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FINA0301 DerivativesFaculty of Business and Economics

University of Hong Kong

Dr. Huiyan Qiu

Chapter 2 An Introduction to Forwards and Options

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Chapter OutlineBasic derivatives contracts• Forward contracts• Call options• Put options

Types of positions• Long / Short position

Graphical representation• Payoff / Profit diagrams

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TodayExpirationdate

Forward ContractsForward contract: a binding agreement (obligation) to buy/sell an underlying asset in the future, at a price set today

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Forward ContractsA 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

Futures contracts are the same as forwards in principle except for some institutional and pricing differences.

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Reading Price QuotesIndex futures

Expiration month

The open price

High of the day

Low of the daySettlement price

Daily changeOpen interest

Hang Seng Index Futures

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Hang Seng Index Futures Daily market report on January 27, 2012. Source: www.hkex.com.hkHSI - HANG SENG INDEX FUTURES HK$50 PER INDEX POINT Contract Open Daily Daily Settle- Chg in Contract Contract Volume Open Change Month Price High Low ment Setl High Low Interest in OI Price Price JAN-12 20,340 20,606 20,340 20,594 +180 20,606 17,780 74,019 33,520 -22,356 FEB-12 20,388 20,620 20,381 20,614 +179 20,620 18,276 49,911 76,335 +25,553 MAR-12 20,337 20,560 20,337 20,558 +172 22,590 16,050 1,021 5,884 +2 JUN-12 19,950 20,200 19,950 20,196 +177 20,200 17,220 179 2,458 +18 All Contracts Total 125,130 118,197 +3,217

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Payoff and ProfitPayoff for a contract is its value at expiration. Payoff diagrams show the gross value of a position at expiration.Profit for a position in a contract is net value at expiration of all relevant cash flows. Forward: (1) zero cash flow at initiation, (2) pay forward price at expiration, (3) get asset (value ST) at expiration For forward contract, payoff = profit

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Payoff on a Forward ContractExample: S&R (special and rich) indexToday: Spot price = $1,000 6-month forward price = $1,020In six months at contract expiration: Case 1: Spot price = $1,050• Long position payoff = $1,050 – $1,020 = $30 • Short position payoff = $1,020 – $1,050 = – $30Case 2: Spot price = $1,000• Long position payoff = $1,000 – $1,020 = – $20 • Short position payoff = $1,020 – $1,000 = $20

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Payoff Diagram for Forwards

S&R (special and rich) indexToday: Spot price = $1,000

6-month forward price = $1,020

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Forward vs. Outright Purchase

Outright purchase: • Invest $1,000 in index and own the index. Forward: • Invest zero, sign the contract• Invest $1,020 at expiration and own the

index. Same outcome: own the index at expiration.Why investing $1,000 now results in the same outcome as investing $1,020 later? Price indication?

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Forward payoff Bond payoff

Forward vs. Outright Purchase

Forward + bond = Spot price at expiration – $1,020 + $1,020 = Spot price at expiration

Figure Comparison of payoff after 6 months of a long position in the S&R index versus a forward contract in the S&R index.

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Additional ConsiderationsType 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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Today Expiration date

or

at buyer’s choosing

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 asked

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Definition and TerminologyDefinition: 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 Terminology: • 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

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Exercise StyleExercise 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 periodsFocus: European-style options.

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Reading Price QuotesS&P500 Index options

Strike priceExpiration month

Option type“c” for call “p” for put

Hang Seng Index Options

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Hang Seng Index Options Daily market report on top-10 traded options on January 27, 2012. Source: www.hkex.com.hk

