Chapter 2- an introduction of forward and option.ppt

Chapter 2An Introduction to Forwards and Options

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IntroductionBasic derivatives contractsForward contractsCall optionsPut OptionsTypes of positionsLong positionShort positionGraphical representationPayoff diagramsProfit diagrams

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Forward ContractsDefinition: a binding agreement (obligation) to buy/sell an underlying asset in the future, at a price set todayFutures contracts are the same as forwards in principle except for some institutional and pricing differences.A forward contract specifiesThe features and quantity of the asset to be deliveredThe delivery logistics, such as time, date, and placeThe price the buyer will pay at the time of delivery

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TerminologiesExpiration date ?Underlying asset ?Spot price ?Future price ?

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Reading Price QuotesSettlement priceDaily changeOpen interestLifetime lowLifetime highThe open priceExpiration month

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The Payoff on a Forward ContractPayoff for a contract is its value at expirationPayoff forLong forward = Spot price at expiration Forward price Short forward = Forward price Spot price at expiration Example 2.1: S&R (special and rich) index:Today: Spot price = $1,000, 6-month forward price = $1,020In six months at contract expiration: Spot price = $1,050Long position payoff = $1,050 $1,020 = $30 Short position payoff = $1,020 $1,050 = ($30)

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Payoff Diagram for ForwardsLong and short forward positions on the S&R 500 index

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Forward Versus Outright PurchaseIf we invest $1000 in zero- coupon bonds that will pay $1020 after 6-months( Treasury Bill) along with the forward contract. In this case this position will initially costs $1000 (for the bond) at time 0 => The initial outlay is the same as buying the physical S&R index.The position of the portfolio ( zero-coupon bond + forward contract) = the position of buying the physical S&R index.

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Forward Versus Outright PurchaseForward + bond = Spot price at expiration $1,020 + $1,020 = Spot price at expirationForward payoffBond payoff

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Additional ConsiderationsType of settlementCash settlement: less costly and more practicalPhysical delivery: often avoided due to significant costs Credit risk of the counter partyMajor issue for over-the-counter contractsCredit check, collateral, bank letter of credit Less severe for exchange-traded contractsExchange guarantees transactions, requires collateral

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Call OptionsA non-binding agreement (right but not an obligation) to buy an asset in the future, at a price set todayPreserves the upside potential, while at the same time eliminating the unpleasant downside (for the buyer)The seller of a call option is obligated to deliver if askedTodayExpiration dateorat buyers choosing

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ExamplesExample 2.3: S&R index Today: call buyer acquires the right to pay $1,020 in six months for the index, but is not obligated to do soIn 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 = $0Example 2.4: S&R index Today: call seller is obligated to sell the index for $1,020 in six months, if asked to do soIn 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 = $0Why would anyone agree to be on the seller side?

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Definition and TerminologyA 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 exerciseExercise: the act of paying/receiving the strike price to buy/sell the assetExpiration: the date by which the option must be exercised or become worthlessExercise style: specifies when the option can be exercisedEuropean-style: can be exercised only at expiration dateAmerican-style: can be exercised at any time before expirationBermudan-style: Can be exercised during specified periods

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Payoff/Profit of a Purchased CallPayoff = Max [0, spot price at expiration strike price]Profit = Payoff future value of option premiumExamples 2.5 & 2.6:S&R Index 6-month Call OptionStrike price = $1,000, Premium = $93.81, 6-month risk-free rate = 2%If index value in six months = $1100Payoff = max [0, $1,100 $1,000] = $100Profit = $100 ($93.81 x 1.02) = $4.32If index value in six months = $900Payoff = max [0, $900 $1,000] = $0Profit = $0 ($93.81 x 1.02) = $95.68

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Diagrams for Purchased CallPayoff at expirationProfit at expiration

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Payoff/Profit of a Written CallPayoff = max [0, spot price at expiration strike price]Profit = Payoff + future value of option premiumExample 2.7S&R Index 6-month Call OptionStrike price = $1,000, Premium = $93.81, 6-month risk-free rate = 2%If index value in six months = $1100Payoff = max [0, $1,100 $1,000] = $100Profit = $100 + ($93.81 x 1.02) = $4.32If index value in six months = $900Payoff = max [0, $900 $1,000] = $0Profit = $0 + ($93.81 x 1.02) = $95.68

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Put OptionsA put option gives the owner the right but not the obligation to sell the underlying asset at a predetermined price during a predetermined time period The seller of a put option is obligated to buy if askedPayoff/profit of a purchased (i.e., long) putPayoff = max [0, strike price spot price at expiration]Profit = Payoff future value of option premiumPayoff/profit of a written (i.e., short) putPayoff = max [0, strike price spot price at expiration]Profit = Payoff + future value of option premium

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Put Option ExamplesExamples 2.9 & 2.10S&R Index 6-month Put OptionStrike price = $1,000, Premium = $74.20, 6-month risk-free rate = 2%If index value in six months = $1100Payoff = max [0, $1,000 $1,100] = $0Profit = $0 ($74.20 x 1.02) = $75.68If index value in six months = $900Payoff = max [0, $1,000 $900] = $100Profit = $100 ($74.20 x 1.02) = $24.32

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Profit for a Long Put PositionProfit tableProfit diagram

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A Few Items to NoteA 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 immediatelyAt-the-money option: zero payoff if exercised immediatelyOut-of-the money option: negative payoff if exercised immediately

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Options are InsuranceSuppose that you own a house that costs $200,000 to build.You buy a $15,000 insurance policy to compensate you for damage to the house.Like most insurance policies, this insurance policy has a deductible of $25,000, meaning that there is an amount of damage for which you are obligated to pay before the insurance company pays anything.If the house suffers $4,000 damage from a storm, you pay for all repairs yourself. If the house suffer $45,000 in damage from a storm, you pay $25,000 and the insurance company pay the remaining $20,000.How much will insurance company make payoff if the house is destroyed by the storm ?How much will insurance company make payoff if the house suffers a damage of $50,000.

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Options are InsuranceThe insurance in this example is equivalent to a put option at a strike price of $175,000 and a premium of $15,000.

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Options are InsuranceHomeowners insurance is a put option

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Options are InsurancePut option is an insurance on long position.Call option is an insurance on short position.Example: The current price of a S&R index is $1,000 and that you plan to the index in the future to cover the short-sell position => If you buy a call option with a strike price of $1,000, this give you the right to buy S&R for a maximum cost of $1,000 / share. By buying a call, we have bought insurance against an increase in the price.

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Brief Summary

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Three basic long positions

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Three basic short position

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Option and Forward Positions: A Summary

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.2-*

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.2-*

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.2-*

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.2-*

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.2-*

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.2-*

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.2-*

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.2-*

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.2-*

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.2-*

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