Option Markets

Options

An Option is a financial instrument which derives its value from the price of other securities. It is a type of derivative.

Also called a contingent claim because the payoff is contingent on the value of other securities.

The underlying securities may be stocks, currencies, commodities, weather etc...

An option can be traded on both an organized exchange like the ASX (exchange-traded) or negotiated privately (over the counter).

Types of options-Call

A Call option gives the holder the right to purchase an asset

At a specified price called the exercise or strike price.

On or before the expiration date.

No obligation to purchase the asset. The holder of the option will usually exercise when the market price of the underlying asset is greater than the strike price.

Types of options-Put

A Put option gives the holder the right to sell an asset

At a specified price called the exercise or strike price.

On or before the expiration date.

No obligation to sell the asset. The holder of the option will usually exercise when the market price of the underlying asset is less than the strike price.

Option Contract

The purchase price of the option is called the premium.

Sellers (writers) of options receive premium income.

Two types of settlement

Physical- If holder exercises the option, the option writer must make (call) or take (put) delivery of the underlying asset.

Cash-If holder exercises the option, the option write must make/receive a cash payment.

Market and Exercise Price Relationship

In the money

Call: Exercise price < Market Price

Put: Exercise price > Market price

Out of the money

Call: Exercise price > Market Price

Put: Exercise price < Market price

At the money

Exercise price=Market Price

American vs. European options

American-The option can be exercised at any time before expiration or maturity.

European-The option can only be exercised on the expiration on maturity date.

In Australia and the US, most single name equity options (options on one stock) are American style.

Option Premium

The option premium(price) consists of two components: C(P)=Intrinsic Value + Time Value Intrinsic value (IV): Measures the exercise value of an option

Call: max (St –X,0)

Put: max (X-St,0)

X is the exercise price, St is the stock price at time t.

Time value: Measures the potential of the option to increase in value.

A function of time to maturity and volatility of underlying stock.

The higher the volatility the higher the time value.

The longer the time to maturity, the greater the time value.

At expiration, time value is zero, is always positive before expiration.

ASX Example (RIO)

St=$66.31, X=$72, Exp=26/04/2013, Today=2/4/2013 C (Bid)=$.05, C (Offer)=$.08

CALL—Out the money

Intrinsic Value: $0

Time Value(Bid):$.05, Time Value(Offer):$.08

St=$66.31, X=$64, Exp=26/04/2012, Today=2/4/2012 C (Bid)=$2.95, C (Offer)=$3.08

CALL—In the money

Intrinsic Value: $2.31

Time Value (Bid):$.64, Time Value (Offer):$.77

The call gives the owner the right to purchase 100 shares in RIO at the strike price.

Long Call

Consider a call with strike price, X=10, and call price, C=2. T is the time when the option expires.

We want to understand the payoff and profit for the holder of the call option when the option expires, at time T.

These are different plausible scenarios for the stock price.

ST =6 ST =8 ST =10 ST =12 ST =15

Payoff 0 0 0 2 5

Profit -2 -2 -2 0 3

Long Call Payoff/Profit Diagram

Payoff and Profit graphs are typically drawn at expiration (T).

Long Call with X=10 C=2

10 ST

Payoff

15

5

10 ST

Profit

15 -2

3

Breakeven price

Payoff: If ST>X then Payoff= ST-X If ST<X then Payoff= 0

Profit: Profit= Payoff-Call price

Why buy a call option?

Allows leveraged exposure to stock price. Downside is limited to option premium. St=$66.31, X=$72, Exp=26/04/2012, Today=2/4/2012

C (Bid)=$.05, C (Offer)=$.08

If price goes to $75 by 26/04/2012. If you had bought 100 shares today, cost is $6,631.

Profit would be $7,500- $6,631=$869. Return is 13.1%

If you had bought one option contract today, cost is $8. Profit would be $300- $8=292. Return is 3650%

If the price instead goes to $60 at 26/04/2012.

If you bought a 100 shares, loss is $631. If you bought one option contract, loss is $8.

What is the downside of buying a call option?

Short Call

Consider a call with strike price, X=10, and call price, C=2. T is the time when the option expires.

We want to understand the payoff and profit for the seller of the call option when the option expires, at time T.

These are different plausible scenarios for the stock price.

ST =6 ST =8 ST =10 ST =12 ST =15

Payoff 0 0 0 -2 -5

Profit 2 2 2 0 -3

Short Call Payoff/Profit

Payoff and profit graphs for writers of a call.

Short Call with X=10 C=2

10 ST

Payoff

15

-5

10 ST

Profit

15

2

-3

Payoff: If ST>X then Payoff= -(ST-X) If ST<X then Payoff= 0

Profit: Profit= Call price-Payoff

Long Put

Consider a put with strike price, X=10, and put price, P=2. T is the time when the option expires.

We want to understand the payoff and profit for the buyer of the put option when the option expires, at time T.

