# 1 FINA0301 Derivatives Faculty of Business and Economics University of Hong Kong Dr. Huiyan Qiu Chapter 2 An Introduction to Forwards and Options.

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1 FINA0301 Derivatives Faculty of Business and Economics University of Hong Kong Dr. Huiyan Qiu Chapter 2 An Introduction to Forwards and Options

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

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

4 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.

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

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

7 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 S T ) at expiration For forward contract, payoff = profit

8 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

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

10 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?

11 Forward payoffBond 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.

12 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

13 TodayExpiration date or at buyer’s choosing 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

14 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

15 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.

16 Reading Price Quotes S&P500 Index options Strike price Expiration month Option type “c” for call “p” for put

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

18 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

19 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

20 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

21 Diagrams for Purchased Call Payoff at expirationProfit at expiration

22 Payoff/Profit of a Written Call 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

23 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.

24 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

25 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

26 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.

27 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.

28 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

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

30 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.)

31 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.)

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

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

34 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

35 End of the Notes!

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