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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