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 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 December $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 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 $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 = $56.00 Price of 50-strike Call Option = 8.00 Strike Price = 50 Option Premium (or Price) = 8.00 Intrinsic Value = 6.00 Time Value = 2.00 Stock Price = 56

Intrinsic Value Intrinsic value of a call with a strike price = K is Intrinsic value of a put with a strike price = K is

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 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

Ticker Symbol Example M S Q J L The underlying Type and Expiration Strike 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 Right to buy Right to sell CALLPUT 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 Long strike 3

Put Payoff at Expiration Long strike 3

Straddle Payoff at Expiration Long strike 5

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 = current value of an associated call P = current value of an associated put K = strike price S* = market price of underlying on x-date t = time to expiration r = one plus the rate of interest on a default-free loan over a given period

Arbitrage Table Illustrating Put-call Parity Relationship CurrentExpiration Date DateS*< KK < S* Write CallC0K – S* Buy Put– PK – S*0 Buy Stock– SS* BorrowKr – t – K Total00

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

The Mystery ABC three-month 60 3 SMB three-month 55 2 XYZ three-month XXYZ three-month 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 ADRIVER B $25,000 Car Price$25,000 $500 Deductible$500 6 months Time6 months 5% Interest Rate5% $450 Premium$650

Premiums STOCK ASTOCK B 48 Stock Price48 45 Strike Price45 3 months Time3 months 5% Interest Rate5% $100 Premium$275

Pricing Components Insurance 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 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 8% $ $ % $ $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.

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 K = $50, expiring at the end of the period Rate, r =25% Can We Determine C ?

Basic Idea Behind Option Pricing Consider the hedge portfolio 1.Write three calls at C each 2.Buy two shares at $50 each 3.Borrow $40 at 25%, to be paid back at the end of the period

Arbitrage Table for Leveraged Hedge Portfolio CurrentExpiration Date DateS*= 25S* = 100 Write 3 Calls3C0– 150 Buy 2 shares– Borrow40– 50 Total00

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 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