Chapter 2 An Introduction to Forwards and Options

Chapter 2 An Introduction to Forwards and Options FINA 0301 Derivatives Faculty of Business and Economics University of Hong Kong Dr. Huiyan Qiu 1

Chapter Outline Basic derivatives contracts • Forward contracts • Call options • Put options Types of positions • Long / Short position Graphical representation • Payoff / Profit diagrams 2

Forward Contracts Forward contract: a binding agreement (obligation) to buy/sell an underlying asset in the future, at a price set today Today Expiration date 3

Forward Contracts 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 Futures contracts are the same as forwards in principle except for some institutional and pricing differences. 4

Low of the day High of the day The open price Reading Price Quotes Index futures Settlement price Daily change Open interest Expiration month 5

Hang Seng Index Futures Daily market report on January 27, 2012. Source: www. hkex. com. hk 6

Payoff and Profit Payoff 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 7

Payoff on a Forward Contract Example: S&R (special and rich) index Today: Spot price = $1, 000 6 -month forward price = $1, 020 In 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 = – $30 Case 2: Spot price = $1, 000 • Long position payoff = $1, 000 – $1, 020 = – $20 • Short position payoff = $1, 020 – $1, 000 = $20 8

Payoff Diagram for Forwards S&R (special and rich) index Today: Spot price = $1, 000 6 -month forward price = $1, 020 9

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? 10

Forward vs. Outright Purchase Forward payoff Bond payoff 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. 11

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 12

Call Options A non-binding agreement (right but not an obligation) to buy an asset in the future, at a price set today Preserves 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 Today Expiration date or at buyer’s choosing 13

Definition and Terminology Definition: 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 14

Exercise Style 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 Focus: European-style options. 15

Reading Price Quotes S&P 500 Index options Expiration month Strike price Option type “c” for call “p” for put 16

Hang Seng Index Options Daily market report on top-10 traded options on January 27, 2012. Source: www. hkex. com. hk 17

Example: S&R Index Today: • 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 so In 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 18

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 19

Payoff and Profit for the Buyer Payoff = Max [0, spot price at expiration – strike price] Profit = Payoff – future value of option premium Suppose 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 20

Diagrams for Purchased Call Payoff at expiration Profit at expiration 21

Payoff/Profit of a Written Call 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 22

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. 23

Put Options A 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 asked Payoff/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 24

Put Option Examples 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 = $1, 100 • 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 25

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. 26

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. 27

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 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 28

Summary on Forward & Option Table: Maximum possible profit and loss at maturity for long and short forwards and purchased and written calls and puts. 29

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. ) 30

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. ) 31

Summary on Forward & Option Table: Forwards, calls, and puts at a glance: a summary of forward and option positions. 32

Options and Insurance Homeowner’s insurance as a put option Figure: Profit from insurance policy on a $200, 000 house. $25, 000 deductible. 33

Example: Equity Linked CDs The 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 34

End of the Notes! 35