Option Markets

1. Option Markets

2. Options • Options are contracts. • There are two sides to the contract • Long Side (option holder): • Pays a premium upfront • Gets to “call the shots” in the future • Short Side (option writer): • Receives a premium upfront • Must agree to go along with the decision of the “long side”

3. Payoffs vs. Profit • Options are contracts with two transactions • Transaction 1: the premium is exchanged • Transaction 2: payoff at maturity • Profit: Sum of both transactions.

4. Call Options • The option to buy an asset at a pre-specified price called the “strike” • Notation: • T = the time at which the option matures • ST = the price of the asset at time T • X = the strike price • Long position • Pays a premium upfront • Can buy the asset in the future at the strike price • Payoff: Max(ST -X,0) • Short position: sell the option • Receives a premium upfront • Must sell the asset for X • Payoff: -Max(ST -X,0)

5. Put Options • The option to sell an asset at a pre-specified price called the “strike” • Notation: • T = the time at which the option matures • ST = the price of the asset in the future • X = the strike price • Long position • Pays a premium upfront • Can sell the asset in the future at the strike price • Payoff: Max(X-ST ,0) • Short position: sell the option • Receives a premium upfront • Must buy the asset for X • Payoff: -Max(X-ST ,0)

6. Example • Call option on Apache stock with strike=100. • “Premium” or “option price” = $8 • At maturity what is total profit to the long side if • S=110? • S=95? • S=115? • What is the total profit to the short side?

7. Example: If S=110 • In this case, it makes sense to exercise the option. The long side can buy Apache for 100 (strike) and sell it for 110 (market value) on the maturity date. The option payoff is therefore 10. The profit to the long side is 10-8=2, since the long side paid 8 to buy the option. • The short side suffers a negative payoff. She must buy Apache for 110 (market value) and sell it for 100 (strike). The option payoff is therefore -10. Total profit is -2, since the short side received 8 upfront to take the short side.

8. Example • Put option on Apache stock with strike=100. • Price = $8 • At maturity what is total profit to the long side get if • S=110? • S=95? • S=115? • What is the total profit to the short side?

9. Example: If S=95 • In this case, it makes sense to exercise the option. The long side can buy Apache for 95 (market value) sell it for 100 (strike) on the maturity date. The option payoff is therefore 5. The profit to the long side is 5-8=-3, since the long side paid 8 to buy the option. • The short side suffers a negative payoff. She must buy Apache for 100 (strike) when it is only worth 95 (market value). The option payoff is therefore -5. Total profit is 3, since the short side received 8 upfront to take the short side.

10. Relation Between S and X • For calls: • S = X: Option is at-the-money. • S > X: Option is in-the-money. • S < X: Option is out-of-the-money. • For puts: • S = X: Option is at-the-money. • S > X: Option is out-of-the-money. • S < X: Option is in-the-money.

11. Option Contracts • European option: can only be exercised on the expiration date. • American option: can be exercised on any day prior to and including the expiration date. • Options Clearing Corporation: • Guarantees contract performance • Members (brokers) post margins with the OCC • Brokers require investor clients to post margins • OCC is “middle man” for exercising options

12. Underlying Assets • Stocks • Indices • Futures Contracts • Foreign Currencies • Swaps (Swaptions) • Beef • Lumber

13. Why do options markets exist? • To allow market participants hedge risks. • In order for some market participants to hedge, we need speculators. • Hence a secondary use of options: • To allow speculators the ability to speculate

14. Profit Diagrams • Own an asset and want to sell it in future. Example: Wheat farmer international trader who needs to sell Yen Future profit relative to profit you would get if you sold the asset now. 45o Future Price Today’s price

15. Profit Diagrams • Need to buy an asset in future. Future gain/loss relative to gain/loss if you bought the asset now. 45o Future Price Today’s price Example: Airliners need to buy jet fuel.

16. Option Profit Diagrams • Long Call: Max(S-X,0) – premium • Short Call: -Max(S-X,0) + premium • Assume: • Option is exercised at the maturity date. X 450 S 450 X

17. Option Profit Diagrams • Long Put: Max(X-S,0) – premium • Short Put: -Max(X-S,0) + premium X 450 S 450 X

18. Hedged Position • Own an asset and want to sell it in future. Long Put Position Cost of “insurance”. Hedged position Future Price Gold=green+red

19. Hedged Position • Need to buy an asset in future. Cost of “insurance”. Future Price

20. Speculative Position:Covered Call • Profit diagrams: Short Call Long Stock Both Together P P P Profit for Covered Call 15 15 15 10 10 10 5 5 5 0 S S S 100 90 90 90 100 100

21. Why Covered Calls? • Used by institutional investors who invest heavily in stocks. • Write (short) out of the money calls. • Collect premiums. • Potential loss on upside

22. Speculative Position: Straddle Long Call and Long Put at Same Strike Price Profit Bet that volatility will be high in future. Future Stock Price

23. Hedging and Speculation:Collar Investor buys protection Against losses – long put X1 X2 Investor raises money to buy put by shorting a call – betting price of stock won’t go above X2. Investor owns stock

24. Factors that Affect Option Prices (Premiums) Premiums CallPut

25. Example • Which option has the higher strike price or impossible to determine? • Call #1 • Vol = 0.19 • S0= 110 • Time to maturity = 1 month • price = $5 • Call #2 • Vol=0.18 • S0= 110 • Time to maturity = 1 month • price = $7