Lecture 8 Options on Futures

1. Lecture 8Options on Futures Primary Text Edwards and Ma: Chapters 18, 19, & 20

2. Options on FuturesCall • The structure of a futures option is very similar to an option on the physical. For both instruments, an option owner has the right to exercise, and the seller has a duty to perform upon exercise. • Upon exercising a futures option, a call holder receives a long position in the underlying futures at the settlement price prevailing at the time of exercise, plus a payment that equals the futures settlement price (FPT) minus the exercise price (SPT) of the futures option. • The call writer receives a short position in the underlying futures at the settlement price prevailing at the time of exercise and makes a payment to the call holder that equals the futures settlement price (FPT) minus the exercise price (SPT) .

3. Options on FuturesPut • Upon exercising a put option on futures, a put holder receives a short position in the underlying futures at the settlement price prevailing at the time of exercise. • The put holder also receives a payment that equals the exercise price of the futures option (SPT) minus the futures settlement price (FPT). • The put writer receives a long position in the underlying futures at the settlement price prevailing at the time of exercise and makes a payment to the put holder equal to the strike price (SPT) minus the futures settlement price (FPT).

4. Options on FuturesCall and Put Payoffs • In every exercise, the option holder and writer receive a futures position. The traders may offset the futures position or continue to hold the positions. For both the call and put, the purchaser originally paid the option premium to the seller.

5. Options on FuturesProfit/Loss from Call and Put Upon Exercise of the option: • Profit/Loss of the Call Holder =Max (FPT −SPT, 0) − Cf • Profit/Loss of the Call Writer = Cf− Max (FPT −SPT, 0) • Profit/Loss of the Put Holder = Max (SPT −FPT, 0) − Pf • Profit/Loss of the Put Writer = Pf− Max (SPT −FPT, 0) • Note that, in addition to the profit or loss upon exercise of the option, option holder and writer obtain futures positions which need to be offset before expiration

6. Options on FuturesProfit Potentials and Risk Exposure • Consider three simple trading strategies in S&P 500 futures: • a simple long position of a S&P 500 futures purchased at $300 per share • a long call option position in a S&P 500 futures with strike price $300 and premium $10 per share, and • a short put option position in a S&P 500 futures with strike price $300 and premium $10 per share. • Upon exercise of any of these contracts, the trader receives a long position in S&P 500 index futures contract (with 500 shares) at the settlement price prevailing at the time of exercise. • The ultimate profits or losses associated with these positions depend on the value of the S&P 500 futures contract at expiration.

7. Options on FuturesProfit Potentials and Risk Exposure • Potential profits and losses from these positions for alternative hypothetical futures prices at expiration, ranging from $280 to $330 per share.

8. Options on Futures Profit Potentials and Risk Exposure • Consider three simple trading strategies with S&P 500 futures: • a short position (500 shares) at $300 per share, • a short call option position with strike price $300 and premium $10 per share, and • a long put option position with strike price $300 and premium $10 per share. • Upon exercise of any of these contracts, the trader receives a short position in S&P 500 index futures contract (with 500 shares) at the settlement price prevailing at the time of exercise. • The ultimate profits or losses associated with these positions depend on the value of the S&P 500 futures contract at expiration.

9. Options on FuturesProfit Potentials and Risk Exposure • Potential profits and losses from these positions for alternative hypothetical futures prices at expiration, ranging from $280 to $330 per share.

10. Options on FuturesProfit Potentials and Risk Exposure

11. Options on FuturesPut-Call Parity Relationship for Futures Options • The put-call parity relationship for futures options: Pf = Cf + SP - FP • Pf= Put option premium • Cf= Call option premium • SP = Strike Price of the Call and Put options • FP = Futures settlement price • The put-call parity relationship states that put premium will be equal to the call premium plus the difference between the strike price and underlying futures price (i.e., SP – FP). • Since at-the-money calls and puts have no intrinsic value (i.e., SP = FP, or SP – FP =0), their premiums are identical. • The relationship can also be expressed as Cf = Pf + FP - SP

