Part 1: Mechanics of Options Markets and Properties of Stock Options

Options, Futures, and Other Derivatives Part 1 Mechanics of Options Markets and Properties of Stock Options P ELEVENTH EDITION OPTIONS, FUTURES, AND OTHER DERIVATIVES Pearson John Hull Copyright © 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved Mechanics of Options Markets . Review of Option Types A call is an option to buy. A put is an option to sell. • A European option can be exercised only at the end of its life. An American option can be exercised at any time. Pearson Copyright © 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved Option Positions Long call (own a call option) Long put (own a put option) Short call (sell a call option) Short put (sell a put option) Pearson Copyright © 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved Long Call (Figure 10.1) Profit from buying one European call option: option price = $5, strike price = $100, option life = 2 months 30 Profit ($) Pearson 20 10 70 80 90 100 Terminal stock price ($) 아 -5 110 120 130 Copyright © 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved Short Call (Figure 10.3) Profit from writing one European call option: option price = $5, strike price = $100 Pearson Profit ($) 5 110 120 130 70 80 90 100 -10 Terminal stock price ($) -20 -30 Copyright © 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved Long Put (Figure 10.2) Profit from buying a European put option: option price = $7, strike price = $70 Pearson 30 Profit ($) 20 10 Terminal stock price ($) 0 40 50 60 70 80 90 100 -7 Copyright 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved Short Put (Figure 10.4) Profit from writing a European put option: option price = $7, strike price = $70 Pearson Profit ($) 7- 40 50 60 Terminal stock price ($) 0 70 80 90 100 -10 -20 -30 Copyright © 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved Payoffs from Options (Figure 10.5) What is the Option Position in Each Case? K = Strike price, S, = Price of asset at maturity Pearson Payoff Payoff K K ST ST Payoff Payoff K K Sp ST Copyright © 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved Assets Underlying Exchange-Traded Options • Stocks ETFs - Exchange Traded Funds (and other ETPs) . Foreign Currency Stock Indices Futures Pearson Copyright © 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved • Specification of Exchange-Traded Options Expiration date Strike price (or exercise price) European or American Call or Put (option class) Pearson Copyright 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved Terminology (1 of 2) Moneyness: At-the-money option In-the-money option (can give some profit) Out-of-the-money option If S is the stock price and K is the strike price, a call option is in the money when S > K, at the money when S = K, and out of the money when S < K. A put option is in the money when S < K, at the money when S = K, and out of the money when S > K. Clearly, anoption will be exercised only when it is in the money. In the absence of transaction costs, an in-the-money option will always be exercised on the expiration date if it has not been exercised previously. P Pearson Copyright © 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved Terminology (2 of 2) Option class: call or put Intrinsic value of an option: the value it would have if there were no time to maturity, so that the exercise decision had to be made immediately. Time value of an option: The excess of an option's value over its intrinsic value. The total value of an option is therefore the sum of its intrinsic value and its time value. Pearson Copyright © 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved Dividends & Stock Splits (1 of 2) • 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, Pearson Π the strike price is reduced to mK/n Π the no. of options is increased to nN/m Stock dividends are handled similarly to stock splits Copyright © 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved Dividends & Stock Splits (2 of2) Consider a call option to buy 100 shares for $20/share How should terms be adjusted: for a 2-for-1 stock split? for a 5% stock dividend? Pearson Copyright © 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved Market Makers • Most exchanges use market makers to facilitate options trading. A market maker quotes both bid and ask prices when requested. The market maker does not know whether the individual requesting the quotes wants to buy or sell. Pearson Copyright © 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved Margin Margin is required when options are sold. Options margins are the