1 Lecture 4 Options & Option trading strategies * Option strategies can ...
Lecture 4 Options & Option trading strategies * Option strategies can be divided into three main categories: • Taking a position in an option and the underlying asset; • A spread which involved taking a position in two or more options of the same type; and, • A combination which involved taking a position in a mixture of call and put options. 1. Option basics -‐ Call option: * Long (holder): right but not obligation to buy, pay off = max(ST-‐X, 0) * Short (writer, receive premium): obligated to sell, pay off = min(X-‐ ST, 0) -‐ Put option: * Long (holder): right but not obligation to sell, pay off = max(X-‐ ST, 0) * Short (writer, receive premium): obligated to buy, pay off = min(ST-‐X, 0) *profit ≠ payoff, profit includes premium -‐ Moneyness a. At the money: St = X b. In the money: Exercise option -‐ Call: St>X Put: St<X c. Out of the money: Not exercise option -‐ Call: St<X Put: St>X 2. Assets underlying options 2.1 Stock options (on exchange) (American) 2.2 Foreign currency options (OTC & on exchange) (European/American) 2.3 Index options (x$25)(OTC & on exchange) (S&P500, S&P100, ASX200) 2.4 Futures options (double derivative) -‐ Matures just before the delivery period in the futures contract -‐ Call options: the holder acquires a long position in the underlying futures contract + a cash amount equal to the excess of the futures price over the strike price -‐ Put options: the holder acquires a short position in the underlying futures contract + a cash amount equal to the excess of the strike price over the futures price 3. Dividends & stock splits • Suppose you own N options with a strike price of X : – No adjustments are made to the option terms for cash dividends. – When there is an n-‐for-‐m stock split, • strike price: mX/n • # options: nN/m – Stock dividends are handled in a manner similar to stock splits. 4. Extended option topics 4.1 Warrants: – Warrants are options that are issued (or written) by a corporation or a financial institution. – The number of warrants outstanding is determined by the size of the original issue & changes only when they are exercised or when they expire.
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When call warrants are issued by a corporation on its own stock, exercise will lead to new treasury stock being issued. – Primary offering, new capital raised to the firm 4.2 Executive stock options (call options) – Issued by a company to its executives as a performance incentive. – When the option is exercised the company issues more stock. – Options are usually out-‐of-‐the-‐money when issued to incentivise executives to increase the share price of the company. – They usually become vested after a period of time, and cannot be sold by the executive. – They often last for as long as 10 or 15 years. 4.3 Convertible bonds – Regular bonds that can be exchanged for equity at certain times in the future – Very often 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. 5. Stock option properties -‐ Notations: –
What will happen to the option price if … increases?
An American option is worth at least as much as the corresponding European option. C ≥ c， P ≥ 𝑝 6. Option bounds 6.1 Upper bounds -‐ Call options: No matter what happens, the option can never be worth more than the stock. c ≤ S0 and C ≤ S0 -‐ Put options: No matter how low the stock price becomes, the option can never be worth more than X. Hence:
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p ≤ X and P ≤ X • For European options， as it cannot be exercised early, p ≤ Xe-‐rT 6.2 Lower bounds * Two portfolios method @Notes -‐ European call options: c ≥ max(S0-‐Xe-‐rT,0) – Portfolio A • One European call option; plus, • An amount of cash equal to Xe-‐rT – Portfolio B • One share -‐ European put options: p ≥ max(Xe-‐rT-‐S0,0) – Portfolio C • One European put option; plus, • One share. – Portfolio D • An amount of cash equal to Xe-‐rT. 7. Put-‐Call Parity:
c + Xe− rT = p + S0
Portfolio E: European call on a stock + PV of the strike price in cash – Portfolio F: European put on the stock + the stock • Both are worth MAX(ST , X) at the maturity of the options. 8. Early exercise of American options -‐ American option can be exercised early -‐ American call on a non-‐dividend paying stock should NEVER be exercised early: – No income is sacrificed; – We delay paying the strike price; and, – Holding the call provides insurance against the stock price falling below strike price. 9. The impact of dividends on lower bounds to option prices –
c ≥ m ax ( S 0 − P V ( D ) − X e − rT , 0 )
p ≥ m a x ( P V ( D ) + X e − rT − 10. Extensions of Put-‐Call Parity • American options; D = 0, S0 -‐ X < C -‐ P < S0 -‐ Xe -‐rT • European options; D > 0, c + D + Xe -‐rT = p + S0 • American options; D > 0, S0 -‐ D -‐ X < C -‐ P < S0 -‐ Xe –rT
S 0 , 0 )
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Option Trading Strategies
11. Positions in an Option & The underlying assets – Figure (a): writing a covered call option (synthetic short put) • Sell short call, Buy (long) stocks • The long stock position on the stock covers or protects the investor from the payoff on the short call that becomes necessary if there is a sharp rise in the stock price – so is used when expecting the stock price to rise. – Figure (b): reverse of a covered call. • Buy (long) call & sell the stock • Synthetic long put and is used when expecting the stock price to drop. – Figure (c) illustrates a protective put. • Buying a put & buying the underlying stock. • It is known as a synthetic long call and is used when expecting the stock price to rise. – Figure (d) illustrates the reverse of a protective put. • Selling a put option and simultaneously selling the underlying stock. • It is known as a synthetic short call and is used when expecting the stock price to drop. 12. Spreads 12.1 Bull Spread using calls
