Options Spring 2007 Lecture Notes 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 = = +$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 = = -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 Value Value of option if used today Strike price = $100 Intrinsic Value Stock Price

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) versus Intrinsic Value (black) Value of option if used today Strike price = $100 Intrinsic Value Stock Price

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

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 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

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 Graph Plot of net $ gain as a function of stock price Strike price = $100 Option prices: call = $2, put = $3 Net Gain Stock Price

Writing Call Options Writing a naked call Writing a naked put

Writing a Naked Call Option (1 share, option price = $5, strike = 100) Stock Price

Writing a Covered Call Option (1 share, option price = $5, strike = 100, stock purchased at 100) Stock Price

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