12. Options on FuturesThe Black Model for Futures Option Pricing • Fischer Black developed the following futures option pricing model: • Cf= Call option premium ▪ SP = Strike Price of the Call and Put options • FP = Futures settlement price ▪ R = riskless interest rate • T = time to maturity of the option in years • σf= expected annualized volatility of the futures returns • N(d) = the probability that a random draw from a standard normal distribution will be less than d

13. Options on FuturesDeterminants of Futures Option Premiums

14. Options on FuturesSpeculating with Futures Options • Strategies for speculating with options based on price change can be categorized into two major groups: simple and complex. • Simple Speculation Strategies: • Long or short call • Long or short put • Complex Speculations Strategies: • Covered Option Strategies: • Covered call writing = short call + long futures • Covered put writing = short put + short futures • Synthetic Option Strategies: • Synthetic (long) call = long put + long futures • Synthetic (long) put = long call + short futures

15. Options on FuturesSimple Speculation Strategies • Bullish: If a trader believes that stock or futures price will rise, she will adopt a long call position (bullish strategy); • Bearish: If she believes that the stock or futures price will fall, she will adopt a long put position (bearish strategy). • The more bullish or bearish a trader is, the more attractive it will be to purchase an out-of-the-money call or put option. Such options are cheaper, and provide greater leverage with no additional downside risk. • Bearish to neutral: A trader who believes that stock or futures price will either fall or remain constant (bearish to neutral) can earn income from writing call (short call) • Bullish to neutral: A trader who believes that the stock or futures price will either rise or remain constant (bullish to neutral) can earn income from writing puts (short put). • Speculators who strongly hold these beliefs (bearish to neutral or bullish to neutral) will want to write in-the-money options.

16. Options on FuturesSimple Speculation Strategies

17. Options on FuturesComplex Speculation Strategies • Covered Call Writing:Selling a call option against a long futures (or stock) position is known as covered call writing. This strategy permits a trader to receive the call option premium in return for giving up some or all of the upside profit potential due to an increase in the futures price. It is a desirable strategy if futures prices are expected to remain fairly stable. • Example: Covered call writing strategy with S&P 500 futures purchased at $300 per share and a short call option position in a S&P 500 futures with strike price $300 and premium $10 per share. • If the S&P 500 futures price falls below or stays at $300, the call holder does not exercise her right and let the call to expire − the speculator’s net profit or loss is equal to the call premium minus the loss from the futures transaction. • If the S&P 500 futures price rise above $300, the call holder exercises her right and the call writer receives a short position in S&P 500 futures, which is offset by her long position in S&P 500 futures - the speculator’s net profit is equal to the call premium

18. Options on FuturesCovered Call Writing – Profit or Loss

20. Options on FuturesComplex Speculation Strategies • Covered Put Writing:Selling a put option against a short futures (or stock) position is known as covered put writing. This is an income augmenting strategy, since the trader receives the put premium. This strategy again is attractive if futures prices are expected to be fairly stable, since in the event of declining futures price the short futures position will not be profitable because the put holder will exercise her right. • Example: Short a put option in S&P 500 futures with strike price $300 and premium $10 per share and short S&P 500 futures at $300 per share. • If the S&P 500 futures price falls below $300, the put holder will exercise her right and receives a short position in the futures − the speculator’s net profit or loss is equal to the put premium. • If the S&P 500 futures price rise above $300, the put holder will not exercise the option, and the speculator will have to offset the short futures position by purchasing the futures contract - the speculator’s net profit/loss is equal to the put premium minus the loss from the futures transaction

21. Options on FuturesCovered Put Writing – Profit or Loss

23. Options on FuturesComplex Speculation Strategies • Synthetic Options:Synthetic options are created by combining the purchase of a call or put option with an outright short or long futures (or stock) position. • Synthetic option positions are generally used either as an efficient way to alter the risk-return profile of an existing speculative position, perhaps because of a change in a speculator’s price expectation, or as a way to lock in unrealized speculative profits. • Synthetic Calls: Long futures plus a long put option on the futures contract • A synthetic call strategy enables an investor to assume a position that has a risk and return profile similar to an outright long call position. • This strategy may be used by speculators who hold a long futures position and, while confident that futures prices will rise in the long or even intermediate term, fear an interim price decline. • Buying the put protects them against potential losses associated with a large price decline. In effect, the trader is placing a stop lossorder on his long futures position.

