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Copyright 2009 Pearson Prentice Hall. All rights reserved.
Chapter 2
An Introduction
to Forwards
and Options
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Introduction
Basic derivatives contracts
Forward contracts
Call options
Put Options
Types of positions
Long position
Short position
Graphical representation
Payoff diagrams
Profit diagrams
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Forward Contracts
Definition: a binding agreement (obligation) to buy/sell
an underlying asset in the future, at a price set today
Futures contracts are the same as forwards in principleexcept for some institutional and pricing differences.
A forward contract specifies
The features and quantity of the asset to be delivered The delivery logistics, such as time, date, and place
The price the buyer will pay at the time of delivery
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Reading Price Quotes
Daily change
Open interest
Settlement price
Lowof the day
Highof the day
The openprice
Expiration month
Figure 2.1 Indexfutures price listings.
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Payoff on a Forward Contract
Payoff for a contract is its value at expiration
Payoff for
Long forward = Spot price at expirationForward price
Short forward = Forward priceSpot price at expiration
Example 2.1: S&R (special and rich) index:
Today: Spot price = $1,000, 6-month forward price = $1,020
In six months at contract expiration: Spot price = $1,050 Long position payoff = $1,050$1,020 = $30
Short position payoff = $1,020$1,050 = ($30)
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Payoff Diagram for Forwards
Long and short forward positions on the S&R 500 index
Figure 2.2 Long andshort forward positionson the S&R 500 index.
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Forward payoff Bond payoff
Forward Versus Outright Purchase
Forward + bond = Spot price at expiration$1,020 + $1,020= Spot price at expiration
Figure 2.3
Comparison ofpayoff after 6
months of a longposition in the S&Rindex versus aforward contract inthe S&R index.
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Additional Considerations
Type of settlement
Cash settlement: less costly and more practical
Physical delivery: often avoided due to significant costs
Credit risk of the counter party
Major issue for over-the-counter contracts Credit check, collateral, bank letter of credit
Less severe for exchange-traded contracts Exchange guarantees transactions, requires collateral
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Call Options
A non-binding agreement (right but not anobligation) to buy an asset in the future, at a price settoday
Preserves the upside potential, while at the sametime eliminating the unpleasant downside (for the
buyer)
The seller of a call option is obligated to deliver ifasked
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Examples
Example 2.3: S&R index
Today: call buyer acquires the right to pay $1,020 in six months forthe index, but is not obligated to do so
In six months at contract expiration: if spot price is
$1,100, call buyers payoff = $1,100 $1,020 = $80
$900, call buyer walks away, buyers payoff = $0
Example 2.4: S&R index
Today: call seller is obligated to sell the index for $1,020 in six
months, if asked to do so In six months at contract expiration: if spot price is
$1,100, call sellers payoff = $1,020 $1,100 = ($80)
$900, call buyer walks away, sellers payoff = $0
Why would anyone agree to be on the seller side?
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Definition and Terminology
A call option gives the owner the right but not the obligation to buy the
underlying asset at a predetermined price during a predetermined time period
Strike (or exercise) price: the amount paid by the option buyer for the asset if
he/she decides to exercise
Exercise: the act of paying the strike price to buy the asset
Expiration: the date by which the option must be exercised or become
worthless
Exercise style: specifies when the option can be exercised European-style: can be exercised only at expiration date
American-style: can be exercised at any time before expiration
Bermudan-style: Can be exercised during specified periods
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Strike price
Reading Price Quotes
S&P 500
Index Options
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Payoff/Profit of a Purchased Call
Payoff = Max [0, spot price at expirationstrike price]
Profit = Payofffuture value of option premium
Examples 2.5 & 2.6: S&R Index 6-month Call Option
Strike price = $1,000, Premium = $93.81, 6-month risk-free rate = 2%
If index value in six months = $1100
Payoff = max [0, $1,100$1,000] = $100
Profit = $100($93.81 x 1.02) = $4.32 If index value in six months = $900
Payoff = max [0, $900$1,000] = $0
Profit = $0($93.81 x 1.02) =$95.68
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Diagrams for Purchased Call
Payoff at expiration Profit at expirationFigure 2.5 The payoff at expiration ofa purchased S&R call with a $1000 strikeprice.
Figure 2.6 Profit at expiration for purchase of6-month S&R index call with strike price of$1000 versus profit on long S&R index forwardposition.
