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

2. Options on Futures Call 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 (FP T ) minus the exercise price (SP T ) 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 (FP T ) minus the exercise price (SP T ).

3. Options on Futures Put 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 (SP T ) minus the futures settlement price (FP T ). 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 (SP T ) minus the futures settlement price (FP T ).

4. 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. Options on Futures Call and Put Payoffs Futures Position and Cash Flow upon Exercise InitialImmediateFP T < SPFP T > SP PositionCash FlowFutures PositionCash FlowFutures PositionCash Flow Long Call− C f No Exercise0Long FuturesFP T − SP Short Call+ C f No Exercise0Short Futures−(FP T − SP) Long Put− P f Short FuturesSP − FP T No Exercise0 Short Put+ P f Long Futures−(SP − FP T )No Exercise0

5. Upon Exercise of the option: Profit/Loss of the Call Holder =Max (FP T −SP T, 0) − C f Profit/Loss of the Call Writer = C f − Max (FP T −SP T, 0) Profit/Loss of the Put Holder = Max (SP T −FP T, 0) − P f Profit/Loss of the Put Writer = P f − Max (SP T −FP T, 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 Options on Futures Profit/Loss from Call and Put

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

8. Options on Futures 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. Profit Potentials and Risk Exposure

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

11. The put-call parity relationship for futures options: P f = C f + SP - FP P f = Put option premium C f = 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 C f = P f + FP - SP Options on Futures Put-Call Parity Relationship for Futures Options

12. Fischer Black developed the following futures option pricing model: C f = 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 σ f = 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 Options on Futures The Black Model for Futures Option Pricing

13. Options on Futures Determinants of Futures Option Premiums

14. 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 Options on Futures Speculating with Futures Options

15. 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. Options on Futures Simple Speculation Strategies

17. 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 Options on Futures Complex Speculation Strategies

18. Options on Futures Covered Call Writing – Profit or Loss

20. 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 Options on Futures Complex Speculation Strategies

21. Options on Futures Covered Put Writing – Profit or Loss

23. 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 loss order on his long futures position. Options on Futures Complex Speculation Strategies

24. 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 – FP T ). She also incurs a loss from her long futures position equal to the amount of (300 – FP T ). 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 (P f = 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 (P f = 10). But, she makes profit by offsetting her long futures position (i.e., by selling the futures contract) equal to the amount of (FP T – 300). Options on Futures Synthetic Calls – Profit or Loss

27. 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 – FP T ) 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. Options on Futures Synthetic Puts

28. Options on Futures Synthetic Puts – Profit or Loss

30. Options on Futures Speculations with Futures Options – Complex Strategies

31. Options on Futures Option 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 – An option 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 Futures Option 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 (SP L ) and selling a call option with a relatively high strike price (SP H ), 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 (C L ) and the high strike premium (C H ), which is commonly known among the option traders as the net debit. Net Debit = − call premium paid + call premium received = − C L + C H C H )

33. Options on Futures Bull 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 = − C L + C H = Net debit (remember, C L > C H ) 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 (SP H −SP L ) less the net debit (− C L + C H ) Maximum Profit = (SP H −SP L ) − C L + C H = 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 = − C L + C H + (FP−SP L ) = Net debit + Diff. in FP and SP L

34. Options on Futures Bull Vertical Call Option Spreads

35. Spreading with Options: Bull Vertical Call Spreads

36. Options on Futures Option Spreads Bull Vertical Put Option Spreads - A bull vertical put spread is created by purchasing a put option with a low strike price (SP L ) and selling a put option with a higher strike price (SP H ), both with the same expiration date. The premium paid to purchase the lower strike put option (P L ) will always be less than the premium received from the sale of the higher strike put (P H ), 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 = − P L + P H > 0 (because P L < P H ) 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 (SP L – SP H ) plus the net credit (− P L + P H ). Maximum Loss= (SP L − SP H ) − P L + P H = − Strike price diff. + Net credit

37. Options on Futures Bull 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 (− P L + P H ). Maximum Profit = − P L + P H = Net credit (remember, P L < P H ) 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−SP H ) plus the net debit (− P L + P H ), which may be less than, or equal to, or higher than zero. Profit/Loss = (FP−SP H ) − P L + P H = Diff. in FP and SP H + Net Credit