24. Options on FuturesSynthetic Calls – Profit or Loss • Example: Long a put option in S&P 500 futures with strike price $300 and premium $10 per share along with a long S&P 500 futures at $300 per share. • If the S&P 500 futures price falls below $300, the put holder will exercise her right and receives a short position in the futures, plus a cash inflow equal to the amount of (300 – FPT). She also incurs a loss from her long futures position equal to the amount of (300 – FPT). Thus, upon exercise of the put option, the speculator’s futures positions and cash flows are offset, and her maximum loss is equal to the put premium (Pf = 10). • If the S&P 500 futures price rise above $300, the put holder will not exercise her right and let the put option to expire, incurring a loss equal to the premium paid (Pf = 10). But, she makes profit by offsetting her long futures position (i.e., by selling the futures contract) equal to the amount of (FPT – 300).

25. Options on FuturesSynthetic Calls – Profit or Loss

27. Options on FuturesSynthetic Puts • Synthetic Puts: Short futures plus a long call option on the futures contract • This strategy insulates the speculator from losses due to a large price increase, but still permits him to profit from declining prices. • This strategy allows the speculator either to lock in an unrealized profit or limit the loss on the short futures position. The profit/loss profile of this position is similar to that of a long put. • Example: Long a call option in S&P 500 futures with strike price $300 and premium $10 per share along with a short S&P 500 futures at $300 per share. • If the S&P 500 futures price falls below $300, the speculator will not exercise the call option but offsets the short futures position. Her net profit is equal to the gain from futures transaction (300 – FPT) minus the call premium. • If the S&P 500 futures price rise above $300, the speculator will exercise the call option and receive a long position in S&P 500 futures which is offset against her short futures position. Her net loss from the synthetic put strategy is equal to the call option premium paid.

28. Options on FuturesSynthetic Puts – Profit or Loss

30. Options on FuturesSpeculations with Futures Options – Complex Strategies

31. Options on FuturesOption Spreads • Option spreads are a way to speculate on relative price changes. • These strategies involve the simultaneous purchase and sale of different options, creating a price spread that widens or narrows according to what happens to underlying asset prices. • Common option spreads are categorized in three major types: • Vertical Spreads– An option spread in which the two legs of the spread have different strike prices but have the same expiration date • Horizontal Spreads – Anoption spread in which the two legs of the spread have different expiration dates but the same strike price • Diagonal Spreads– An option spread in which the two legs of the spread have both different strike prices and different expiration dates • Diagonal spreads are hybrids of vertical and horizontal spreads • The appropriate spreading strategies differ depending on the market trend in the prices of underlying futures (or assets).

32. Options on FuturesOption Spreads • Bullish Vertical Option Spreads – Bullish option spreads are strategies that yield a profit when underlying asset prices rise. Such spreads are established by purchasing an option with a low strike price and selling an option with a high strike price, both with the same expiration date. • Bull Vertical Call Option Spreads - A bull vertical call option spread is created by buying a call option with a relatively low strike price (SPL) and selling a call option with a relatively high strike price (SPH), both with the same expiration date. • To initiate this spread, the speculator has to invest a cash amount equal to the difference between the low strike premium (CL) and the high strike premium (CH), which is commonly known among the option traders as the net debit. • Net Debit= − call premium paid + call premium received • = − CL +CH < 0 (because CL >CH)