These are different plausible scenarios for the stock price.

ST =6 ST =8 ST =10 ST =12 ST =15

Payoff 4 2 0 0 0

Profit 2 0 -2 -2 -2

Long Put Payoff/Profit

Long Put with X=10 P=2

10 ST

Payoff

15

10

10 ST

Profit

15 -2

8

Payoff: If ST<X then Payoff= X-ST If ST>X then Payoff= 0

Profit: Profit= Payoff-Put price

Short Put

Consider a put with strike price, X=10, and put price, P=2. T is the time when the option expires.

We want to understand the payoff and profit for the seller of the put option when the option expires, at time T.

These are different plausible scenarios for the stock price.

ST =6 ST =8 ST =10 ST =12 ST =15

Payoff -4 -2 0 0 0

Profit -2 0 2 2 2

Short Put Payoff/Profit

Short Put with X=10 P=2

10 ST

Payoff

15

-10

10 ST

Profit

15

2

-8

Payoff: If ST<X then Payoff= -(X-ST ) If ST>X then Payoff= 0

Profit: Profit= Put price-Payoff

Long Stock Payoff/Profit

Payoff and Profit graphs are typically drawn at expiration (T).

Purchase price= SO=10

10 ST

Payoff

10

10 ST

Profit

15

5

Payoff: ST Profit: Payoff-price

Short Stock Payoff/Profit

Shorting a stock involves: Borrowing a stock from broker and selling the stock in the market.

Buying the stock back from the market at a later time (T) and returning the stock.

If stock price has gone down at time (T), the strategy results in a profit.

Short price=10

10 ST

Payoff

-10

10 ST

Profit

15

10

Payoff: ST

Profit: Payoff-price

Protective Put

Components Long stock + long put

Purpose A form of portfolio insurance. Protects against drops in the

value of the stock.

Costs In the case of stock price increases, profit is reduced by the

cost of the put.

Be able to list these 3 points for all option strategies!

Protective Put (So=X=10)

10 ST 15

10

10 ST

10

10 ST

10

Payoff

Put

Stock +

= Protective Put

10 ST 15

10

10 ST

10

10

ST

Put

Stock

Profit

-P

Put Call Parity-Payoff

Protective Put Payoff:

Consider another strategy:

Long Call with strike price X

Long Bond with maturity value X

Payoff

Both strategies yield same payoff!

ST ≤ X ST > X

Stock ST ST

+Put X-ST 0

=Total X ST

ST ≤ X ST > X

Call 0 ST –X

+Bond X X

=Total X ST

Put Call Parity-Cost

Cost must be the same.

C=Price of Call, P=Price of Put, SO=Price of stock

=Price of Bond

This relationship is called put call parity.

Violations lead to arbitrage opportunities.

PSr

XC OT

f

)1(

T

fr

X

)1(

Put Call Parity-Arbitrage Example

Stock price $110

Call price $17 (Strike=105)

Put price $5 (Strike=105)

Risk-free interest rate 5% per year

115117

511005.1

10517

Market prices

PSr

XC OT

f

)1(

•Does the put-call parity relationship hold?

•Plug in the numbers into the equation:

Put Call Parity–Arbitrage Example

Position Cash Flow C a s h F l o w i n 1 Y e a r S T < 1 0 5 S T ≥ 1 0 5

Buy Stock -110 ST ST

Borrow $105/1.05=$100

+100 -105 -105

Sell Call +17 0 -(ST-105)

Buy put -5 105-ST

0

Total 2 0 0

•Arbitrage opportunity! Since two sides of equation are not equal •Buy the side that is cheap (stock and put) •Sell the side that is expensive (call and bond)

Covered Call

Components

Long stock + Short Call

Purpose

A way to boost income by selling calls and collecting premiums.

Costs

In the case of stock price increases, profit is forfeited.

Still have downside risk of owing the stock, although the risk is reduced by the premium earned on the call.

Payoff ST ≤ X ST > X

Stock ST ST

+Call 0 -(ST-X)

=Total ST X

Covered Call (So=X=10)

10 ST 15

10

10 ST

10

10 ST

10

Payoff

Call

Stock +

= Covered Call

10 ST 15

C

10 ST

10

10

ST

Call

Stock

Profit

Straddles & Spreads

Straddles are a bet on volatility.

A long straddle takes a view that volatility on a stock will increase. Consists of a long call and a long put at the same strike price and same expiration. In the event of low volatility , possible loss of premium used to purchase options.

Spreads allow you to subsidize your costs given your view that a stock price will increase (bull spread) or stock price will decrease (bear spread).

A bull spread involves buying a call at strike price XL and selling a call at a higher strike price XH > XL

Collars

Collars bracket the value of a portfolio between two bounds.

A put is purchased to protect downside losses at strike XP

A call is sold to earn premium and finance the purchase of the put at strike XC

The gain/loss is limited between XP and XC