# Goals. Options. Derivatives: Definition. Goals. Definitions Options. Spring 2007 Lecture Notes Readings:Mayo 28.

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1 Goals Options Spring 27 Lecture Notes Readings:Mayo 28 Definitions Options Call option Put option Option strategies Derivatives: Definition Derivative: Any security whose payoff depends on any other security Definitions Options Call option Put option Option strategies Goals 1

2 Two types Call: Option to buy Put: Option to sell Parts: Option price Strike price Expiration Options 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 = \$1 Purchase American call option Option price = \$5 Strike price = \$12 Expiration = 2 months from now Case A: price goes to \$15 Exercise option Buy at \$12, sell at \$15 Total = = +\$25 Case B: price goes to \$5 Don t exercise option Total = -5 (lose entire investment) Example: Writing (selling) a call option on Amazon Amazon share price = \$1 Write American call option Option price = \$5 Strike price = \$12 Expiration = 2 months from now Case A: price goes to \$15 Purchaser exercises option Buy at \$15, sell at \$12 Total = = -25 Case B: price goes to \$5 Purchaser doesn t exercise option Total = +5 2

3 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 (\$2) 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 = 1), strike price = 15 Sell for \$5 You feel very happy (+5) Then Amazon goes to \$25 The other side of your option trade exercises the option You must buy Amazon at \$25, and sell it for \$15 Option Terms Intrinsic Value Value of option if used today 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 Strike price = \$1 5 Intrinsic Value

4 Is it as easy as Option Pricing (Price strike price) when strike < stock price 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 = \$1 5 Intrinsic Value

5 Goals Put Option Definitions Options Call option Put option Option strategies Real options Same as Call Price Strike price Expiration Difference: Option to Sell Example: Put Value Goals Strike price = \$1 Intrinsic Value Definitions Futures Options Call option Put option Option strategies 5

6 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 1 Lock in gains, buy put at strike = 1 Gains will be at least 1-75 Cost = price of the put option Example 1: Buy Stock + Put Strike price = \$1 How much would your portfolio (option + stock) be worth for different prices? Total Value 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)

7 Straddle Example Current stock price = 1 Purchase at-the-money call (strike = 1) for \$2 Purchase at-the-money put (strike = 1) 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 = \$1 Option prices: call = \$2, put = \$3 Writing Call Options Writing a naked call Writing a naked put Net Gain

8 Writing a Naked Call Option (1 share, option price = \$5, strike = 1) Writing a Covered Call Option (1 share, option price = \$5, strike = 1, stock purchased at 1) Stock Price 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 8

9 Other Applications Stock options Investment options Option Summary Can be used to either reduce, or increase risk Have insurance like characteristics Derivatives as fire 9

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