33. Options on FuturesBull Vertical Call Option Spreads • If, upon expiration, the underlying futures price (FP) is less than or equal to the lower of the two strike prices, both options will expire out-of-the-money. In this case, the speculator will lose the difference between the premiums. • Maximum Loss = − CL +CH= Net debit (remember, CL >CH) • If prices rise prior to expiration and the futures price (FP) exceeds the higher strike price, both options will be in-the-money and exercised. In this case, the speculator’s maximum profit will be equal to the difference between the two strike prices (SPH−SPL) less the net debit (− CL +CH) • Maximum Profit = (SPH−SPL) − CL +CH = Strike price diff. - Net debit • If prices rise prior to expiration and the futures price (FP) lies between the two strike prices, long call with the lower strike price will be in-the-money and the short call with the higher strike price will still be out-of-the-money. In this case the speculator will exercise the long call and the higher strike call holder will let the option to expire. • Profit/Loss = − CL +CH + (FP−SPL) = Net debit + Diff. in FP and SPL

34. Options on FuturesBull Vertical Call Option Spreads

35. Spreading with Options: Bull Vertical Call Spreads

36. Options on FuturesOption Spreads • Bull Vertical Put Option Spreads - A bull vertical put spread is created by purchasing a put option with a low strike price (SPL) and selling a put option with a higher strike price (SPH) , both with the same expiration date. • The premium paid to purchase the lower strike put option (PL) will always be less than the premium received from the sale of the higher strike put (PH), so that the net premium will generate a cash inflow, which is commonly known among the option traders as the net credit. • Net Credit= − Put premium paid + Put premium received • = − PL +PH > 0 (because PL <PH) • If, at expiration, the underlying futures price (FP) is less than or equal to the lower of the two strike prices, both options will be in-the-money and will be exercised. In this case, the speculator incurs a net loss equal to the difference of the two strike prices (SPL – SPH) plus the net credit (− PL +PH). • Maximum Loss= (SPL − SPH) − PL +PH = − Strike price diff. + Net credit

37. Options on FuturesBull Vertical Call Option Spreads • If prices rise prior to expiration and the futures price (FP) exceeds the higher strike price, both options will expire out-of-the-money and are not likely to be exercised. Thus, the speculator maximum profit will be equal to the net credit (− PL +PH). • Maximum Profit = − PL +PH = Net credit (remember, PL <PH) • If prices rise prior to expiration and the futures price (FP) lies between the two strike prices, long put with the lower strike price will be out-of-the-money (will not be exercised) and the short put with the higher strike price will be in-the-money (will be exercised). In this case, the speculator’s net profit or loss will be equal to the difference between the futures price and higher strike price (FP−SPH) plus the net debit (− PL +PH), which may be less than, or equal to, or higher than zero. • Profit/Loss = (FP−SPH) − PL +PH = Diff. in FP and SPH + Net Credit

38. Options on FuturesBull Vertical Put Option Spreads • Like a bull vertical call spread, bull vertical put spreads have limited profit and loss potentials. The major distinction is that a call spread results in a net debit (cash outflow), while a bull vertical put spread results in a net credit (cash inflow). A vertical put spread can be profitable even if futures (or asset) price do not rise, as long as they do not fall. Some traders, therefore, prefer a bull put spread to a bull call spread.

39. Spreading with Options: Bull Vertical Put Spreads

40. Options on FuturesOption Spreads • Bearish Vertical Option Spreads – Bearish option spreads are strategies that yield a profit when underlying futures (or asset) prices decline. Such spreads are established by purchasing an option with a high strike price and selling an option with a low strike price, both with the same expiration date. • Bear Vertical Call Option Spreads - A bear vertical call options spread is created by buying a call option with a relatively high strike price (SPH) and selling a call option with a relatively low strike price (SPL), both with the same expiration date. • Initiating this spread, the speculator receives a cash inflow equal to the difference between the low strike premium (CL) and the high strike premium (CH), which is commonly known among the option traders as the net credit. • Net Credit= Call premium received − Call premium paid • = CL −CH > 0 (because CL >CH)

