Options (Chapter 19)

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

Option characteristics Options are created by investors, sold to other investors 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

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.

How Options Work Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady) Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady) At option maturity Option may expire worthless, be exercised, or be sold

Options Trading Option exchanges are continuous primary and secondary markets Chicago Board Options Exchange largest Standardized exercise dates, exercise prices, and quantities Facilitates offsetting positions through Options Clearing Corporation OCC is guarantor, handles deliveries

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.

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.

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!

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!

Options Stock Option Quotations Premiums are often small 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)

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%)

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%

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

Option Trading Strategies There are a number of different option strategies: Buying call options Selling call options Covered call Buying put options Selling put options Protective put

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, S-E] – 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

Buying Call Options Profit from Strategy 3,000 2,500 Exercise Price = $70 Option Price = $6.13 2,000 1,500 1,000 500 (500) Stock Price at Expiration (1,000) 40 50 60 70 80 90 100

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 E-S) 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

Selling Call Options Profit from Uncovered Call Strategy 1,000 Exercise Price = $70 Option Price = $6.13 500 (500) (1,000) (1,500) (2,000) (2,500) Stock Price at Expiration (3,000) 40 50 60 70 80 90 100

Covered call S< E S>E Payoff of stock S S Payoff call -0 -(S-E) Premium C C Total payoff C+S C+E

Covered Call Writing Profit ($) Purchased share Combined Stock Price Stock Price at Expiration Profit ($) Purchased share Written call Combined

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, E-S] – Put Premium Protective put: Buying a put while owning the stock (if the price declines, option gains offset portfolio losses)

Buying Put Options Profit from Strategy 3,000 2,500 2,000 Exercise Price = $70 Option Price = $2.25 1,500 1,000 500 Stock Price at Expiration (500) (1,000) 40 50 60 70 80 90 100

Portfolio Insurance Hedging strategy that provides a minimum return on the portfolio while keeping upside potential Buy protective put that provides the minimum return Put exercise price greater or less than the current portfolio value? Problems in matching risk with contracts

Protective put S< E S>E Payoff of stock S S Payoff put E-S 0 Premium -P -P Total payoff E-P S-P

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)

Selling Put Options Profit from Strategy 1,000 500 Exercise Price = $70 Option Price = $2.25 (500) (1,000) (1,500) (2,000) (2,500) Stock Price at Expiration (3,000) 40 50 60 70 80 90 100

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.

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 Exercise prior to maturity implies the option owner receives intrinsic value only, not time value

Factors Affecting Prices

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(d1) and N (d2) : cumulative density functions for d1 and d2

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, covered call and protective put (numerical application) Know the factors affecting option pricing; no numerical problems with Black-Scholes NOT on the exam: Boundaries on option prices p508-509; Put option valuation, riskless hedging, Stock index options p 513-519; Recommended End-of-chapter questions:19-1 to 14 Recommended End-of-chapter problems:19.1, 2, 3