Class Lecture

Investment AnalysisAdvanced Topics

OptionsJanuary 23, 2014

Option Basics

• A stock option is a derivative security, because the value of the option is “derived” from the value of the underlying common stock.

• There are two basic option types. – Call options are options to buy the underlying asset.– Put options are options to sell the underlying asset.

• Listed option contracts are standardized to facilitate trading and price reporting.– Listed stock options give the option holder the right to

buy or sell 100 shares of stock.

Option Basics, Cont.

• Option contracts are legal agreements between two parties—the buyer of the option, and the seller of the option.

• The minimum terms stipulated by stock option contracts are:– The identity of the underlying stock.– The strike price, or exercise price.– The option contract size.– The option expiration date, or option maturity.– The option exercise style (American or European).– The delivery, or settlement, procedure.

• Stock options trade at organized options exchanges, such as the CBOE, as well as over-the-counter (OTC) options markets.

Option Price Quotes

• A list of available option contracts and their prices for a particular security is known as an option chain.

• Stock option ticker symbols include:– Letters to identify the underlying stock.– A letter to identify the expiration month as well as

whether the option is a call or a put. (A through L for calls; M through X for puts).

– A letter to identify the strike price.

Stock Option Ticker Symbol and Strike Price Codes

Listed Option Quotesat Yahoo! Finance

The Options Clearing Corporation

• The Options Clearing Corporation (OCC) is a private agency that guarantees that the terms of an option contract will be fulfilled if the option is exercised.

• The OCC issues and clears all option contracts trading on U.S. exchanges.

• Note that the exchanges and the OCC are all subject to regulation by the Securities and Exchange Commission (SEC).

Why Options?

• A basic question asked by investors is: “Why stock options instead of shares in the underlying stock?”

• To answer this question, we compare the possible outcomes from these two investment strategies:– Buy the underlying stock.– Buy options on the underlying stock.

Example: Buying the Underlying Stock versus Buying a Call Option

• Suppose IBM is selling for $90 per share and call options with a strike price of $90 are $5 per share.

• Investment for 100 shares:– IBM Shares: $9,000– One listed call option contract: $500

• Suppose further that the option expires in three months.

• Finally, let’s say that in three months, the price of IBM shares will either be: $100, $80, or $90.

Example: Buying the Underlying Stock versus Buying a Call Option, Cont.

• Let’s calculate the dollar and percentage returns given each of the prices for IBM stock:

Buy 100 IBM Shares ($9000 Investment):

Buy One Call Option ($500 Investment):

Dollar Profit:

Percentage Return:

Dollar Profit:

Percentage Return:

Case 1: $100 $1,000 11.11% $500 100%

Case 2: $80 -$1,000 -11.11% -$500 -100%

Case 3: $90 $0 0% -$500 -100%

Why Options? Conclusion

• Whether one strategy is preferred over another is a matter for each individual investor to decide.

– That is, in some instances investing in the underlying stock will be better. In other instances, investing in the option will be better.

– Each investor must weight the risk and return trade-off offered by the strategies.

• It is important to see that call options offer an alternative means of formulating investment strategies.– For 100 shares, the dollar loss potential with call options is lower.– For 100 shares, the dollar gain potential with call options is lower.– The positive percentage return with call options is higher.– The negative percentage return with call options is lower.

Stock Index Options

• A stock index option is an option on a stock market index.

• The most popular stock index options are options on the S&P 100, S&P 500, and Dow Jones Industrial Average.

• Because the actual delivery of all stocks comprising a stock index is impractical, stock index options have a cash settlement procedure.– That is, if the option expires in the money, the option writer simply

pays the option holder the intrinsic value of the option.– The cash settlement procedure is the same for calls and puts.

Option “Moneyness”

• “In-the-money” option: An option that would yield a positive payoff if exercised

• “Out-of-the-money” option: An option that would NOT yield a positive payoff if exercised

• Use the relationship between S (the stock price) and K (the strike price):

Note for a given strike price, only the call or only the put can be “in-the-money.”

In-the-Money Out-of-the-Money

Call Option S > K S ≤ K

Put Option S < K S ≥ K

Option Writing

• The act of selling an option is referred to as option writing.

