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Vicentiu Covrig 1 Options Options (Chapter 18 Hirschey and Nofsinger)

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Vicentiu Covrig 2 Potential Benefits of Derivatives Derivative instruments: Value is determined by, or derived from, the value of another instrument vehicle, called the underlying asset or security Risk shifting - Especially shifting the risk of asset price changes or interest rate changes to another party willing to bear that risk Price formation - Speculation opportunities when some investors may feel assets are mis- priced Investment cost reduction - To hedge portfolio risks more efficiently and less costly than would otherwise be possible

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Vicentiu Covrig 3 Option characteristics Option to buy is a call option Call options gives the holder the right, but not the obligation, to buy a given quantity of some asset at some time in the future, at prices agreed upon today. Option to sell is a put option Put options gives the holder the right, but not the obligation, to sell a given quantity of some asset at some time in the future, at prices agreed upon today Option premium – price paid for the option Exercise price or strike price – the price at which the asset can be bought or sold under the contract Open interest: number of outstanding options Long-term Equity AnticiPation Securities (LEAPS): expiration dates up to three years. - Long-term calls and puts.

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Vicentiu Covrig 4 Option characteristics Expiration date - European: can be exercised only at expiration - American: exercised any time before expiration Option holder: long the option position Option writer: short the option position Hedged position: option transaction to offset the risk inherent in some other investment (to limit risk) Speculative position: option transaction to profit from the inherent riskiness of some underlying asset. Option contracts are a zero sum game before commissions and other transaction costs.

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Vicentiu Covrig 5 Options Contracts: Preliminaries A call option is: In-the-money - The exercise price is less than the spot price of the underlying asset. At-the-money - The exercise price is equal to the spot price of the underlying asset. Out-of-the-money - The exercise price is more than the spot price of the underlying asset.

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Vicentiu Covrig 6 Options Contracts: Preliminaries A put option is: In-the-money - The exercise price is greater than the spot price of the underlying asset. At-the-money - The exercise price is equal to the spot price of the underlying asset. Out-of-the-money - The exercise price is less than the spot price of the underlying asset.

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Vicentiu Covrig 7 Options Example: Suppose you own a call option with an exercise (strike) price of $30. If the stock price is $40 (in-the-money): - Your option has an intrinsic value of $10 - You have the right to buy at $30, and you can exercise and then sell for $40. If the stock price is $20 (out-of-the-money): - Your option has no intrinsic value - You would not exercise your right to buy something for $30 that you can buy for $20!

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Vicentiu Covrig 8 Options Example: Suppose you own a put option with an exercise (strike) price of $30. If the stock price is $20 (in-the-money): - Your option has an intrinsic value of $10 - You have the right to sell at $30, so you can buy the stock at $20 and then exercise and sell for $30 If the stock price is $40 (out-of-the-money): - Your option has no intrinsic value - You would not exercise your right to sell something for $30 that you can sell for $40!

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Vicentiu Covrig 9 Options Stock Option Quotations - One contract is for 100 shares of stock - Quotations give: Underlying stock and its current price Strike price Month of expiration Premiums per share for puts and calls Volume of contracts Premiums are often small - A small investment can be “leveraged” into high profits (or losses)

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Vicentiu Covrig 10 Options Example: Suppose that you buy a January $60 call option on Hansen at a price (premium) of $9. Cost of your contract = $9 x 100 = $900 If the current stock price is $63.20, the intrinsic value is $3.20 per share. What is your dollar profit (loss) if, at expiration, Hansen is selling for $50? Out-of-the-money, so Profit = ($900) What is your percentage profit with options? Return = (0-9)/9 = -100% What if you had invested in the stock? Return = (50-63.20)/63.20 = (20.89%)

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Vicentiu Covrig 11 Options What is your dollar profit (loss) if, at expiration, Hansen is selling for $85? Profit = 100(85-60) – 900 = $1,600 Is your percentage profit with options? Return = (85-60-9)/9 = 77.78% What if you had invested in the stock? Return = (85-63.20)/63.20 = 34.49%

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Vicentiu Covrig 12 Options Payoff diagrams - Show payoffs at expiration for different stock prices (V) for a particular option contract with a strike price of X - For calls: if the V<X, the payoff is zero If V>X, the payoff is V-X Payoff = Max [0, V-X] - For puts: if the V>X, the payoff is zero If V<X, the payoff is X-V Payoff = Max [0, X-V]

