Option Market Basics

An Introduction to Project 2

October 2004

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 Estimate the Price of a European Call Option Using

Excel-Based Simulations and Bootstrapping methods

What is Bootstrapping?

Bootstrapping involves using charts of percentage changes in

past prices, with unknown distributions, to simulate future

price behavior.

Markets and Instruments• Money Markets

• Capital Markets Longer-term fixed income markets Equity markets (Stock Markets) Option markets (derivative products) Futures markets (derivative products) Bond markets (government and other

bonds) Commodities markets (oil, gold, copper,

wheat, electricity, etc are traded)

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.

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 (i.e., the strike price)• On or before a given date

(i.e., the expiration date)

What Are Options?

Option (dictionary.com)A contract that permits the owner,

depending on the type of option held, to purchase or sell an asset at a fixed price until a specific date. An option to purchase an asset is a call and an option to sell an asset is a put. Depending on how an investor uses options, the risks can be quite high. Investors in options must be correct on timing as well as on valuation of the underlying asset to be successful.

Important 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 April 80 Call @ 5.50

100 shares of XYZ stock is the “underlying” of this option

Important Terminology

Strike or Exercise Price: Price at which the underlying may be bought or sold

Example:

XYZ April 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 April 80 Call @ 5.50The Saturday following the third Friday in April is the expiration month of this option.(April 17, 2004)

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 choose to

buy stock at the strike price (from the call seller)

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

Important Terminology

Exercise Styles• European style exercise – option

can be exercised only on the expiration date

• American style exercise – the option can be exercised on any day up and including the expiration date.

Important Terminology

Assigned Being called upon to fulfill an obligation.

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

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

Intrinsic Value and Time Value

Stock Price = $56.00Price of 50-strike Call Option = 8.00

Strike Price = 50

Option Premium (or Price) = 8.00Intrinsic

Value = 6.00

Time Value =

2.00Stock Price = 56

Intrinsic Value

• Intrinsic value of a call is

• Intrinsic value of a put is

0,max StrikeStock

0,max StockStrike

Intrinsic / Time Value Quiz

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 OptionsOut-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

StockPrice Option In, At, Out ? ?

$55 60 Call __________

$33 35 Call __________

$77 75 Call __________

Four Basic Positions

Right to buy

Right to sell

CALL PUT

Obligation to buy

Obligation to sell

Buyer(long)

Seller(short)

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

-5

55 65

+5

0

Long Stock @ 60

60-Strike Call @ 3

Stock Price (on x-date)

Profit/Loss

Put Payoff at Expiration

60

-5

55 65

+5

0

60-strike Put @ 3Profit/Loss

Stock Price (on x-date)

Long Stock @ 60

Stock and T-bill Payoffs

Profit/Loss

Stock Price Stock Price

Profit/Loss Profit/Loss

Yields

Some Options Strategy Payoffs

Put-call Parity RelationshipThe put-call parity relationship for European options on stock that pay no dividends is

Put-call parity: Applies to derivative products. Option pricing principle that says, given a stock's price, a put and call of the same class must have a static price relationship because arbitrage opportunities or activities will always reestablish such a relationship.

(http://www.thefinancialreference.com/glossary/put-call-parity.htm)

SPKrC t

Put-call Parity RelationshipThe put-call parity relationship for European options on stock that pay no dividends is

Put-call parity: Applies to derivative products. Option pricing principle that says, given a stock's price, a put and call of the same class must have a static price relationship because arbitrage opportunities or activities will always reestablish such a relationship.

(http://www.thefinancialreference.com/glossary/put-call-parity.htm)

SPKrC t

Arbitrage

The simultaneous buying and selling of a security at two different prices in two different markets, resulting in profits without risk. Perfectly efficient markets present no arbitrage opportunities. Perfectly efficient markets seldom exist, but, arbitrage opportunities are often precluded because of transactions costs.

http://www.thefinancialreference.com/glossary/arbitrage.htm

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?

PremiumsOptions 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 InsuranceDRIVER A DRIVER B

$25,000 Car Price $25,000

$500 Deductible $500

6 months Time 6 months

5% Interest Rate 5%

$450 Premium $650

PremiumsSTOCK A STOCK B

48 Stock Price 48

45 Strike Price 45

3 months Time 3 months

5% Interest Rate 5%

$100 Premium $275

Pricing ComponentsInsurance Premium

• asset value• deductible• term of policy• cost of money

(interest)• risk assessment

Stock Option Premium

• current stock price• strike price• time to expiration• cost of money

(interest & dividends)

• volatility forecast

Option PricingInputs:• 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 currentmarket price

• Forecasted estimate of future volatility used in computermodels to calculate theoretical values

Changes Affect PremiumsStock Price 50 50 50 50

Strike Price 50 50 50 50 50

I nterest Rate 4% 4% 4% 4%

Time to Exp 30 30 30 30

Volatility 16% 16% 16% 16%

Call Price $1.00

8%

$1.00

60

$1.45

32%

$1.89

51

$1.62

(No Dividend)

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.

Assumptions3. 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.

Preliminary Reports – Project 2

• Begin with the goal of the project

To price a European style call option using Excel-based simulations and bootstrapping methods

• Your analysis is based on the data as of the close of business on Friday, October 15, 2004.

• Give background on underlying security/corporation (be very brief – 1-2 slide will do)

Preliminary Reports – Project 2

• Discuss the specifics of your option contract (discuss option basics here)

• State and discuss the five assumptions of the project.

• Show a sample of downloaded data

• Plot annual high and low of data

• Create a graph in Excel of the change in prices over the years of historical data.