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Buying a call option & selling a call option on the same stock with a higher strike price. – Both options have the same expiration date. – Because a call option price always decreases as the strike price increases, the value of the option sold is always less than the value of the option bought therefore requiring an initial investment. -‐ A Bull Spread strategy limits both the investor’s upside as well as downside risk but they hope that the stock price will increase. 12.2 Bull spread using puts •
Buying a put with a low strike price and selling a put with a high strike price. • Providing a positive cash flow to the investor up front. 12.3 Bear spread using calls •
Buying a call option with a high strike price and selling a call with a low strike price, leading to an initial cash inflow. – Limits both the investor’s upside profit potential and downside risk. • Hoping the price of the stock will decrease. 12.4 Bear spread using puts •
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• Buying a put with one strike price & selling a put with a lower strike price. • Involves an initial cash outflow. 12.5 Butterfly spread using calls
Buying a call option with a relatively low strike price + buying a call option with a relatively high strike price + selling two call options with a strike price half way between the other two. – The strike price of the two call options which are sold is relatively close to the current stock price. • Profit if the stock price does not move by much, and gives rise to a small loss if there is a significant movement in the stock price in either direction. • For an investor who feels that large stock price movements are unlikely. • Requires a small initial outlay. 12.6 Butterfly spread using puts –
Buying a put with a low strike price + buying another put with a high strike price + selling two puts with an intermediate strike price. • Provide exactly the same spread as using call options, and the initial outlay would also be identical. 12.7 Calendar spread using calls •
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Selling a call with a certain strike price and buying a longer maturity call option with the same strike price. – The longer the maturity of an option, usually the more expensive it is. -‐ initial outlay. • Profit if the stock price at the expiration of the short maturity option is close to the strike price of the short maturity option. • Loss when the stock price is significantly above or below the strike price. 12.8 Calendar spread using puts –
Buys a long maturity put option +sells a short maturity put option with the same strike price. • The profit pattern is similar to that obtained from using calls. 12.9 Reverse butterfly spread 12.10 Reverse calendar spread 13. Combinations 13.1 A straddle combination
-‐ Buying a call option and put option with the same strike price and expiration date • Appropriate when an investor believes there will be a large movement in the stock price, but they are unsure as to the direction. • Expensive strategy 13.2 Strip & Strap
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A Strip: a long call + a long position in two puts with the same strike price and expiration date. – Betting that there will be a large stock price move and considers a decrease in the stock price to be more likely. • A Strap: a long position in two call options + a long position in one put option with the same strike price and expiration date. – Betting that there will be a large stock price move and considers an increase in the stock price to be more likely. • As in both cases you are purchasing three options, this is a very expensive strategy. 13.3 Strangle combination •
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Buying a put and a call option with the same expiration date and different strike prices. – The call strike price > put strike price. – Betting that there will be a large movement in the stock price, but is uncertain as to the direction. For the investor to make a profit, the stock price has to move much further than in a Straddle.
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When call warrants are issued by a corporation on its own stock, exercise will lead to new treasury stock being issued. – Primary offering, new capital raised to the firm 4.2 Executive stock options (call options) – Issued by a company to its executives as a performance incentive. – When the option is exercised the company issues more stock. – Options are usually out-‐of-‐the-‐money when issued to incentivise executives to increase the share price of the company. – They usually become vested after a period of time, and cannot be sold by the executive. – They often last for as long as 10 or 15 years. 4.3 Convertible bonds – Regular bonds that can be exchanged for equity at certain times in the future – Very often 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. 5. Stock option properties -‐ Notations: –
What will happen to the option price if … increases?