• The seller of an option contract is called the writer. – The writer of a call option contract is obligated to sell the underlying

asset to the call option holder.– The call option holder has the right to exercise the call option (i.e., buy

the underlying asset at the strike price).– The writer of a put option contract is obligated to buy the underlying

asset from the put option holder.– The put option holder has the right to exercise the put option (i.e., sell

the underlying asset at the strike price).

• Because option writing obligates the option writer, the option writer receives the price of the option today from the option buyer.

Option Exercise

• Option holders have the right to exercise their option.– If this right is only available at the option expiration date, the option is

said to have European-style exercise.– If this right is available at any time up to and including the option

expiration date, the option is said to have American-style exercise.

• Exercise style is not linked to where the option trades. European-style and American-style options trade in the U.S., as well as on other option exchanges throughout the world.

• Very Important: Option holders also have the right to sell their option at any time. That is, they do not have to exercise the option if they no longer want it.

Option Payoffs versus Option Profits

• Option investment strategies involve initial and terminal cash flows.– Initial cash flow: option price (often called the option premium).– Terminal cash flow: the value of an option at expiration (often

called the option payoff.

• The terminal cash flow can be realized by the option holder by exercising the option.

Option Profits = Terminal cash flow − Initial cash flow

Call Option Payoffs

Put Option Payoffs

Call Option Profits

Put Option Profits

Using Options to Manage Risk

• Protective put - Strategy of buying put options to protect against falling values.

• Protective puts provide “insurance” for the value of an asset or a stream of cash inflows.

Using Options to Manage Risk cont.

• Protective call - Strategy of buying call options to protect against rising prices.

• Protective calls provide a way to “lock-in” the value of a liability or a stream of cash outflows.

The Three Types of Option Trading Strategies

• Type I: Traders add an option position to their stock position. – These strategies help traders modify their stock risk.– Example: Covered Calls (Selling a call option on a stock already owned).

• Type II: Spreads.– A position with two or more options of the same type (i.e., only calls or only puts).– Example: Butterfly Spread.

Three option positions using: equally-spaced strikes with the same expiration. Buy one call option with the lowest strike. Buy one call option with the highest strike. Sell two call options with the middle strike.

• Type III: Combinations.– A position in a mixture of call and put options. – Example: Straddle (buy one call and one put with the same strike and expiration).

Option Intrinsic Values

• The intrinsic value of an option is the payoff that an option holder receives if the underlying stock price does not change from its current value.

• That is, if S is the current stock price, and K is the strike price of the option:

• Call option intrinsic value = MAX [0, S – K ]– In words: The call option intrinsic value is the maximum of zero or the

stock price minus the strike price.

• Put option intrinsic value = MAX [0, K – S ]– In words: The put option intrinsic value is the maximum of zero or the

strike price minus the stock price.

More Option “Moneyness”

• “In the Money” options have a positive intrinsic value.– For calls, the strike price is less than the stock price.– For puts, the strike price is greater than the stock price.

• “Out of the Money” options have a zero intrinsic value.

– For calls, the strike price is greater than the stock price.– For puts, the strike price is less than the stock price.

• “At the Money” options is a term used for options when the stock price and the strike price are about the same.

Arbitrage and Option Pricing Bounds

• Arbitrage:– No possibility of a loss– A potential for a gain– No cash outlay

• In finance, arbitrage is not allowed to persist.– “Absence of Arbitrage” = “No Free Lunch” – The “Absence of Arbitrage” rule is often used in finance to

calculate option prices.

• Think about what would happen if arbitrage were allowed to persist. (Easy money for everybody)

The Upper Bound for a Call Option Price

• Call option price must be less than the stock price.

• Otherwise, arbitrage will be possible.

• How?– Suppose you see a call option selling for $65, and the underlying stock is

selling for $60.– The Arbitrage: sell the call, and buy the stock.

• Worst case? The option is exercised and you pocket $5.• Best case? The stock sells for less than $65 at option expiration, and

you keep all of the $65. – Zero cash outlay today, no possibility of loss, and potential for gain.

The Upper Bound for European Put Option Prices

• European put option price must be less than the strike price.

• Suppose a put option with a strike price of $50 is selling for $50.

