Options Markets

1
Options Markets
14
2
Option Basics

• A stock option is a derivative security, because
  the value of the option is derived from the
  value of the underlying common stock.
• There are two basic option types.
• Call options are options to buy the underlying
  asset.
• Put options are options to sell an underlying
  asset.
• Listed Option contracts are standardized to
  facilitate trading and price reporting.
• Listed stock options give the option holder the
  right to buy or sell 100 shares of stock.

3
Option Basics, Cont.

• Option contracts are legal agreements between two
  partiesthe buyer of the option, and the seller
  of the option.
• The minimum terms stipulated by stock option
  contracts are
• The identity of the underlying stock.
• The strike price, or exercise price.
• The option contract size.
• The option expiration date, or option maturity.
• The option exercise style (American or European).
• The delivery, or settlement, procedure.
• Stock options trade at organized options
  exchanges, such as the CBOE, as well as
  over-the-counter (OTC) options markets.

4
Why Options?

• A basic question asked by investors is Why buy
  stock options instead of shares in the underlying
  stock?
• To answer this question, we compare the possible
  outcomes from these two investment strategies
• Buy the underlying stock
• Buy options on the underlying stock

5
Example Buying the Underlying Stock versus
Buying a Call Option

• Suppose IBM is selling for 90 per share and call
  options with a strike price of 90 are 5 per
  share.
• Investment for 100 shares
• IBM Shares 9,000
• One listed call option contract (500)
• Suppose further that the option expires in three
  months.
• Finally, lets say that in three months, the
  price of IBM shares will either be 100, 90, or
  80.

6
Example Buying the Underlying Stock versus
Buying a Call Option, Cont.

• Lets calculate the dollar and percentage return
  given each of the prices for IBM stock

7
Why Options? Conclusion

• Whether one strategy is preferred over another is
  a matter for each individual investor to decide.
• Each investor must weight the risk and return
  trade-off offered by the strategies.
• It is important to see that call options offer an
  alternative means of formulating investment
  strategies.
• For 100 shares, the dollar loss potential with
  call options is lower.
• For 100 shares, the dollar gain potential with
  call options is lower.
• The positive percentage return with call options
  is higher.
• The negative percentage return with call options
  is lower.

8
Option Writing

• The act of selling an option is referred to as
  option writing.
• The seller of an option contract is called the
  writer.
• The Writer of a call option contract is obligated
  to sell the underlying asset to the call option
  holder.
• The call option holder has the right to exercise
  the call option (i.e., buy the underlying asset
  at the strike price).
• The Writer of a put option contract is obligated
  to buy the underlying asset from the put option
  holder.
• The put option holder has the right to exercise
  the put option (i.e., sell the underlying asset
  at the strike price).
• Because option writing obligates the option
  writer, the option writer receives the price of
  the option today from the option buyer.

9
Option Exercise

• Option holders have the right to exercise their
  option.
• If this right is only available at the option
  expiration date, the option is said to have
  European-style exercise.
• If this right is available at any time up to and
  including the option expiration date, the option
  is said to have American-Style exercise.
• Exercise style is not linked to where the option
  trades. European-style and American-Style options
  trade in the U.S., as well as on other option
  exchanges throughout the world.

10
Option Payoffs versus Option Profits

• It is useful to think about option investment
  strategies in terms of their initial cash flows
  and terminal cash flows.
• The initial cash flow of an option is the price
  of the option.
• The initial cash flow is often called the option
  premium.
• The terminal cash flow of an option is the value
  of an option at expiration. (The terminal cash
  flow can be realized by the option holder by
  exercising the option.)
• The terminal cash flow is often called the option
  payoff.
• Option Profits are calculated by subtracting the
  initial cash flow (option premium) from the
  terminal cash flow (option payoff).

11
Call Option Payoffs
12
Put Option Payoffs
13
Call Option Profits
14
Put Option Profits
15
Option Strategies

• Bullish strategies
• Long call purchasing call options
• Naked put writing put options
• Bearish strategies
• Naked call writing call options
• Long put purchasing put options

16
Option Strategies

• Hedging strategies
• Protective put - Strategy of buying a put option
  on a stock already owned. This protects against a
  decline in value (i.e., it is "insurance")
• Covered call - Strategy of selling a call option
  on stock already owned. This exchanges upside
  potential for current income.
• Neutral strategy
• Straddle - Buying or selling a call and a put
  with the same exercise price. Buying is a long
  straddle selling is a short straddle.

17
Sirius Satellite Radio (SIRI)

• SIRI call options

18
Sirius Satellite Radio (SIRI)

• January 06 Call
• Strike price of 7.50
• Up 25.00

• January 06 Put
• Strike price of 7.50
• Down 16

The days news Martha Stewart radio to launch on
Nov. 21!!!!
19
Arbitrage

• Arbitrage
• Riskless profits due to
• potential for a gain
• No cash outlay
• In finance, arbitrage is not allowed to persist.
• The Absence of Arbitrage rule is often used in
  finance to figure out prices of derivative
  securities.
• Boundaries must be set on prices to prevent
  arbitrage

20
Option Price Boundaries

• In order to prevent arbitrage
• Option prices must be at least zero.
• Call option price must be less than the stock
  price.
• Put option price must be less than the strike
  price.