38. Options on Futures Bull 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 Futures Option 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 (SP H ) and selling a call option with a relatively low strike price (SP L ), both with the same expiration date. Initiating this spread, the speculator receives a cash inflow equal to the difference between the low strike premium (C L ) and the high strike premium (C H ), which is commonly known among the option traders as the net credit. Net Credit = Call premium received − Call premium paid = C L − C H > 0 (because C L > C H )

41. Options on Futures Bear 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 = C L − C H = Net Credit (remember, C L > C H ) 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 (C L − C H ) minus the difference between the strike prices of the tow options (SP H −SP L ). Maximum Loss = C L − C H − (SP H −SP L ) = 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 = C L − C H − (FP−SP L ) = Net credit − Diff. in FP and SP L

42. Options on Futures Bear Vertical Call Option Spreads

43. Spreading with Options: Bear Vertical Call Spreads

44. Options on Futures Option Spreads Bear Vertical Put Option Spreads - A bear vertical put spread is created by purchasing a put option with a relatively higher strike price (SP H ) and selling a put option with a lower strike price (SP L ), both with the same expiration date. The premium paid to purchase the higher strike put option (P H ) will always be higher than the premium received from the sale of the lower strike put (P L ), 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 = P L − P H < 0 (because, P L < P H ) 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, P L − P H ) plus the difference between the strike prices of the two options Maximum Profit = P L − P H + (SP H − SP L ) = Net debit +Strike Price Diff.

45. Options on Futures Bear 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 (− P H + P L ). Maximum Loss= P L − P H = 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 (P L − P H ) plus the difference between the higher strike price and futures price (SP H − FP). Profit/Loss = P L − P H + (FP−SP H ) = Net debit + Diff. in FP and SP H

46. Options on Futures Bear 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 Futures Horizontal 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 Futures Straddles 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. FP T <SPFP T >SP TraderActivityProfit/LossActivityProfit/Loss Long CallDo not exerciseExercise Long PutExerciseDo not exercise Net Returns Options on Futures Long Straddle

51. FP T <SPFP T >SP TraderActivityProfit/LossActivityProfit/Loss Long CallDo not exercise−Cf−Cf Exercise−C f + (FP T −SP ) Long PutExercise−P f + (SP − FP T )Do not exercise−Pf−Pf Net Returns−(C f +P f ) + (SP−FP T )−(C f +P f ) +(FP T −SP ) The maximum loss from the straddle: The cost of the straddle, that is the sum of call and put premiums paid, −(C f + P f ) – which will occur if the futures price at expiration is the same as the strike price of the option. The maximum profit from the straddle: Unlimited. To the extent that the gain on the profitable option exceeds the total premium cost of establishing the straddle, there will be a net profit. Options on Futures Long Straddle

53. Options on Futures Short Straddles Short Straddle: A short straddle is formed by selling 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 remain stable. If futures prices move substantially in either direction, the trader incurs loses If prices fall – the put option will be exercised by the holder If prices rise – the call option will be exercised by the holder The maximum profit from short straddle: Limited to the premiums received from selling the call and put options, that is (C f + P f ) The maximum loss from short straddle: Unlimited. To the extent that the loss from the exercised option exceeds the total premium received, there will be a net loss.

54. FP T < SPFP T > SP TraderActivityProfit/LossActivityProfit/Loss Short Call Call holder does not exercise Call holder exercises Short Put Put holder exercises Put holder does not exercise Net Returns Options on Futures Short Straddle

55. FP T <SPFP T >SP TraderActivityProfit/LossActivityProfit/Loss Short Call Call holder does not exercise CfCf Call holder exercises C f − (FP T −SP ) Short Put Put holder exercises P f − (SP − FP T ) Put holder does not exercise PfPf Net RetunsC f +P f − (SP−FP T )C f +P f − (FP T −SP ) Options on Futures Short Straddle Short straddles are more popular of the two strategies. These are employed to take advantage of the declining time value of options in markets where asset prices are expected to remain constant

56. Options on Futures Short Straddle

57. Options on Futures Straddles and Strangles Strangles: A strangle is a straddle in which the two legs do not share a common strike price – that is the call and put have different strike prices. A long strangle is used to profit from a volatile price scenario. A short strangle is used to profit from a stable price scenario. Long Strangle: A long strangle is formed by buying an equal number of calls and puts with different strike prices but 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

