Chapter 10 Mechanics of Options Markets Options Futures

Review of Option Types A call is an option to buy A put is

Type of options Options Call Long The right to buy Put Short An obligation

Option Positions Long call Long put Short call Short put Long position (buyer) must

2 Styles of options Call European A European option can be exercised only at

Underlying asset Asset underlying the options can be any asset. Ex. Stock, stock indices,

Call option Call Long call • Pay premium to have the right to buy

Long call European call option Strike price = $100 (K) Current price = $98

Spot price ST Strike price Pay off K Max (ST– K, 0) Profit/Loss Max

Long Call Profit and Loss Diagram 30 Profit ($) 20 10 -c 0 -5

Long call Maximum profit = infinity (unlimited profit) Maximum loss = -c Breakeven =

Short call Obligated to sell the underlying asset to the long call if the

Short call Zero-sum game Same payoff & profit but the sign is opposite to

Short call P&L diagram Profit ($) C 5 0 -10 120 130 70 80

Short Call Profit ($) 5 0 -10 120 130 70 80 90 100 Terminal

Problem 10. 2 An investor sells a European call on a share for $4.

Problem 10. 2 C = 4, K = 50 Short position Investor makes profit

Diagram Profit ($) C=4 K+c 50 54 Stock price ($) ST K Options, Futures,

Dividends & Stock Splits Suppose you own N options with a strike price of

Dividends and Stock split : Individual stock option Cash dividend -> No adjustment are

Stock split Ex. Call option N = 100 shares K = $20/ share 2

Stock split Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright ©

Stock dividend Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright ©

Problem 10. 17 Consider an exchange-traded call option contract to buy 500 shares with

Problem 10. 17 N = 500, K 40 A. N’ = 500 x 1.

Put option Put Long put • Pay premium to have the right to sell

Long put Example European put option Strike price (K) = $70 Option price (p)

Long put Spot price ST Strike price Pay off K Max ( K-ST, 0)

Long Put Profit / Loss diagram Profit ($) K- p = $63 30 20

Long put Maximum profit = K – p (This is where ST = 0)

Problem 10. 1 An investor buys a European put on a share for $3.

Problem 10. 1 P = $3 K =$40 Make profit when ST < K-

Diagram Profit ($) $37 K 40 p = -3 37 Stock price ($) ST

Short put Obligated to buy the underlying asset from the long put if the

Short put Zero-sum game Same payoff and profit but the sign is opposite to

Short Put diagram Profit from writing a European put option: option price = $7,

Short put Maximum profit = p Maximum loss = -K+p Options, Futures, and Other

Problem 10. 10 Suppose that a European put option to sell a share for

Problem 10. 10 K = $60 P= $8 Short put Make profit when ST

Diagram K Profit ($) K-p Stock price ($) ST 52 60 -K+p = -52

Payoffs from Options What is the Option Position in Each Case? K = Strike

Terminology Moneyness : A function of the payoff that long position will experience should

Terminology In-the-money option • Long position will earn a positive payoff if it exercises

Terminology Call Put ITM S 0 > K 1 S 0 < K 3

Terminology Whether a long position, a short position , or a third party, each

Terminology (continued) Option class All options of the same type (calls or puts) on

Terminology Intrinsic value The value it would have if there were no time to

Terminology A call option only has intrinsic value when the underlying asset price is

Terminology Time value or optionality value The value of having the right to decide

Slides: 50

Download presentation

Type of options Options Call Long The right to buy Put Short An obligation to sell Long The right to sell Short An obligation to buy Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 3

Option Positions Long call Long put Short call Short put Long position (buyer) must pay the short position a free for providing the right. Because it is advantageous to have a right and not an obligation. The fee is known as “premium”. Premium is paid at initiation. Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 4

2 Styles of options Call European A European option can be exercised only at the end of its life Put American Call Put An American option long position has the right to exercised at any time (before or at expiration) Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 5

Underlying asset Asset underlying the options can be any asset. Ex. Stock, stock indices, currencies, commodities. Strike price or exercise price is the price at which the long position has the right to Buy (in case of call option) Sell (in case of put option) Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 6

