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 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 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 The 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 $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 is Intrinsic value of a put 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

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 Stock Price (on x-date) Profit/Loss

Put Payoff at Expiration strike 3 Profit/Loss Stock Price (on x-date) Long 60

Stock and T-bill Payoffs Profit/Loss Stock Price Profit/Loss Yields

Some Options Strategy Payoffs

Put-call Parity Relationship The 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.Optionstock'sputcallclassarbitrage (

Put-call Parity Relationship The 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.Optionstock'sputcallclassarbitrage (

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.buying securitypricesmarketsprofitsriskefficient markets transactionscosts

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.

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, 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.