options spring 2007 lecture notes 4.6.1 readings:mayo 28
TRANSCRIPT
Options
Spring 2007
Lecture Notes 4.6.1
Readings:Mayo 28
Goals
• Definitions
• Options– Call option– Put option
• Option strategies
Derivatives: Definition
• Derivative: Any security whose payoff depends on any other security
Goals
• Definitions
• 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
Intrinsic ValueValue of option if used today
• Strike price = $100
Intrinsic Value
Stock Price
100 105
5
0104
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
Option Price (red) versusIntrinsic Value (black)
Value of option if used today
• Strike price = $100
Intrinsic Value
Stock Price
100 105
5
0104
Goals
• Definitions
• 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
• Strike price = $100
Intrinsic Value
Stock Price
100
5
95 9690
10
0
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”
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: 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
Writing Call Options
• Writing a naked call
• Writing a naked put
Writing a Naked Call Option(1 share, option price = $5, strike = 100)
StockPrice
100
+5
0105 110
-5
Writing a Covered Call Option(1 share, option price = $5, strike = 100, stock purchased at
100)
StockPrice
100
+5
0
-5
95
90
Other Combinations
• Many other combinations are possible
• As with futures, you can use options to reduce risk or increase risk if you want
Exotic Options
• More complicated functions of prices
• Often involve time path of prices
• Ordinary options do not care about path
• Example: Barrier option– “deactivates” if price crosses a barrier any time
during a given period
Other Applications
• Stock options
• Investment options
Option Summary
• Can be used to either reduce, or increase risk
• Have insurance like characteristics
• Derivatives as fire