58. FP T < SP P < SP C SP P < FP T < SP C SP P < SP C < FP T TraderActivityProfit/LossActivityProfit/LossActivityProfit/Loss Long Call (SP C ) Do not exercise Exercise Long Put (SP P ) Exercise Do not exercise Net Returns Options on Futures Long Strangle Consider a out-of-the-money strangle: established by purchasing a call with higher strike price (SP C ) and a put with lower strike price (SP P ). SP C > SP P

59. FP T < SP P < SP C SP P < FP T < SP C SP P < SP C < FP T TraderActivityProfit/LossActivityProfit/LossActivityProfit/Loss Long Call (SP C ) Do not exercise −Cf−Cf −Cf−Cf Exercise −C f + (FP T − SP C ) Long Put (SP P ) Exercise −P f + (SP P − FP T ) Do not exercise −Pf−Pf −Pf−Pf Net Returns −(C f +P f ) + (SP P − FP T ) −(C f +P f ) −(C f +P f ) + (FP T −SP C ) Options on Futures Long Strangle The maximum loss from the strangle: The cost of the strangle, that is the sum of call and put premiums paid, −(C f + P f ). The net returns profile is characterized by a broad flat zone of losses – between the two strike prices. The maximum profit from the straddle: Unlimited.

60. Options on Futures Long Strangle

61. Options on Futures Strangles Short Strangle: A short strangle is formed by selling an equal number of calls and puts with different strike prices but with the same expiration date. This strategy will be profitable if underlying asset prices remain fairly stable. If futures prices move substantially in either direction, the trader incurs loses If prices fall – the put option will be exercised by the holder If prices rise – the call option will be exercised by the holder The maximum profit from short strangle: Limited to the premiums received from selling the call and put options, that is (C f + P f ) The maximum loss from short strangle: Unlimited. To the extent that the loss from the exercised option exceeds the total premium received, there will be a net loss.

62. FP T < SP P < SP C SP P < FP T < SP C SP P < SP C < FP T TraderActivityProfit/LossActivityProfit/LossActivityProfit/Loss Short Call (SP C ) Holder does not exercise Holder Exercises Short Put (SP P ) Holder Exercises Holder does not exercise Net Returns Options on Futures Short Strangle Consider a out-of-the-money strangle: established by selling a call with higher strike price (SP C ) a put with lower strike price (SP P ). SP C > SP P

63. FP T < SP P < SP C SP P < FP T < SP C SP P < SP C < FP T TraderActivityProfit/LossActivityProfit/LossActivityProfit/Loss Short Call (SP C ) Holder does not exercise CfCf CfCf Holder Exercises C f − (FP T − SP C ) Short Put (SP P ) Holder Exercises P f − (SP P − FP T ) Holder does not exercise PfPf PfPf Net Returns (C f +P f ) − (SP P − FP T ) C f +P f (C f +P f ) − (FP T −SP C ) Options on Futures Short Strangle Short strangles are more popular of the two strategies. These are employed to take advantage of the declining time value of options in markets where asset prices are expected to remain constant

64. Options on Futures Short Strangle

65. Options on Futures Hedging with Options on Futures Hedgers using futures basically attempt to lock in a specific price. In contrast, hedgers using options seek to set a specific floor or ceiling price. Hedging with futures allows hedgers to lock in a specific price but restricts them to benefit from favorable price movements. hedging with options allows hedgers to lock in a floor or ceiling price at the expense of option premiums. A futures hedger generally assumes a futures position opposite that of his cash position, hoping to offset any cash market loss with a profit on futures position. An option hedger, however, can establish a floor price (with a long put position), or a ceiling price (with a long call position), and still retain the possibility of profiting from favorable price movement.

66. Options on Futures: Short Hedge Hedging with Options on Futures Assume that on 24 April 2010, a US soybean farmer plants soybean in her farmland with an expectation of harvesting 50,000 bushels of soybean in October 2010. The cash price for soybeans in the local spot market is $10.00 per bushel (60 pounds) during plantation. The farmer is worried that cash prices for soybeans will decrease during the fall months, and she may not be able to recover her production costs. In order to minimize her price risk, the farmer considers the potentials of hedging with futures and options. The two simple ways of hedging are: 1. Sell November 2010 Soybean futures contract, and 2. Purchase put option on November 2010 Soybean futures contract.