HANG SENG INDEX OPTION HK$ 50 PER INDEX POINT TOP 10 TRADED (BY VOL) VOLUME O.Q.P. IV% DAILY DAILY OPEN O.Q.P. CLOSE HIGH LOW INTEREST CHANGE P JAN-12 20200 3301 17 17 46 11 2069 -42 C JAN-12 20600 3145 98 13 119 37 2438 +36 C JAN-12 21000 3142 14 16 15 3 2922 +7 P JAN-12 20400 2820 43 15 123 22 1322 -78 P FEB-12 19600 2570 185 23 227 180 2974 -45 C JAN-12 20800 2386 38 14 45 10 2467 +16 C JAN-12 20400 2076 231 14 237 99 2022 +91 C FEB-12 21400 1893 196 19 199 152 2517 +25 P JAN-12 20000 1816 7 19 44 6 2043 -21 C FEB-12 21200 1325 256 20 261 202 1550 +37

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Example: S&R IndexToday: • call buyer acquires the right to pay $1,000 in six

months for the index, but is not obligated to do so• call seller is obligated to sell the index for $1,000

in six months, if asked to do soIn six months at contract expiration:

Spot price $1,100 $900

Buyer’s payoff $1,100 – $1,000 = $100 $0

Seller’s payoff $1,000 – $1,100 = ($100) $0

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Example: S&R Index (cont’d)In six months at contract expiration,• If the spot price is higher than $1,000, the option will

be exercised.• If the spot price is lower than $1,000, the option

buyer will walk away and do nothing.• Payoff for buyer = Max [0, spot price – strike price]

Why would anyone agree to be on the seller side? • The option buyer must pay the seller an initial

premium of $93.81 (option pricing)• For a forward contract, the initial premium is zero

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Payoff and Profit for the Buyer

Payoff = Max [0, spot price at expiration – strike price]Profit = Payoff – future value of option premiumSuppose 6-month risk-free rate is 2% • If index value in six months = $1,100

• 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 CallPayoff at expiration Profit at expiration

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Payoff/Profit of a Written CallCall writer: the option seller• To receive the premium for option sold• To have the obligation to sell if requested

Seller’s payoff and profit is opposite to the buyer• Payoff = - max [0, spot price at expiration – strike

price]• Profit = Payoff + future value of option premium

The payoff and profit diagram of a written call is the mirror image of a purchased call, symmetric with regard to the X-axis

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Profit Diagram for a Written Call

Figure:Profit for writer of 6-month S&R call with strike of $1000 versus profit for short S&R forward.

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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) put• Payoff = max [0, strike price – spot price at expiration]• Profit = Payoff – future value of option premium

Payoff/profit of a written (i.e., short) put• Payoff = – max [0, strike price – spot price at

expiration]• Profit = Payoff + future value of option premium

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Put Option ExamplesS&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 = $1,100• Payoff = max [0, $1,000 – $1,100] = $0• Profit = $0 – ($74.20 x 1.02) = – $75.68If 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 Table for Long Put Position

Table: Profit after 6 months from a purchased 1000-strike S&R put option with a future value of premium of $75.68.

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Profit Diagram for a Long Put Position

Figure: Profit on a purchased S&R index put with strike price of $1000 versus a short S&R index forward.

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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 of option:• In-the-money: positive payoff if exercised

immediately• At-the-money: zero payoff if exercised

immediately• Out-of-the money: negative payoff if exercised

immediately

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Summary on Forward & OptionTable: Maximum possible profit and loss at maturity for long and short forwards and purchased and written calls and puts.

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Summary on Forward & Option

Figure: Profit diagrams for the three basic long positions: long forward, purchased call, and written put.(Long w.r.t. the underlying asset.)

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Summary on Forward & Option

Figure: Profit diagrams for the three basic short positions: short forward, written call, and purchased put.(Short w.r.t. the underlying asset.)

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Summary on Forward & OptionTable: Forwards, calls, and puts at a glance: a summary of forward and option positions.

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Options and InsuranceHomeowner’s insurance as a put option

Figure: Profit from insurancepolicy on a $200,000house. $25,000 deductible.

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Example: Equity Linked CDsThe 5.5-year CD promises to repay initial invested amount and 70% of the gain in S&P 500 index• Assume $10,000 invested when S&P 500 =

1300• Final payoff =

• Where = value of the S&P 500 after 5.5 years

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1300,0max7.01000,10$ finalS

finalS

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End of the Notes!