Call option Call Long call • Pay premium to have the right to buy • Long call exercise the right to buy when St > K • (Able to buy at lower price K, and sell in market at higher price St) C Call premium Short call • Have an obligation to sell when St > K • Where St = Spot price K = Strike price Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 7

Long call European call option Strike price = $100 (K) Current price = $98 (St) Option premium = $5 , c, to purchase 1 share Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 8

Spot price ST Strike price Pay off K Max (ST– K, 0) Profit/Loss Max (ST– K, 0)- c 90 100 0 -5 105 100 5 0 115 100 15 10 120 100 20 15 Payoff = The cashflow that occurs at expiration. Profit/Loss = Cashflow at expiration – Cashflow at initiation Call option’s intrinsic value = St - K Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 9

Long Call Profit and Loss Diagram 30 Profit ($) 20 10 -c 0 -5 K+c =105 70 80 90 100 K Terminal stock price ($) 110 120 130 10

Long call Maximum profit = infinity (unlimited profit) Maximum loss = -c Breakeven = ? (at what ST , Profit = 0 ? ) Profit = max(ST – K) - c (ST – K) – c = 0 ST = K+ c If ST = K +c, profit = 0 Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 11

Long Call Profit and Loss Diagram 30 Profit ($) 20 10 -c 0 -5 K+c =105 70 80 90 100 Problem 10. 9 Make profit when ST > K+c ST > 100+5 => 105 Exercised when. ST > K ST > 100 K Terminal stock price ($) 110 120 130 12

Short call Obligated to sell the underlying asset to the long call if the long call exercise its right to purchase. The short call has no choice. The decision is made by long call. Short call payoff = min (K- ST , 0) Short call profit & loss = min (K- ST , 0)+ c Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 13

Short call Zero-sum game Same payoff & profit but the sign is opposite to long call. Break-even = ? (at what ST , profit = 0 ? ) -(ST –K )+c = 0 ST – K = c ST = K+ c Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 14

Short call P&L diagram Profit ($) C 5 0 -10 120 130 70 80 90 100 K Terminal stock price ($) (ST) -20 K+c = 105 -30 Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 15

Short Call Profit ($) 5 0 -10 120 130 70 80 90 100 Terminal stock price ($) -20 -30 Short call maximum profit = c Maximum loss = infinity, unlimited loss Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 16

Problem 10. 2 An investor sells a European call on a share for $4. The stock price is $47 and the strike price is $50. Under what circumstances does the investor make a profit? Under what circumstances will the option be exercised? Draw a diagram showing the variation of the investor’s profit with the stock price at the maturity of the option. Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 17

Problem 10. 2 C = 4, K = 50 Short position Investor makes profit when ST < K+c ST < 50+4 ST < 54 Exercised when ST > K , ST > 50 Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 18

Dividends & Stock Splits Suppose you own N options with a strike price of K : No adjustments are made to the option terms for cash dividends When there is an n-for-m stock split, • the strike price is reduced to m. K/n • the no. of options is increased to n. N/m Stock dividends are handled similarly to stock splits Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 20

Dividends and Stock split : Individual stock option Cash dividend -> No adjustment are made to the option terms Stock split Number of shares outstanding increase Price per share decrease 0 Stock split 1 -> 2 2 -for-1 stock split Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 T 21

Stock split Ex. Call option N = 100 shares K = $20/ share 2 -for-1 stock split Adjust the option term to N’ = 200 shares K’ = $10 / share Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 22

Problem 10. 17 Consider an exchange-traded call option contract to buy 500 shares with a strike price of $40 and maturity in four months. Explain how the terms of the option contract change when there is A 10% stock dividend B 10% cash dividend C 4 -for-1 stock split Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 25

Problem 10. 17 N = 500, K 40 A. N’ = 500 x 1. 1 = 550 K’ = 40/1. 1 = 36. 36 B. No effect C. N’ = 500 x 4 = 2000 K’ = 40/4 = 10 Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 26

Put option Put Long put • Pay premium to have the right to sell • Long put exercise the right to sell when St < K • (Able to sell at higher price K, and buy in market at lower price St) p put premium Short put • Have an obligation to sell when St < K • Where St = Spot price K = Strike price Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 27

