Futures and Options

Econ71a: Spring 2007

Mayo, chapters 28-29

Section 4.6.1, 4.6.2

Goals

• Definitions

• Futures

• Options– Call option– Put option

• Option strategies

Derivatives: Definition

• Derivative: Any security whose payoff depends on any other security

Types

• Futures

• Options

• Swaps

• SPDR (S+P 500 Depository Receipts)– GM page 565

• WEBS (World Equity Benchmark Shares)– GM page 510

Goals

• Definitions

• Futures

• Options– Call option– Put option

• Option strategies

Futures

• Contract allowing delivery at a specified future data (delivery date) at a certain price

• Price is decided on today• Used for:

– Commodities• Wheat, Soy, Oil

– Financial• Treasury Bills• S+P 500• Foreign Exchange

Mechanics

• Buy or sell contracts for a specified delivery date

• Price is agreed on today for payment at the delivery date

• Essentially, no money changes hands today

• Margin (often 10%) is paid today to guarantee parties will hold to contract

Mechanics(more)

• Contracts: – Traded in organized exchanges

• Most in Chicago

– Uniform time periods• Contracts ending in March, June, Sept, December

Usage: Insurance vs. Speculation

• Insurance (Hedging)– Farmer has 100 bushels of soy that will be harvested in

Sept.

– What should he do?• Wait until Sept. and sell on the spot market

• Sell futures contracts today (short position)

– In the first case he is open to risk in the price movement

– In the second, he has no risk since the futures contract sets price today

Speculation• Oil market:

– You think that oil prices will go up in the future– How can you try to “bet” on this idea?

• Buy (go long) oil futures for some month in the future

• You have no intention of buying oil

• You hope that the spot price will rise and,– Buy with your (now lower) futures price

– Turn around and sell for the (now higher) spot price

Winning and Losing with Speculation

• Winning– Oil price goes up

• Since the margins are low, you can make many more times the money you actually put in when you purchased the future

• Losing– Oil price goes down

• Can end up in big trouble

• You must purchase oil for what your contract price says, and sell on the spot market

• You can now lose a lot of money this way

Example of Losing Money in a Futures Contract

• It is April, oil sells for $50 a barrel • The June futures contract sells at $48• Buy (go long) the June futures for 1 barrel

– Pay margin amount now (10% = $4.80)

• June arrives and the price of oil falls to $30• You have to buy oil at the futures price of $48, and then

sell for $30, losing $18• You get your margin back, so you end up with a net value

of –4.8–48+30+4.8 = -18• Nothing (except the margin) to stop you from taking big

positions and losing big money

Settlement

• Actual– Take delivery of the actual stuff

• Pork bellies in your driveway

• Cash– Cash value of the good is transferred to your

account– More common for financial futures– Example S+P futures

Goals

• Definitions

• Futures

• Options– Call option– Put option

• Option strategies

Options

• Two types– Call: Option to buy– Put: Option to sell

• Parts:– Option price– Strike price– Expiration

Call Option

• Option to purchase asset at the strike price

• Horizon:(two types)– American: Anytime between now and the

expiration date– European: On the expiration date only

• Strike price: Price at which the security can be purchased

Example: Buying a call option on Amazon

• Amazon share price = $100• Purchase American call option

– Option price = $5– Strike price = $120– Expiration = 2 months from now

• Case A: price goes to $150– Exercise option

• Buy at $120, sell at $150• Total = 150-120-5 = +$25

• Case B: price goes to $50• Don’t exercise option• Total = -5 (lose entire investment)

Example: Writing (selling) a call option on Amazon

• Amazon share price = $100• Write American call option

– Option price = $5– Strike price = $120– Expiration = 2 months from now

• Case A: price goes to $150– Purchaser exercises option

• Buy at $150, sell at $120• Total = -150+120+5 = -25

• Case B: price goes to $50• Purchaser doesn’t exercise option• Total = +5

Options and Insurance

• The writer is kind of selling insurance to the buyer

• As long as the price doesn’t go up by too much ($20) the writer gets to pocket the $5

• Like an insurance premium

• Danger: If price rises by large amount, option writer can lose lots of money

How do you lose big money with options?

• Write (sell) a naked call on Amazon.com (p = 100), strike price = 150– Sell for $5

• You feel very happy (+5)• Then Amazon goes to $250• The other side of your option trade exercises the

option• You must buy Amazon at $250, and sell it for

$150

Option Terms

• In-the-money• Stock price > call option strike price

• At-the-money• Stock price = call option strike price

• Out-of-the-money• Stock price < call option strike price

Contingency GraphPlot of net $ gain as a function of stock price

• Strike price = $100

• Option price = $4

Net Gain

Stock Price

100 105

1

-4

0

104

Option Pricing

• Is it as easy as• (Price – strike price) when strike < stock price

• 0 if strike is > stock price

• Why does this get more complicated?• Have to consider today plus all days to the

expiration date• Even though the price is in the zero value range

today (out-of-the-money, it might move into the positive value range tomorrow

General Properties of an option price

• Option value will be higher:– When the expiration date is farther in the future– When the stock price moves around more

• (This is known as higher volatility)

Option Pricing

• There are different formulas that try to take account of all this stuff

• Black/Scholes is the most famous of these

• Techniques used– Arbitrage– Stochastic calculus

Goals

• Definitions

• Futures

• Options– Call option– Put option

• Option strategies

• Real options

Put Option

• Same as Call– Price– Strike price– Expiration

• Difference: Option to Sell

Example: Put Value

• Option price = $4

• Strike price = $100

Net Gain

Stock Price

100

01

95 9690

6

-4

Goals

• Definitions

• Futures

• Options– Call option– Put option

• Option strategies

Options+Stocks

• Holding option alone is known as holding a “naked option”

• Holding option with the stock is known as a “covered option”

Example 1: Insuring gains by buying a put option

• Purchasing a put option on stock you already own sets a floor on what you can sell

• Buy stock at 75, price rises to 100

• Lock in gains, buy put at strike = 100

• Gains will be at least 100-75

• Cost = price of the put option

Example 1: Buy Stock + Put

• Strike price = $100

• How much would your portfolio (option + stock) be worth for different prices?

Total Value

Stock Price

100 105

105

100

Example 2: Writing a covered call option

• Own stock

• Write a covered call option, strike = 100, sell for $5

• Price goes below 100, nothing happens

• Price goes above 100, option may get exercised

• Puts a ceiling on your gains

Writing a Covered Call OptionValue of stock + written (sold) call

Stock Price

Total Value

100

100

If the option is exercised,Then stock must be sold for $100

Why do this?

• Trading “upside potential” for $5

Example 3: Option Straddle

• Purchase a put and call at the same strike price

• Strategy makes money when stock price moves a lot (volatility is high)

Straddle Example

• Current stock price = 100

• Purchase at-the-money call (strike = 100) for $2

• Purchase at-the-money put (strike = 100) for $3

• What is the total value of your option portfolio for different stock prices?

Straddle Performance

• Lose money when no change in price

• Price goes up: Call makes money

• Price goes down: Put makes money

• Strategy makes money when price moves a lot (depends on option prices)

Straddle Contingency GraphPlot of net $ gain as a function of stock price

• Strike price = $100

• Option prices: call = $2, put = $3

Net Gain

Stock Price

100 106

1

-5

0

1059594

Other Combinations

• Many other combinations are possible

• As with futures, you can use options to reduce risk or increase risk if you want

Option + Future Summary

• Both can be used to either reduce, or increase risk

• Have insurance like characteristics

• Derivatives as fire

Goals

• Definitions

• Futures

• Options– Call option– Put option

• Option strategies