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© 2007 Thomson South-Western
Chapter 18Options Basics
2
Economic Benefits Provided by Options
Derivative securities are instruments that derive their value from the value of other
assets.Derivatives include options, futures, and
swaps.
Options and other derivative securities have several important economic functions:
– Help bring about more efficient allocation of risk – Save transactions costs…sometimes it is cheaper to trade a
derivative than its underlying asset.– Permit investments strategies that would not otherwise be possible
3
Options Basics
Options: contracts that grant the buyer the right to buy or sell stock at a fixed price.
Options provide real economic benefit to society.
Put-call parity establishes a link between market prices of calls, puts, shares, and
bonds.
Factors that affect option prices: underlying price, time to maturity, strike price,
interest rate and volatility.
4
Options Vocabulary
Long position
• The buyer of an option has a long position, and has the ability to exercise the option.
Short position
• The seller (or writer) of an option has a short position, and must fulfill the contract if the buyer exercises.
• As compensation, the seller receives the option premium.
Options trade on an exchange (such as CBOE) or in the over-the-counter market.
5
Options Vocabulary
Call option • Gives the holder the right to
purchase an asset at a specified price on or before a certain date
Put option • Gives the holder the right to sell as
asset at a specified price on or before a certain date
Strike price or exercise price: the price specified for purchase or sale in an option contract
American or European
option
• American options allow holders to exercise at any point prior to expiration.
• European options allow holders to exercise only on the expiration date.
6
Option Price
Call Put
S>X In-the-money Out-of-the-money
S=X At-the-money At-the-money
S<X Out-of-the-money
In-the-money
S = current stock price
X = strike price
7
Option Quotations
50
50
45
45
Strike
6.503.50June46.31
5.251.50March46.31
3.885.88June46.31
2.384.00March46.31
PutCallExpire
sGeneral Electric
In-the-money callsOut-of-the-money puts
In-the-money putsOut-of-the-money calls
• Option quotations specify the per share price for an option contract, which is a contract to buy or sell 100 shares of the underlying stock
8
Intrinsic and Time Value of Options
Intrinsic value
• For in the money options: the difference between the current price of the underlying asset and the strike price
• For out of the money options: the intrinsic value is zero
Time value• The difference between the option’s
intrinsic value and its market price (premium)
9
Payoff Diagrams
Show the value of an option, or the value at expiration
Y-axis plots exercise value or “intrinsic value.”
X-axis plots price of underlying asset.
Use payoff diagrams for:
Long and short positions
Gross and net positions (the net positions subtract the option
premium)
Payoff: the price of the option at expiration date
10
Long Call Option Payoffs
11
Short Call Option Payoffs
12
Long Put Option Payoffs
13
Short Put Option Payoffs
14
Naked Option Positions
Naked call option position - occurs when an investor buys or sells an option on a stock without already owning the underlying stock
Naked put option positions – occurs when a trader buys or sells a put option without owning the underlying stock
15
Portfolios of Options
Look at payoff diagrams for combinations of options rather than just one.
Diagrams show the range of potential strategies made possible by options.
Some positions, in combination with other positions, can be a form of portfolio insurance.
16
Straddle Positions
Long straddle - a portfolio consisting of long positions in calls and puts on the same stock with the same strike price and expiration date
Short straddle - a portfolio consisting of short positions in calls and puts on the same stock with the same strike price and expiration date
17
Long Straddle
18
Short Straddle
Call x = 60, premium = $5, Put x = 60, premium = $4
60
+9
51 69
Net payoff
Gross payoff
19
Payoff Diagrams for Stocks and Bonds
20
Covered Call Strategy
Writing covered calls –common trading strategy that mixes stock and call options An investor who owns a share of stock
sells a call option on that stock. The investor receives the option
premium immediately. The trade-off is that if the stock price
rises the holder of the call option will exercise
the right to purchase it at the strike pricethe investor will lose the opportunity to
benefit from the appreciation in the stock.
21
Payoff Diagram for Covered Call Strategy
22
Payoff of a Put Option and a Share of Stock – a Protective Put
23
Payoff of a Call Option and a Zero-Coupon Bond
24
Put-Call Parity
Following conditions must be met:1. The call and put options must be on the
same underlying stock.2. The call and put options must have the
same exercise price.3. The call and put options must share the
same expiration date.4. The underlying stock must not pay a
dividend during the life of the options.5. The call and put options must be European
options.6. The bond must be a risk-free, zero-coupon
bond with a face value equal to the strike price of the options and with a maturity date identical to the options’ expiration date.
25
Synthetic Put Option
Traders can create a synthetic put option by purchasing a bond and a call option while simultaneously short-selling the stock.
26
Put-Call Parity Arbitrage
27
Using Put-Call Parity to Create Synthetic Positions
28
Factors Affecting Option Values
Price of underlying
asset
• Asset price and call price are positively related.
• Asset price and put price are negatively related.
Time to expiration
• More time usually makes options more valuable.
Strike price
• Higher X means higher put price; lower X means higher call price.
Interest rate
• Calls: higher “r” means higher call value
• Puts: higher “r” reduces put value
29
Factors Affecting Option Values
Holding other factors constant, call and put option prices increase as the time to expiration increases.
Call prices decrease and put prices increase when the difference between the underlying stock price and the exercise price (S − X) decreases.
Call and put option prices increase as the volatility of the underlying stock increases.
30
Calculating Option Prices
The binomial options model recognizes that investors can combine options (either calls or puts) with shares of the underlying asset to construct a portfolio with a risk-free payoff.
31
Binomial Option Pricing
32
Binomial Option Pricing
Data needed:The current price of the underlying
stockThe amount of time remaining before
the option expiresThe strike price of the optionThe risk-free rateThe possible values of the underlying
stock in the future
33
Multistage Binomial Trees
34
Multistage Binomial Trees
35
Risk-Neutral Method
If a combination of stock and options is risk-free, it must sell for the same price as a risk-free bond.
If an asset promises a risk-free payoff, risk-averse and risk-neutral investors agree on how it should be valued.
Whether investors are risk averse or risk neutral, the binomial model’s calculations are the same.
We can assume investors are risk neutral, which gives us a new way to value options.