Long put Spot price ST Strike price Pay off K Max ( K-ST, 0) Profit/Loss Max (K-ST, 0)- p 55 70 15 8 63 70 7 0 80 70 0 -7 115 100 15 10 120 100 20 15 Payoff = The cashflow that occurs at expiration. Profit/Loss = Cashflow at expiration – Cashflow at initiation Put option’s intrinsic value = K- St Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 29

Long Put Profit / Loss diagram Profit ($) K- p = $63 30 20 Breakeven = K-p 10 0 p -7 Terminal stock price ($) K =70 40 50 60 70 80 ST 90 100 63 Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 30

Long put Maximum profit = K – p (This is where ST = 0) Limited profit Maximum loss = -p Breakeven Profit = max (K –ST, 0 ) –p (K-ST) – p =0 ST = K– p So if ST = K-p, Profit = 0 Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 31

Problem 10. 1 An investor buys a European put on a share for $3. The stock price is $42 and the strike price is $40. Under what circumstances does the investor make a profit? Under what circumstances will the option be exercised? Draw a diagram showing the variation of the investor’s profit with the stock price at the maturity of the option. Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 32

Problem 10. 1 P = $3 K =$40 Make profit when ST < K- p ST < $40 -$3 ST < $37 Exercised when ST < K ST < $40 Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 33

Short put Obligated to buy the underlying asset from the long put if the long put exercise the right to sell. Short put payoff = min(ST –K, 0) Short put profit & loss. = min (ST – K, 0) +p Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 35

Short put Zero-sum game Same payoff and profit but the sign is opposite to long put. Breakeven = ? -(K-ST)+ p= 0 -K+ ST + p = 0 ST = K-p Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 36

Short Put diagram Profit from writing a European put option: option price = $7, strike price = $70 K = 70 Profit ($) P=7 0 -10 40 50 Terminal stock price ($) , ST 60 70 80 90 100 K-p = 63 -20 -30 -K+p 37

Problem 10. 10 Suppose that a European put option to sell a share for $60 costs $8 and is held until maturity. Under what circumstances will the seller of the option (the party with the short position) make a profit? Under what circumstances will the option be exercised? Draw a diagram illustrating how the profit from a short position in the option depends on the stock price at maturity of the option. Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 39

Problem 10. 10 K = $60 P= $8 Short put Make profit when ST > K-p ST > $60 -$8 ST > $52 Exercised when ST < K ST < 60 Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 40

Payoffs from Options What is the Option Position in Each Case? K = Strike price, ST = Price of asset at maturity Payoff K K ST Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 ST 42

Terminology Moneyness : A function of the payoff that long position will experience should it exercise. At-the-money option • Long position will earn a payoff of zero if it exercise the option • Indifferent to exercise or not exercise 43

Terminology In-the-money option • Long position will earn a positive payoff if it exercises the option • Will exercise Out-of-the-money option • Long position will earn a negative payoff if it exercises the option • Will not exercise Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 44

Terminology Call Put ITM S 0 > K 1 S 0 < K 3 ATM S 0 = K 2 OTM S 0 < K 3 S 0 > K 1 *Same underlying asset, same price (S 0) but different exercise price (K) *Different premium, ITM most expensive, OTM the cheapest Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 45

Terminology Whether a long position, a short position , or a third party, each determines an option’s moneyness through determining the long position’s payoff should exercise. ITM is the highest premium because only requires the smallest move in the price of the underlying asset to reach breakeven point. Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 46

Terminology (continued) Option class All options of the same type (calls or puts) on a stock are referred to as an option class Option series Consist of all the options of a given class with the same expiration date and strike price. Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 47

Terminology Intrinsic value The value it would have if there were no time to maturity, so that the exercise decision had to b made immediately Intrinsic value Call Put Max (S –K), 0 Max (K-S), 0 Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 48

Terminology A call option only has intrinsic value when the underlying asset price is greater than the strike price (when ITM, S 0 > K) Otherwise, the intrinsic value = 0 A put option has intrinsic value(when ITM, S 0<K) Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 49

Terminology Time value or optionality value The value of having the right to decide whether to exercise or not An option has time value regardless of its moneyness. Total value of an option Intrinsic value +time value Options, Futures, and Other Derivatives, 9 th Edition, Global Edition, Copyright © John C. Hull 2018 50