cash or security that traders must submit to the broker as collateral before writing or selling options. Pearson Copyright © 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved Warrants (Chứng quyèn) Warrants are options that are issued by a corporation or financial institution. The corporation issues call warrants giving the holder the right to buy its own stock for a certain price at a certain future time and then attaches them to the bonds to make the bonds more attractive to investors. The issuer settles up with the holder when a warrant is exercised. a Pearson Copyright 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved • Employee Stock Options (see also Chapter 16) Employee stock options are a form of remuneration (/r mju:.nə'rer.Jən/, thù lao) issued by a company to its executives. They are usually at the money when issued. When options are exercised, the company issues more stock and sells it to the option holder for the strike price. Expensed on the income statement. Pearson Copyright © 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved Convertible Bonds Convertible bonds are regular bonds that can bе exchanged for equity at certain times in the future according to a predetermined exchange ratio. Usually a convertible is callable. The call provision is a way in which the issuer can force conversion at a time earlier than the holder might otherwise choose. Pearson Copyright © 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved Exercises at the end of chapter 10 Pearson Copyright © 2022, 2018, 2012 Pearson Education, Inc. All Rights Reserved Properties of Stock Options Notation C: European call option price p: European put option price So: Stock price today K: Strike price T: Life of option σ Volatility of stock price C: American call option price P: American put option price S,: Stock price at option maturity D: PV of dividends paid during life of option r Risk-free rate for maturity T with cont. comp. Effect of Variables on Option Pricing (Table 11.1) Variable C S + C P + K + + T ? ? + + σ + + + + r + + D - + - + Discuss with your groups and explain (post on forum LMS)? American vs European Options An American option is worth at least as much as the corresponding European option, C≥c P≥p Calls: An Arbitrage Opportunity? (p236) Suppose that c = 3 So = 20 T= 1 r = 10% (compounded continuously) K= 18 D= 0 Is there an arbitrage opportunity? Lower Bound for European Call Option Prices; No Dividends (Equation 11.4) c ≥ max(S-Ke,0) Puts: An Arbitrage Opportunity? (p237) Suppose that P=1 S =37 T= 0.5 r = 5% (compounded continuously) K= 40 D=0 Is there an arbitrage opportunity? Lower Bound for European Put Prices; No Dividends (Equation 11.5) -rT p≥max(Ke -S, 0) Put-Call Parity: No Dividends • Consider the following 2 portfolios: Portfolio A: European call on a stock + zero-coupon bond that pays K at time T Portfolio C: European put on the stock + the stock Values of Portfolios (Table 11.2) S> K S < K Portfolio A Call option S-k 이 Zero-coupon bond K K Total K S Portfolio C Put Option 이 K-S Share S ST Total S K The Put-Call Parity Result (Equation 11.6) . Both are worth max (S, K) at the maturity of the options. They must therefore be worth the same today. This means that -rT c+Ke = p+S Arbitrage Opportunities (p239) Suppose that c=3 So = 31 T = 0.25 r = 10% (compounded continuously) K = 30 D= 0 What are the arbitrage possibilities when P = 2.25? P=1? • Early Exercise Usually there is some chance that an American option will be exercised early. An exception is an American call on a non-dividend paying stock. This should never be exercised early. Why? Reasons For Not Exercising a Call Early (No Dividends) • . No income is sacrificed. You delay paying the strike price. Holding the call provides an insurance. Bounds for European or American Call Options (No Dividends) Figure 11.3 Call Price So European or American Call price in this region max(S-Ker7,0) S Should Puts Be Exercised Early? Are there any advantages to exercising an American put when: S = 60; T = 0.25; r = 10% (compounded continuously) K = 100; D=0 Bounds for European and American Put Options (No Dividends) Figure 11.4 P KerT max(Ke+T-S0,0) European put price in this region P K max(K-So,0) American put price in this region The Impact of Dividends on Lower Bounds to Option Prices (Equations 11.8 and 11.9) D: present value of all dividends, can be 0 or positive c≥ s-D-KerT Ο p>D+ Ke-T Ο Extensions of Put-Call Parity American options: D = 0 S-K< C - P < S Ke-T Equation 11.7 . European options: D> 0 c+D+KeT = p+So Equation 11.10 American options: D>0 rT S,-D-K