• The Arbitrage: Sell the put, and invest the $50 in the bank. (Note you have zero cash outlay).

– Worse case? Stock price goes to zero.• You must pay $50 for the stock (because you were the put writer).• But, you have $50 from the sale of the put (plus interest).

– Best case? Stock price is at least $50 at expiration.• The put expires with zero value (and you are off the hook).• You keep the entire $50, plus interest.

• So, we see that if the put option price equals the strike price, there is an arbitrage.

The Upper Bound for European Put Option Prices cont.

• There will be an arbitrage if price of the put, plus the interest you could earn over the life of the option, is greater than the stock price. – For example, suppose the risk-free rate is 3 percent per quarter.– We have a put option with an exercise price of $50 and 90 days to maturity.

• What is the maximum put value that does not result in an arbitrage?

• Notice that the answer, $48.54, is the present value of the strike price computed at the risk-free rate.

• Therefore: The maximum price for a European put option is the present value of the strike price computed at the risk-free rate.

$48.54 $50/1.03 price put Maximum$50 1.03 price put Maximum

The Lower Bound on Option Prices

• Option prices must be at least zero. – An option holder can simply discard the option.– This means that no one would pay someone to take an option off their hands.– Therefore, the price of the option cannot be negative.

• American Calls. Can an American call sell for less than its intrinsic value? No.– Suppose S = $60, and a call option has a strike price of K = $50 and a price of $5.– The $5 call price is less than the intrinsic value of S - K = $10.

• The Arbitrage Strategy:– Buy the call option at its price of C = $5. – Immediately exercise the call option and buy the stock at K = $50. – Then, sell the stock at the current market price of S = $60.

• Therefore, an American call option price is never less than its intrinsic value.

American call option price = MAX[S - K, 0]

The Lower Bound on American Puts

• Can an American put sell for less than its intrinsic value? No.– Suppose S = $40, and a put option has a strike price of K = $50 and a

price of $5.– The $5 put price is less than the intrinsic value of K - S = $10.

• The Arbitrage Strategy:– Buy the put option at its price of P = $5.– Buy the stock at its price of S = $40. – Immediately exercise the put option and sell the stock at K = $50.

• Therefore, an American put option price is never less than its intrinsic value.

American put option price = MAX[K - S, 0]

The Lower Bounds for European Options

• European Calls. European options cannot be exercised before expiration. – Therefore, we cannot use the arbitrage strategies to set lower bounds for

American options.– We must use a different approach (which can easily be found).

• The lower bound for a European call option is greater than its intrinsic value.

European call option price ≥ MAX[S - K/(1 + r)T, 0]

• European Puts. The lower bound for a European put option price is less than its intrinsic value. – In fact, in-the-money European puts will frequently sell for less than their intrinsic

value. How much less? – Using an arbitrage strategy that accounts for the fact that European put options

cannot be exercised before expiration:

European put option price ≥ MAX[K/(1 + r)T – S, 0]

Put-Call Parity

• Put-Call Parity is perhaps the most fundamental relationship in option pricing.

• Put-Call Parity is generally used for options with European-style exercise.

• Put-Call Parity states: the difference between the call price and the put price equals the difference between the stock price and the discounted strike price.

The Put-Call Parity Formula

• In the formula:– C is the call option price today– S is the stock price today– r is the risk-free interest rate– P is the put option price today– K is the strike price of the put and the call– T is the time remaining until option expiration

• Note: this formula can be rearranged:

Tr)K/(1SPC

CPSr)K/(1 T

Why Put-Call Parity Works• If two securities have the same risk-less pay-off in the future, they

must sell for the same price today.

• Today, suppose an investor forms the following portfolio:– Buys 100 shares of Microsoft stock.– Writes one Microsoft call option contract.– Buys one Microsoft put option contract.

• At option expiration, this portfolio will be worth:

Put-Call Parity Notes

• Notice that the portfolio is always worth $K at expiration. That is, it is riskless.

• Therefore, the value of this portfolio today is $K/(1+r)T.

• That is, to prevent arbitrage: today’s cost of buying 100 shares and buying one put (net of the proceeds of writing one call), should equal the price of a risk-less security with a face value of $K, and a maturity of T.