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Payoff/Profit of a Written Call
Payoff =max [0, spot price at expirationstrike price]
Profit = Payoff + future value of option premium
Example 2.7 S&R Index 6-month Call Option
Strike price = $1,000, Premium = $93.81, 6-month risk-free rate = 2%
If index value in six months = $1100
Payoff =max [0, $1,100$1,000] =$100
Profit =$100 + ($93.81 x 1.02) =$4.32
If index value in six months = $900
Payoff =max [0, $900$1,000] = $0
Profit = $0 + ($93.81 x 1.02) = $95.68
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Put Options
A put option gives the owner the right but not the obligation tosell the underlying asset at a predetermined price during a
predetermined time period
The seller of a put option is obligated to buy if asked
Payoff/profit of a purchased (i.e., long) put
Payoff = max [0, strike pricespot price at expiration]
Profit = Payofffuture value of option premium
Payoff/profit of a written (i.e., short) put
Payoff =max [0, strike pricespot price at expiration]
Profit = Payoff + future value of option premium
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Put Option Examples
Examples 2.9 & 2.10
S&R Index 6-month Put Option
Strike price = $1,000, Premium = $74.20, 6-month risk-free rate = 2%
If index value in six months = $1100
Payoff = max [0, $1,000$1,100] = $0
Profit = $0($74.20 x 1.02) =$75.68
If index value in six months = $900
Payoff = max [0, $1,000$900] = $100
Profit = $100($74.20 x 1.02) = $24.32
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Profit for a Long Put Position
Profit table
Table 2.4 Profit after 6
months from a purchased1000-strike S&R putoption with a future valueof premium of $75.68.
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A Few Items to Note
A call option becomes more profitable when the underlying asset
appreciates in value
A put option becomes more profitable when the underlying asset
depreciates in value
Moneyness
In-the-money option: positive payoff if exercised immediately
At-the-money option: zero payoff if exercised immediately Out-of-the money option: negative payoff if exercised immediately
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Options and Insurance
Homeowners insurance as a put option
Figure 2.12Profit frominsurancepolicy on a$200,000
house.
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Option and Forward Positions: ASummary
Figure 2.13 Thebasic profit diagrams:long and shortforward, long andshort call, and longand short put.
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Chapter 2
Additional Art
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Equation 2.1
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Equation 2.2
T bl 2 1 P ff ft 6 th f l S&R f d t t d h t
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Table 2.1 Payoff after 6 months from a long S&R forward contract and a shortS&R forward contract at a forward price of $1020. If the index price in 6 months is$1020, both the long and short have a 0 payoff. If the index price is greater than$1020, the long makes money and the short loses money. If the index price is lessthan $1020, the long loses money and the short makes money.
Fi 2 4 P ff di f l S&R f d t t
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Figure 2.4 Payoff diagram for a long S&R forward contract,together with a zero-coupon bond that pays $1020 at maturity.Summing the value of the long forward plus the bond at eachS&R index price gives the line labeled Forward + bond.
Table 2 2 Closing prices daily volume and open interest
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Table 2.2 Closing prices, daily volume, and open interestfor S&P 500 options, listed on the Chicago Board OptionsExchange, on August 14, 2007. The S&P 500 index closedthat day at 1426.54.
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Equation 2.3
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Equation 2.4
Table 2.3 Payoff and profit after 6 months from a purchased 1.000-
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Table 2.3 Payoff and profit after 6 months from a purchased 1.000strike S&R call option with a future value of premium of $95.68. Theoption premium is assumed to be $93.81 and the effective interest rate is2% over 6 months. The payoff is computed using equation (2.3) and theprofit using equation (2.4).
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Equation 2.5
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Equation 2.6
Figure 2 7 Profit for writer of 6 month S&R
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Figure 2.7 Profit for writer of 6-month S&Rcall with strike of $1000 versus profit forshort S&R forward.
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Equation 2.7
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Equation 2.8
Figure 2 8 Profit on a purchased S&R
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Figure 2.8 Profit on a purchased S&Rindex put with strike price of $1000versus a short S&R index forward.
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Equation 2.9
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Equation 2.10
Figure 2 9 Written S&R index put
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Figure 2.9 Written S&R index putoption with strike of $1000 versus a longS&R index forward contract.
Table 2.5 Maximum possible profit and loss at
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p pmaturity for long and short forwards and purchasedand written calls and puts. FV(premium) denotes thefuture value of the option premium.
Figure 2.10 Profit diagrams for the
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Figure 2.10 Profit diagrams for thethree basic long positions: long forward,purchased call, and written put.
Figure 2 11 Profit diagrams for the
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Figure 2.11 Profit diagrams for thethree basic short positions: short forward,written call, and purchased put.
Table 2.6 Forwards calls and puts at a
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Table 2.6 Forwards, calls, and puts at aglance: a summary of forward and optionpositions.