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Copyright 2009 Pearson Prentice Hall. All rights reserved.

Chapter 2

An Introduction

to Forwards

and Options

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Copyright 2009 Pearson Prentice Hall. All rights reserved. 2-2

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



Payoff =max [0, $1,100$1,000] =$100

Profit =$100 + ($93.81 x 1.02) =$4.32


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



Payoff = max [0, $1,000$1,100] = $0

Profit = $0($74.20 x 1.02) =$75.68


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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Copyright 2009 Pearson Prentice Hall. All rights reserved.

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.

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