlying”

this option of

Important Terminology

•

Strike or Exercise Price

Price at which the underlying may be bought or sold Example: XYZ December

80

Call @ 5.50

$80 per share is the price at which the buyer of this call has the right to buy 100 shares of XYZ stock.

Important Terminology

•

Expiration Date

The day on which the option ceases to exist. Typically, the expiration date is the Saturday following the third Friday of the expiration month.

Example: XYZ

December

80 Call @ 5.50

The Saturday following the third Friday in December is the expiration date of this option.

Important Terminology

•

Premium

The price of an option that is paid by the buyer and received by the seller. Example: XYZ December 80 Call @

5.50

$5.50 per share, or $550 per option, not including commissions, is paid by the option buyer and received by the option writer.

Important Terminology

•

Exercise

Buyers invoke their rights •

Call Exercise

: Call buyers stock at the strike price (from the call seller) choose to buy •

Put Exercise

seller) : Put buyers choose to sell stock at the strike price (to the put

Important Terminology

•

Exercise Styles

•

European style exercise

– option can be exercised only on the expiration date •

American style exercise

can be exercised on any day up and including the expiration date.

– the option

Important Terminology

Assigned

obligation.

Being called upon to fulfill an

Call Assignment

chosen and are Call sellers are randomly required to sell stock at the strike price to the call buyer.

Put Assignment

chosen and are Put sellers are randomly required to buy stock at the strike price from the put buyer.

Intrinsic Value and Time Value

Stock Price = $56.00

Price of 50-strike Call Option = 8.00

Stock Price = 56 Time Value = 2.00

Option Premium (or Price) = 8.00

Strike Price = 50 Intrinsic Value = 6.00

Intrinsic Value • Intrinsic value of a call with a strike price =

K

is max 

S



K

, 0  • Intrinsic value of a put with a strike price =

K

is max 

K



S

, 0 

Intrinsic / Time Value Quiz

Stock Price Option Option Price Intrinsic Value Time Value $78.00

70 Call 10.50

______ ______ $36.00

35 Call 3.75

______ ______ $128.00 130 Call 5.25

______ ______

The In’s and Out’s of Options

In-The-Money Calls

: • Stock price is above strike price • In-the-money calls have intrinsic value Example: With a stock price of $63, the 60 Call is in-the money. Specifically, it is in-the-money by $3, and it has $3 (per share) of intrinsic value.

The In’s and Out’s of Options

Out-of-The-Money Calls

• Stock price below strike price • Out-of-the-money calls do not have intrinsic value Example: With a stock price of $63, the 65 Call is out of-the-money. Specifically, it is out-of-the money by $2, and it has no intrinsic value.

The In’s and Out’s of Options

At-The-Money Calls:

• Stock price equal to strike price • At-the-money calls do not have intrinsic value Example: With a stock price of $60, the 60 Call is at the-money.

The In’s and Out’s Quiz

Stock Price Option $55 60 Call $33 35 Call $77 75 Call In, At, Out ? ?

__________ __________ __________

Ticker Symbol Example

M S Q J L The underlying Strike Type and Expiration

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec CALLS A B C D E F G H I J K L PUTS M N O P Q R S T U V W X

Four Basic Positions

CALL PUT Buyer (long)

Right to buy Right to sell

Seller (short) Obligation

to sell

Obligation

to buy

I’m Long, Now What?

•

Exercise it

•

Let it expire

•

Sell it

I’m Short, Now What

•

Live with assignment

•

Let it expire

•

Buy it back

Call Payoff at Expiration

60-strike Call @ 3

+5 0 -5 55 60 65 Long Stock @ 60

Put Payoff at Expiration

60-strike Put @ 3

+5 0 -5 55 60 65 Long Stock @ 60

Straddle Payoff at Expiration

60-strike Straddle @ 5

+5 0 -5 55 60 65 Long Stock @ 60

Arbitrage Table

• • • An

arbitrage table

describes the returns of a specially constructed portfolio of securities associated with the same underlying stock.

The Future value of the portfolio is calculated for each possible level of the stock price at option expiration.

A portfolio yielding zero returns must have zero current value to prevent riskless profitable arbitrage.

Symbols

S

= current market price of underlying stock

C P

= current value of an associated call = current value of an associated put

K S*

= strike price = market price of underlying on x-date

t r

= time to expiration = one plus the rate of interest on a default-free loan over a given period

Arbitrage Table Illustrating Put-call Parity Relationship

Write Call Buy Put Buy Stock Borrow Total Current Date C – P – S Kr – t Expiration Date S*< K 0 K – S* K < S* K – S* 0 S* – K 0 S* – K 0

Put-call Parity Relationship

The put-call parity relationship on European options on stock that pay no dividends is

C



Kr



t



P



S

The Mystery

• ABC three-month 60 call @ 3 • SMB three-month 55 call @ 2 • XYZ three-month 35 put @ 2.25

• XXYZ three-month 45 put @ 2.75

What determines these prices?

