Chapter 15
Other Derivative Assets
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© 2004 South-Western Publishing

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Futures Options
 Characteristics
 Speculators and Hedging
 Early exercise of futures options
 Pricing Futures Options
 Deltas and Implied volatility

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Characteristics

Are futures options “uniquely worthless”?
 Futures options give users of the futures market an enhanced ability to tailor their risk/return exposure to individual needs
 Futures options provide an opportunity for the speculator to avoid the potentially unlimited losses associated with futures contracts

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Characteristics (cont’d)
 Futures options are relatively new
– Non-agricultural futures since 1982
– Agricultural futures since 1984
 Commodity Futures Trading Commission
Act of 1974
–
Futures options must not be “contrary to the public interest”
– Futures options must serve legitimate hedging purposes

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Characteristics (cont’d)
 Futures options are no different from listed options
– Futures calls give the right to go long
– Call writer has the obligation to go short if the call holder exercises
– Futures puts give the right to go short
– Put writer has the obligation to go long if the put holder exercises

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Characteristics (cont’d)
 The underlying security is the futures contract, not the physical commodity represented by the futures contract
 The option holder decides if and when to exercise
 Exercise of a futures call does not result in delivery of the underlying commodity

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Characteristics (cont’d)
Futures Prices
S&P 500
Index
MAR
JUN
SEP
DEC
Open
1138.30
1137.00
….
1139.00
Futures Options Prices
S&P 500
Index
Strike
Price
1140
1150
1160
1170
1180
FEB
Calls
MAR APR
11.60
22.50
30.20
6.60
17.00
24.80
3.30
12.60
20.00
1.45
9.00
15.80
0.65
6.20
12.40

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Characteristics (cont’d)
Futures Prices
S&P 500
Index
MAR
JUN
SEP
DEC
Open
1138.30
1137.00
….
1139.00
Futures Options Prices
Puts
FEB
8.40
13.40
20.10
28.20
37.40
MAR
19.30
23.80
29.40
35.80
….
APR
27.90
32.50
37.60
….
….

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Characteristics (cont’d)
 Like other puts and calls, futures options have both intrinsic value and time value
 Expiration
– The option month refers to the futures contract delivery month
–
–
–
Depending on the commodity, the option may expire on a specific date in the preceding month
The actual expiration date varies by commodity
Some futures options have a serial expiration feature

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Speculating With Futures
Options
 Speculation principles for futures options are the same as for equity options
 Buying futures options involves a predetermined, known, and limited maximum loss, just as with options on other assets
– The option premium is the most the option buyer can lose

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Speculating With Futures
Options (cont’d)
Money At Risk Example
In early September, a speculator anticipates lower demand for soybeans and anticipates a drop in the price of soybeans. She decides to buy a put option on soybean futures. Specifically, she purchases 3
APR 8300 puts at a listed price of 25.25 cents. The money at risk is
3 contracts x 5,000bu/contract x $0.2525/bu = $3,787.50

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Hedging With Futures Options
 There are as many ways to hedge with futures options as there are with equity or index options
– Any hedge serves to limit risk with some tradeoff in potential return
– In the commodities market, there can be several levels of hedging

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Hedging With Futures Options
(cont’d)
Hedging Example
William Bob operates a 1,500-acre farm in the midwest and plans on harvesting 50,000 bushels of soybeans. To hedge price risk, Bob could go short 10 soybean contracts, covering
50,000 bushels. However, to protect himself against unexpected problems with the crop (such as tornadoes), Bob could hedge by only going short 9 soybean contracts. This reduces the inconvenience and cost of having to either close out some contracts at a financial loss or acquire soybeans in the cash market to deliver against the short contracts.

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Speculators and Hedging
 Futures options are particularly useful to speculators of interest rate of stock index futures
– If a speculator buys an S&P 500 index futures contract, a market decline results in a reduced account balance as the contract is marked to market each day
– Puts on the S&P futures would provide some protection against the potentially large losses

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Early Exercise of Futures
Options
 Listed call options on equity securities or indexes will not normally be exercised early
– This would result in an abandonment of the remaining time value of the option

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Early Exercise of Futures
Options (cont’d)
 With futures options, there are circumstances in which it is optimal to exercise a call early
– E.g., exercising a call allows the speculator to go long in futures and to earn interest with the futures contract

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Pricing Futures Options
 Futures option pricing model
 Disposing of valuable options
 Futures option deltas
 Implied volatility

Futures Option Pricing Model
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
Black’s futures option pricing model for
European call options:
C
 e

RT

FN ( a )

KN ( b )
 where a
 and b

F ln
K
 a
 
T


2
2
T
T

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Futures Option Pricing Model
(cont’d)

Black’s futures option pricing model for
European put options:
P
 e

RT

KN (
 b )

FN (
 a )

 Alternatively, value the put option using put/call parity:
P

C
 e

RT
( F

K )

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Disposing of Valuable Options
 The holder of a futures option has three alternatives:
– Keep the option
– Exercise the option
– Sell the option
 The risk of holding onto the option is that prices may move adversely

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Disposing of Valuable Options
(cont’d)
 The early exercise of option is normally suboptimal
– Deep-in-the-money options have little time value and it is often advantageous to exercise them early
 Selling the option has the merit of capturing the remaining time value and converts the intrinsic value to cash

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Futures Option Deltas
 Slightly different from delta for equity or index options
– Call delta: e

RT
N ( a )
– Put delta: e

RT
N (
 b )

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Implied Volatility
 Implied volatility is the standard deviation of returns that will cause the pricing model to predict the actual option premium
 Calculating implied volatility must be done via trial and error

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Summary
 New Derivatives combining options and futures
 Pricing includes the extra time gained
 Deltas (C&P) are different from that of an option (do not add up to one!)
 Research on Implied volatility in Financial
Modeling!