week 10 option markets(1)
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Week 10 Option Markets(1)TRANSCRIPT
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