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Vicentiu Covrig 13 Option Trading Strategies There are a number of different option strategies: Buying call options Selling call options Buying put options Selling put options Option spreads

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Vicentiu Covrig 14 Buying Call Options Position taken in the expectation that the price will increase (long position) Profit for purchasing a Call Option: Per Share Profit =Max [0, V-X] – Call Premium The following diagram shows different total dollar profits for buying a call option with a strike price of $70 and a premium of $6.13

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Vicentiu Covrig 15 Buying Call Options 405060708090100 1,000 500 0 1,500 2,000 2,500 3,000 (500) (1,000) Exercise Price = $70 Option Price = $6.13 Profit from Strategy Stock Price at Expiration

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Vicentiu Covrig 16 Selling Call Options Bet that the price will not increase greatly – collect premium income with no payoff Can be a far riskier strategy than buying the same options The payoff for the buyer is the amount owed by the writer (no upper bound on V-X) Uncovered calls: writer does not own the stock (riskier position) Covered calls: writer owns the stock Moderately bullish investors sell calls against holding stock to generate income

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Vicentiu Covrig 17 Selling Call Options 405060708090100 (1,000) (1,500) (2,000) (500) 0 500 1,000 (2,500) (3,000) Exercise Price = $70 Option Price = $6.13 Stock Price at Expiration Profit from Uncovered Call Strategy

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Vicentiu Covrig 18 Buying Put Options Position taken in the expectation that the price will decrease (short position) Profit for purchasing a Put Option: Per Share Profit = Max [0, X-V] – Put Premium Protective put: Buying a put while owning the stock (if the price declines, option gains offset portfolio losses)

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Vicentiu Covrig 19 Buying Put Options 405060708090100 1,000 500 0 1,500 2,000 2,500 3,000 (500) (1,000) Exercise Price = $70 Option Price = $2.25 Profit from Strategy Stock Price at Expiration

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Vicentiu Covrig 20 Selling Put Options Bet that the price will not decline greatly – collect premium income with no payoff The payoff for the buyer is the amount owed by the writer (payoff loss limited to the strike price since the stock’s value cannot fall below zero)

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Vicentiu Covrig 21 Selling Put Options 405060708090100 (1,000) (1,500) (2,000) (500) 0 500 1,000 (2,500) (3,000) Exercise Price = $70 Option Price = $2.25 Stock Price at Expiration Profit from Strategy

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Vicentiu Covrig 22 Exam type question An investor bought two Google June 425 (exercise price is $425) put contracts for a premium of $20 per share. At the maturity (expiration), the Google stock price is $370. (i) Draw the payoff diagram of the investment position. (ii) Calculate the total profit/loss of the position at the expiration.

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Vicentiu Covrig 23 Combinations Spread: both buyer and writer of the same type of option on the same underlying asset - Price spread: purchase or sale of options on the same underlying asset but different exercise price - Time spread: purchase or sale of options on the same underlying asset but different expiration dates Bull call spread: purchase of a low strike price call and sale of a high strike price call. Bull put spread: sale of high strike price put and purchase or a low strike price put

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Vicentiu Covrig 24 Payoff Long call Short call Bull call spread Payoff Long put Short put Bull put spread Payoff Long call Short put Straddle Straddle : purchasing a call and Writing a put on the same asset, exercise price, and expiration date

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Vicentiu Covrig 25 Option pricing Factors contributing value of an option - price of the underlying stock - time until expiration - volatility of underlying stock price - cash dividend - prevailing interest rate. Intrinsic value: difference between an in-the-money option ’ s strike price and current market price Time value: speculative value. Call price = Intrinsic value + time value

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Vicentiu Covrig 26 Black-Scholes Option Pricing Model Where C: current price of a call option S: current market price of the underlying stock X: exercise price r: risk free rate t: time until expiration N(d 1 ) and N (d 2 ) : cumulative density functions for d 1 and d 2

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Vicentiu Covrig 27 Learning outcomes: discuss the benefits of using financial derivatives know the basic characteristics of options know the options’ payoffs know how to calculate the profits/losses of a long/short call and put options (numerical application) Know the factors affecting option pricing (slide 24); no numerical problems with Black-Scholes Recommended End-of-chapter questions: 18.1, 18.4,18.6 Recommended End-of-chapter problems: 18.7, 18.8, 18.9, 18.10

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