67. Options on Futures Hedging with Options on Futures On 24 April 2010, the November 2010 Soybean futures price is $10.40 per bushel, resulting in a basis – $0.40 per bushel. Assume that cash, futures, and options prices are highly correlated with each other. Also assume that the basis remains constant from April through September. Consider two cash price scenarios at the time of harvest: cash price for soybeans declines to $9.00 per bushel, and cash price for soybeans increases to $11.00 per bushel. Since the basis is assumed to remain constant, the futures prices for these scenarios will be $9.40 and $11.40 per bushel, respectively.

68. Hedging with Futures: Short Hedge Soybeans: Planted in April and Harvested in September DateCash (soybeans)Futures (soybeans) 24 April 2010US$ 10.00 per bushel (Basis is − 0.40) Price Decline 30 Sep 2010Sell 50,000 bushels @ US$ 9.00 per bushel (Basis is − 0.40)Gain/Loss = Effective price Price Increase 30 Sep 2010Sell 50,000 bushels @ US$ 11.00 per bushel (Basis is − 0.40)Gain/Loss = Effective price

69. Hedging with Futures: Short Hedge

70. Hedging with Options on Futures: Short Hedge Soybeans: Planted in April and Harvested in September DateCash (soybeans)Options (soybeans) 24 April 2010US$ 10.00 per bushel (Basis is − 0.40) Price Decline 30 Sep 2010Sell 50,000 bushels @ US$ 9.00 per bushel (Basis is − 0.40)Gain/Loss = Effective price Price Increase 30 Sep 2010Sell 50,000 bushels @ US$ 11.00 per bushel (Basis is − 0.40)Gain/Loss = Effective price

71. Hedging with Options: Short Hedge

72. Options on Futures: Long Hedge Hedging with Options on Futures Assume that on 24 April 2010, a US soybean oil producer estimates that she will need 50,000 bushels of soybean in October 2010 for full capacity utilization of her processing plant. The cash price for soybeans in the local spot market is $10.00 per bushel (60 pounds) in April. The soybean crusher is worried that cash prices for soybeans may increase during the fall months. In order to minimize her price risk, the soybean crusher considers the potentials of hedging with futures and options. The two simple ways of hedging are: 1. Buy November 2010 Soybean futures contract, and 2. Buy a call option on November 2010 Soybean futures contract.

73. Options on Futures: Long Hedge Hedging with Options on Futures On 24 April 2010, the November 2010 Soybean futures price is $10.40 per bushel, resulting in a basis – $0.40 per bushel. Assume that cash, futures, and options prices are highly correlated with each other. Also assume that the basis remains constant from April through September. Consider two cash price scenarios at the time of harvest: cash price for soybeans declines to $9.00 per bushel, and cash price for soybeans increases to $11.00 per bushel. Since the basis is assumed to remain constant, the futures prices for these scenarios will be $9.40 and $11.40 per bushel, respectively.

74. Hedging with Futures: Long Hedge Soybeans: Planted in April and Harvested in September DateCash (soybeans)Futures (soybeans) 24 April 2010US$ 10.00 per bushel (Basis is − 0.40) Price Decline 30 Sep 2010Buy 50,000 bushels @ US$ 9.00 per bushel (Basis is − 0.40)Gain/Loss = Effective cost Price Increase 30 Sep 2010Buy 50,000 bushels @ US$ 11.00 per bushel (Basis is − 0.40)Gain/Loss = Effective cost

75. Hedging with Futures: Long Hedge

76. Hedging with Options on Futures: Long Hedge Soybeans: Planted in April and Harvested in September DateCash (soybeans)Options (soybeans) 24 April 2010US$ 10.00 per bushel (Basis is − 0.44) Price Decline 30 Sep 2010Buy 50,000 bushels @ US$ 9.00 per bushel (Basis is − 0.44)Gain/Loss = Effective cost Price Increase 30 Sep 2010Buy 50,000 bushels @ US$ 11.00 per bushel (Basis is − 0.44)Gain/Loss = Effective cost

77. Hedging with Options: Long Hedge