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Option Markets

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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”

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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.

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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)

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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)

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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?

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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.

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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?

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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.

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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.

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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

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

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

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Profit Diagrams Own an asset and want to sell it in future.

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Future PriceToday’s price

Future profit relative to profityou would get if you sold the asset now.

Example: Wheat farmer international trader who needs to sell Yen

45o

Profit Diagrams Need to buy an asset in future.

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Future PriceToday’s price

Future gain/lossrelative to gain/loss if you bought the asset now.

45o

Example: Airliners need to buy jet fuel.

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Option Profit Diagrams Long Call: Max(S-X,0) – premium

Short Call: -Max(S-X,0) + premium

X450

S

X450

Assume:

Option is exercised at the maturity date.

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Option Profit Diagrams Long Put: Max(X-S,0) – premium

Short Put: -Max(X-S,0) + premium

X450

S

X450

Hedged Position Own an asset and want to sell it in future.

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Future Price

Long Put Position

Hedged positionCost of “i

nsurance

”.

Gold=green+red

Hedged Position Need to buy an asset in future.

Future Price

Cost of “insurance”.

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Speculative Position:Covered Call Profit diagrams:

5

100S S S

90 90 1000

P P P

Short Call Long Stock

10 10 10

5 5

90 100

151515

Both Together

Profit for Covered Call

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

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Speculative Position: StraddleLong Call and Long Put at Same Strike Price

Profit

Future Stock Price

Bet that volatility will be highin future.

Hedging and Speculation:Collar

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Investor owns stock

Investor buys protectionAgainst losses – long put

Investor raises money to buy put by shorting acall – betting price ofstock won’t go aboveX2.

X1 X2

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Factors that Affect Option Prices (Premiums)

Maturity to Time

Price AssetUnderlying of Volatility

Price Strike

Price AssetUnderlying

Premiums Call Put

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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