Premiums

Options can be considered insurance policies

• Put options can insure stock holdings

- puts allow you to fix a selling price

• Call options can insure cash holdings

- calls allow you to fix a buying price

Car Insurance

DRIVER A $25,000 Car Price $500 6 months 5% Deductible Time Interest Rate $450 Premium DRIVER B $25,000 $500 6 months 5% $650

Premiums

STOCK A 48 Stock Price 45 3 months 5% Strike Price Time Interest Rate $100 Premium STOCK B 48 45 3 months 5% $275

Pricing Components

Insurance Premium Stock Option Premium

• • • • • asset value deductible term of policy cost of money (interest) risk assessment • • • • • current stock price strike price time to expiration cost of money (interest & dividends) volatility forecast

Option Pricing

• • • •

Inputs:

• Stock price Strike price Time until expiration Cost of money (interest rates less dividends) Volatility (a measure of risk)

Outputs:

• Call and Put Premiums

Types of Volatility

• • • •

Historical

actual volatility during a specified time period

Future

actual volatility from present to option expiration

Implied

volatility that justifies an option’s current market price

Forecasted

estimate of future volatility used in computer models to calculate theoretical values

Changes Affect Premiums

Stock Price Strike Price Interest Rate

(No Dividend)

Time to Exp Volatility Call Price

50 50 4% 30 50 50

8%

30 50 50 4%

60

50 50 4% 30

51

50 4% 30 16% 16% 16%

32%

16% $1.00

$1.08

$1.45

$1.89

$1.62

Basic Ideas About Option Pricing

We when attempt to model physical phenomena (in this case, option prices), we usually must make simplifying assumptions, otherwise, our model is likely to be so unwieldy as to make it of little value.

However, if our model is too simplistic, it made not provide an adequate description of the phenomena that we wish to study.

Assumptions

1. Past history cannot be used to predict the future price of a stock.

If this could be done, all investors would move their money to the stock with the best predicted return. This would drive up the price of that stock, destroying its potential value.

2. The past history of prices for a given stock can be used to predict the amount of future variation in the price of that stock.

Market history indicates that stocks whose price has fluctuated widely in the past will continue to show such fluctuation, those with limited variability will retain that trait. The extent of a stock price’s variability is called its

volatility

.

Assumptions

3. All investments, whose values can be predicted probabilistically, are

assumed to give the same rate of return.

If this was not so, then all smart investors would switch their money to the investment with the highest predicted rate of return. Such movement of capital is called

arbitrage

. This would raise the cost of the chosen investment, and destroy its predicted rate of return.

4. We will assume that the common growth rate for all investments whose

future values can be predicted is the rate of return on a United States Treasury Bill.

Since the rate for this investment is guaranteed by the federal government, it is called the

risk-free

rate.

5. All investments with the same expected rate of growth are considered

to be of equal value to investors.

Obviously, some people will prefer one type of investment over another.

However, tastes will vary, so we will ignore it in our pricing. This is called the

risk neutral

assumption.

Basic Idea Behind Option Pricing Suppose the following prices exist: • Current stock price is

S

=$50 • • • Price at end of a period of time is

S

*=$25 or

S

*=100 Call with strike price the end of the period Rate,

r

=25%

K

= $50, expiring at

Can We Determine

C

?

Basic Idea Behind Option Pricing

Consider the hedge portfolio

1.

2.

3.

Write three calls at

C

each Buy two shares at $50 each Borrow $40 at 25%, to be paid back at the end of the period

Arbitrage Table for Leveraged Hedge Portfolio

Write 3 Calls Buy 2 shares Borrow Total

Current Date 3C

– 100 40

Expiration Date S

*= 25 0

50

–

50

0

S

* = 100 – –

150 200 50

0

Arbitrage Table for Leveraged Hedge Portfolio

Regardless of the outcome, the hedge exactly breaks even on the expiration date. Therefore, to prevent profitable riskless arbitrage, the current cash flow of portfolio must be zero

Arbitrage Table for Leveraged Hedge Portfolio

Since the current cash flow to establish the portfolio must be zero, we have 3

C

 100  40  0

C

 20 We did not need to know the probability that the stock will rise or fall!

Preliminary Reports

• • • • • • • • Read Business Background for Project 2 Begin with the goal of the project – to price a European style call option Give background on underlying security Discuss the assumptions Discuss option basics Show a sample of downloaded data Plot annual high and low of data Show a graph of the previous 5 years of closing prices