An American option is worth at least as much as the corresponding European option. C ≥ c， P ≥ 𝑝 6. Option bounds 6.1 Upper bounds -‐ Call options: No matter what happens, the option can never be worth more than the stock. c ≤ S0 and C ≤ S0 -‐ Put options: No matter how low the stock price becomes, the option can never be worth more than X. Hence:
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p ≤ X and P ≤ X • For European options， as it cannot be exercised early, p ≤ Xe-‐rT 6.2 Lower bounds * Two portfolios method @Notes -‐ European call options: c ≥ max(S0-‐Xe-‐rT,0) – Portfolio A • One European call option; plus, • An amount of cash equal to Xe-‐rT – Portfolio B • One share -‐ European put options: p ≥ max(Xe-‐rT-‐S0,0) – Portfolio C • One European put option; plus, • One share. – Portfolio D • An amount of cash equal to Xe-‐rT. 7. Put-‐Call Parity:
c + Xe− rT = p + S0
Portfolio E: European call on a stock + PV of the strike price in cash – Portfolio F: European put on the stock + the stock • Both are worth MAX(ST , X) at the maturity of the options. 8. Early exercise of American options -‐ American option can be exercised early -‐ American call on a non-‐dividend paying stock should NEVER be exercised early: – No income is sacrificed; – We delay paying the strike price; and, – Holding the call provides insurance against the stock price falling below strike price. 9. The impact of dividends on lower bounds to option prices –
c ≥ m ax ( S 0 − P V ( D ) − X e − rT , 0 )
p ≥ m a x ( P V ( D ) + X e − rT − 10. Extensions of Put-‐Call Parity • American options; D = 0, S0 -‐ X < C -‐ P < S0 -‐ Xe -‐rT • European options; D > 0, c + D + Xe -‐rT = p + S0 • American options; D > 0, S0 -‐ D -‐ X < C -‐ P < S0 -‐ Xe –rT
S 0 , 0 )
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Option Trading Strategies
11. Positions in an Option & The underlying assets – Figure (a): writing a covered call option (synthetic short put) • Sell short call, Buy (long) stocks • The long stock position on the stock covers or protects the investor from the payoff on the short call that becomes necessary if there is a sharp rise in the stock price – so is used when expecting the stock price to rise. – Figure (b): reverse of a covered call. • Buy (long) call & sell the stock • Synthetic long put and is used when expecting the stock price to drop. – Figure (c) illustrates a protective put. • Buying a put & buying the underlying stock. • It is known as a synthetic long call and is used when expecting the stock price to rise. – Figure (d) illustrates the reverse of a protective put. • Selling a put option and simultaneously selling the underlying stock. • It is known as a synthetic short call and is used when expecting the stock price to drop. 12. Spreads 12.1 Bull Spread using calls
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Buying a call option & selling a call option on the same stock with a higher strike price. – Both options have the same expiration date. – Because a call option price always decreases as the strike price increases, the value of the option sold is always less than the value of the option bought therefore requiring an initial investment. -‐ A Bull Spread strategy limits both the investor’s upside as well as downside risk but they hope that the stock price will increase. 12.2 Bull spread using puts •
Buying a put with a low strike price and selling a put with a high strike price. • Providing a positive cash flow to the investor up front. 12.3 Bear spread using calls •
Buying a call option with a high strike price and selling a call with a low strike price, leading to an initial cash inflow. – Limits both the investor’s upside profit potential and downside risk. • Hoping the price of the stock will decrease. 12.4 Bear spread using puts •
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• Buying a put with one strike price & selling a put with a lower strike price. • Involves an initial cash outflow. 12.5 Butterfly spread using calls
Buying a call option with a relatively low strike price + buying a call option with a relatively high strike price + selling two call options with a strike price half way between the other two. – The strike price of the two call options which are sold is relatively close to the current stock price. • Profit if the stock price does not move by much, and gives rise to a small loss if there is a significant movement in the stock price in either direction. • For an investor who feels that large stock price movements are unlikely. • Requires a small initial outlay. 12.6 Butterfly spread using puts –
Buying a put with a low strike price + buying another put with a high strike price + selling two puts with an intermediate strike price. • Provide exactly the same spread as using call options, and the initial outlay would also be identical. 12.7 Calendar spread using calls •
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Selling a call with a certain strike price and buying a longer maturity call option with the same strike price. – The longer the maturity of an option, usually the more expensive it is. -‐ initial outlay. • Profit if the stock price at the expiration of the short maturity option is close to the strike price of the short maturity option. • Loss when the stock price is significantly above or below the strike price. 12.8 Calendar spread using puts –
Buys a long maturity put option +sells a short maturity put option with the same strike price. • The profit pattern is similar to that obtained from using calls. 12.9 Reverse butterfly spread 12.10 Reverse calendar spread 13. Combinations 13.1 A straddle combination
-‐ Buying a call option and put option with the same strike price and expiration date • Appropriate when an investor believes there will be a large movement in the stock price, but they are unsure as to the direction. • Expensive strategy 13.2 Strip & Strap
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A Strip: a long call + a long position in two puts with the same strike price and expiration date. – Betting that there will be a large stock price move and considers a decrease in the stock price to be more likely. • A Strap: a long position in two call options + a long position in one put option with the same strike price and expiration date. – Betting that there will be a large stock price move and considers an increase in the stock price to be more likely. • As in both cases you are purchasing three options, this is a very expensive strategy. 13.3 Strangle combination •
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Buying a put and a call option with the same expiration date and different strike prices. – The call strike price > put strike price. – Betting that there will be a large movement in the stock price, but is uncertain as to the direction. For the investor to make a profit, the stock price has to move much further than in a Straddle.
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