21
The Lower Bound on Option Prices

• Option prices must be at least zero.
• To derive a meaningful lower bound, we need to
  introduce a new term intrinsic value.
• The intrinsic value of an option is the payoff
  that an option holder receives if the underlying
  stock price does not change from its current
  value.

22
Option Intrinsic Values

• That is, if S is the current stock price, and K
  is the strike price of the option
• Call option intrinsic value max 0, S K
• The call option intrinsic value is the maximum of
  zero or the stock price minus the strike price.
• Put option intrinsic value max 0, K S
• The put option intrinsic value is the maximum of
  zero or the strike price minus the stock price.

23
Option Moneyness

• In the Money options have a positive intrinsic
  value.
• For calls, the strike price is less than the
  stock price.
• For puts, the strike price is greater than the
  stock price.
• Out of the Money options have a zero intrinsic
  value.
• For calls, the strike price is greater than the
  stock price.
• For puts, the strike price is less than the stock
  price.
• At the Money options is a term used for options
  when the stock price and the strike price are
  about the same.

24
Intrinsic Values and Arbitrage, Calls

• Call options with American-style exercise must
  sell for at least their intrinsic value.
  (Otherwise, there is arbitrage)
• Suppose Current stock price (S) 60 Call
  premium (C) 5 Strike price (K) 50.
• Instant Arbitrage. How?
• Buy the call for 5.
• Immediately exercise the call, and buy the stock
  for 50.
• In the next instant, sell the stock at the market
  price of 60.
• Profit 60 - (50 5) 5

25
Intrinsic Values and Arbitrage, Puts

• Put options with American-style exercise must
  sell for at least their intrinsic value.
  (Otherwise, there is arbitrage)
• Suppose Current price (S) 40 Put premium
  (P) 5 Strike price (K) 50.
• Instant Arbitrage. How?
• Buy the put for 5.
• Buy the stock for 40.
• Immediately exercise the put, and sell the stock
  for 50.
• Profit Outflows Inflows (50 - 40) - 5 5

26
Back to Lower Bounds for Option Prices

• As we have seen, to prevent arbitrage, option
  prices cannot be less than the option intrinsic
  value.
• Using equations If S is the current stock price,
  and K is the strike price
• Call option price ? max 0, S K
• Put option price ? max 0, K S

27
Put-Call Parity

• Put-Call Parity is perhaps the most fundamental
  relationship in option pricing.
• Put-Call Parity is generally used for options
  with European-style exercise.
• Put-Call Parity states the difference between
  the call price and the put price equals the
  difference between the stock price and the
  discounted strike price.

28
The Put-Call Parity Formula

• In the formula
• C is the call option price today
• S is the stock price today
• r is the risk-free interest rate
• P is the put option price today
• K is the strike price of the put and the call
• T is the time remaining until option expiration
• Note this formula
• can be rearranged

e-rT is a discount factor, so Ke-rT is simply the
discounted strike price.
29
Sirius Satellite Radio (SIRI)

• SIRI Jun 06 Call
• Call price (C) 1.50
• Current price (S) 7.28
• 6-month risk free rate 4.09

• SIRI Jun 06 Put
• Put price (P) 0.95
• Both options have a strike price of 7
• Assume the options expire in 6 months

Examine SIRI option prices using the Put-Call
Parity.
30
Put-Call Parity

• If the put-call parity does not hold, then one
  (or both) of the options is (are) mis-priced
• The put-call parity does not determine option
  pricing, it determines if actual prices are
  correct

31
Quick Quiz

• If you purchase a call option, what is your
  sentiment regarding the underlying asset?
• Can the put-call parity be used to generate the
  price of an option?

32
Chapter 15

• Option Valuation

33
The Black-Scholes Formulas
N(d) is the probability that a standardized
normally distributed variable will be less than
or equal to d. Input parameters S0 todays
stock price, X option exercise price, r risk
free, continuously compounded annual interest
rate, T time to option maturity, in years, ?
standard deviation of annual stock returns.
34
Option Valuation

• Stock price 100
• Exercise price 95
• Interest rate 10
• Time to expiration 0.25 years
• Standard deviation 0.50

35
Step 1 Calculate d1

• d1 ln(100/95) (0.10 (0.52/2))0.25
• (0.520.25)0.5
• d1 (.0513 .05625)/0.25 0.43

36
Step 2 Calculate d2

• d2 0.43 (0.52 0.25)0.5
• d2 0.43 0.25 0.18

37
Step 3 Find N(d1) and N(d2)

• Values for N(d1) and N(d2) will be provided
• N(0.43) 0.6664
• N(0.18) 0.5714

38
Step 4 Solve for C

• C0 100(0.6664) 95e-0.100.25(0.5714)
• C0 66.64 950.9750.5714
• 66.64 52.94 13.70

39
B/S Excel Model
40
Assumptions of the B/S Model

• Stocks will pay a constant dividend yield until
  the expiration date
• The interest rate and variance are constant
• Variance of returns is a subject of debate
• Sudden extreme jumps in stock prices are ruled out

41
Factors Affecting Option Values
42
Quick Quiz

• What are some faults of the Black-Scholes model?
• Name 2 factors that affect the price of an option