© 2004 South-Western Publishing 1

Chapter 15

Other Derivative Assets

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Outline

Futures options Pricing futures options Warrants Other derivative assets

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Futures Options

Characteristics Speculating with futures options Spreading with futures options Basis risk with spreads Hedging with futures options Speculators and hedging Early exercise of futures options

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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

February 10, 2004

S&P 500 Index

Open High Low Settle Change

MAR 1138.30 1146.50 1137.60 1143.20 +330

JUN 1137.00 1145.00 1137.00 1142.30 +340

SEP …. …. …. 1141.40 +320

DEC 1139.00 1141.20 1139.00 1141.20 +350

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Characteristics (cont’d)

Futures Options Prices

February 10, 2004

S&P 500 Index

Calls Puts

Strike Price

FEB MAR APR FEB MAR APR

1140 11.60 22.50 30.20 8.40 19.30 27.90

1150 6.60 17.00 24.80 13.40 23.80 32.50

1160 3.30 12.60 20.00 20.10 29.40 37.60

1170 1.45 9.00 15.80 28.20 35.80 ….

1180 0.65 6.20 12.40 37.40 …. ….

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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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Spreading With Futures Options

Used by speculators in futures options to reduce their money at risk– E.g., construct a bullspread

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Spreading With Futures Options (cont’d)

Bullspread Example

Consider MAR 8600 and 8700 calls on soybeans with settlement prices of 7 cents and 5 cents per bushel, respectively. The table on the next slide shows the profit and loss summary for a soybean bullspread.

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Spreading With Futures Options (cont’d)

Bullspread ExampleFutures Settlement Price (cents per bushel)

858 860 862 864 866

Buy 8600 call @ $.07

-7 -7 -5 -3 -1

Write 8700 call @ $.05

+5 +5 +5 +5 +5

Net -2 -2 0 +2 +4

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Basis Risk With Spreads

If the basis of two futures contracts underlying a long position in futures options and a short position in futures options are different, it is possible that both contracts will move against you

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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

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Futures Option Pricing Model

Black’s futures option pricing model for European call options:

Tab

T

TK

F

a

bKNaFNeC RT

and

2ln

where

)()(2

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Futures Option Pricing Model (cont’d)

Black’s futures option pricing model for European put options:

Alternatively, value the put option using put/call parity:

)()( aFNbKNeP RT

)( KFeCP RT

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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:

– Put delta:

)(aNe RT

)( bNe RT

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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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Warrants

Characteristics Pricing Hedging with stock warrants

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Characteristics

A warrant is a non-dividend-paying security giving its owner the right to buy a certain number of shares at a set price directly from the issuing company

Warrants are relatively rare– Traded on the New York Stock Exchange, the

American Stock Exchange, and Nasdaq

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Characteristics (cont’d)

Warrants are really long-term call options Warrants give the owners the right to

purchase a set number of shares of stock directly from the issuing company

There is a predetermined exercise price and expiration date

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Characteristics (cont’d)

Warrants pay no dividends and their owners have no voting rights– Investors like them because they provide

leverage and let them assume a bullish position with a low investment

Warrants can have very unusual exercise terms and conditions

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Characteristics (cont’d)

The vast majority of warrants are from small, relatively risky firms, often issued in conjunction with an IPO

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Pricing

Primary factor is the relationship between the price of the underlying common stock and the exercise price– When the stock price rises above the exercise

price, the warrant is in-the-money

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Pricing (cont’d)

Actual

Maximum warrant

Warrant value price Minimum

Price value

Exercise

price

Stock price

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Pricing (cont’d)

The theoretical maximum price of a warrant is equal to the stock price

The theoretical minimum value is the warrant’s intrinsic value

The gap between the market price of the warrant and its minimum value is largest when the stock price equals the exercise price

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Pricing (cont’d)

New York Stock Exchange Warrants

February 11, 2004

Issuer Symbol Exercise price

Expiration Warrant price

Stock price

Chiquita Brands

CQB $19.23 3-19-09 $8.00 $23.23

Collegiate Pacific

BOO $5.00 5-26-05 $5.15 $10.05

Image Ware Systems

IW $12.00 4-5-05 $0.05 $4.40

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Hedging With Stock Warrants

A warrant hedge is similar to covered call writing

Warrant hedging involves the warrant lender

An investor buys shares of stock and simultaneously sell short warrants on the same company– To short sell, investor borrows warrants

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Hedging With Stock Warrants (cont’d)

If the stock price is below the exercise price at warrant expiration, the warrants are worthless– Short seller owes lender nothing and keeps

short sale proceeds– Loss in value of the underlying stock is reduced

by warrant proceeds

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Hedging With Stock Warrants (cont’d)

Warrants are exercised if stock price rises– Investor must repay the lender the loan– Investor’s profit is limited to the exercise price

plus the proceeds from the short sale

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Other Derivative Assets

Foreign currency options When-issued stock

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Foreign Currency Options

Foreign currency options began trading in 1982

Commercial banks arrange most currency option trading

Contracts guaranteed by Options Clearing Corporation

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Foreign Currency Options (cont’d)

Different from options on foreign currency futures– Currency call gives you the right to buy the

foreign currency– Currency futures call gives you the right to go

long the futures contract

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Foreign Currency Options (cont’d)

A foreign currency call is equivalent to a dollar put on the currency

The contract size is one-half the size of the futures contract

Unlike futures, options must be paid in full or a significant margin posted

The Black-Scholes model does not work well with foreign currency options

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When-Issued Stock

The NYSE permits investors to trade shares of stock issued in conjunction with a stock split even before new shares are distributed to existing shareholders

Both the new shares and the old shares trade simultaneously

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When-Issued Stock (cont’d)

The old shares will go ex-distribution on the second business day before the date of record– Purchase after this date is a purchase with a due

bill for the additional shares– Holders of the due bill are entitled to the new

shares when they are issued