41. Options on FuturesBear Vertical Call Option Spreads • If, upon expiration, the underlying futures price is less than or equal to the lower of the two strike prices, both options will expire out-of-the-money. In this case, the speculator will earn the difference between the premiums. • Maximum Profit = CL −CH= Net Credit (remember, CL >CH) • If prices rise prior to expiration and the futures price exceeds the higher strike price, both options will be in-the-money and exercised. The maximum loss in that case will be the net premium earned (CL −CH) minus the difference between the strike prices of the tow options (SPH−SPL). • Maximum Loss = CL −CH − (SPH−SPL) = Net Credit − Strike price diff. • If prices rise prior to expiration and the futures price lies between the two strike prices, long call with the lower strike price will be in-the-money (exercised) and the short call with the higher strike price will still be out-of-the-money (expire). • Profit/Loss = CL −CH − (FP−SPL) = Net credit − Diff. in FP and SPL

42. Options on FuturesBear Vertical Call Option Spreads

43. Spreading with Options: Bear Vertical Call Spreads

44. Options on FuturesOption Spreads • Bear Vertical Put Option Spreads - A bear vertical put spread is created by purchasing a put option with a relatively higher strike price (SPH) and selling a put option with a lower strike price (SPL) , both with the same expiration date. • The premium paid to purchase the higher strike put option (PH) will always be higher than the premium received from the sale of the lower strike put (PL), so that the net premium will generate a cash outflow, which is commonly known among the option traders as the net debit. • Net Debit= Put premium received − Put premium paid • = PL −PH < 0 (because, PL <PH) • If futures price (FP) declines to a level lower than the lower strike price, both options will be in-the-money and exercised. The maximum profit in that case will be the net premium paid (net debit, PL − PH ) plus the difference between the strike prices of the two options • Maximum Profit = PL − PH + (SPH − SPL) = Net debit +Strike Price Diff.

45. Options on FuturesBear Vertical Put Option Spreads • If futures price rise to a level greater than the higher strike price, both options will expire out-of-the-money. In this case, the spreader incurs a net loss equal to the net debit (− PH +PL). • Maximum Loss= PL − PH = Net debit < 0 • If the futures price lies between the two strike prices, the (short) put option with the higher strike price will be in-the-money and exercised, and the (long) put with the lower strike price will be out-of-the-money and expire unexercised. In this case, the spreader’s net profit or loss will be equal to the net debit (PL −PH) plus the difference between the higher strike price and futures price (SPH− FP). • Profit/Loss = PL −PH + (FP−SPH) = Net debit + Diff. in FP and SPH

46. Options on FuturesBear Vertical Put Option Spreads • The difference between bear vertical call and put spread strategies is that a vertical call spread will be profitable even if asset prices do not decline, as long as prices do not rise. A vertical put spread will not be profitable unless prices actually decline. Therefore, speculators often prefer bear vertical call spreads to bear vertical put spreads.

47. Spreading with Options: Bear Vertical Put Spreads

48. Options on FuturesHorizontal or Time Spreads • Horizontal or Time Spreads: • If an investor believes that underlying asset prices will be stable for a foreseeable period of time, he or she can attempt to profit from the declining time value of options by setting up a horizontal option spread. • A horizontal option spread is created by selling an option with a relatively short time to expiration and buying an option of the same time with a longer time to expiration, both with the same strike prices. • In general, the time value of a short-maturity option will decline at a faster rate than will the time value of a longer maturity option. • Thus, as long as the underlying asset price remains stable, or does not move significantly against the investor, he or she can make profit from “riding down” the time value of the near-term option, since the loss on the longer-term option will be less than the profit on the near-term option.

49. Options on FuturesStraddles and Strangles • Straddles: • Like spreads, straddles involve the simultaneous sale and purchase of options. • Unlike spreads, straddles entail the purchase of a call and put (a long straddle), or the sale of a call and put (a short straddle). • This strategy is often used by speculators who believe that asset prices either will move substantially in one direction or the other (but are uncertain as to which direction) or will remain fairly constant. • Long Straddle: • A long straddle is formed by buying an equal number of calls and puts with the same strike price and with the same expiration date. • This strategy will be profitable if underlying asset prices move substantially in either direction. • If prices fall – the put option will become profitable • If prices rise – the call option will become profitable

50. Options on FuturesLong Straddle