Lecture 22: Options

1
Topic Options and Corporate Securities
Objectives

• Calculate the payoffs to buyers and sellers of
  call and put options
• Describe the determinants of call option values

2
Call and Put Options

• Call Option The right to buy an asset at a fixed
  price on or before the expiration date
• Put Option The right to sell an asset at a fixed
  price on or before the expiration date. The
  opposite of a call option

3
Examples of Options

• Issued by Investors
• -Exchange-traded options - side bets between
  investors on a wide range of financial assets
• Issued by Firms
• - Warrants give the holder the right to purchase
  shares of stock at a fixed price over a given
  period of time
• - Rights give the shareholder an option to buy a
  specified number of new shares from the firm at
  a specified price within a specified time
• - Convertibles debt or preferred shares
• - Stock options given as executive or employee
  compensation

4
Examples of Options Prices

5
Payoffs to Options Buyers at Expiration

• Payoffs to buyers of call and put options on Air
  Canada stock with exercise price 8.00

6
Payoffs at Expiration

• Payoff to the call buyer at expiration
• Stock Price at Expiration Call Payoff at
  Expiration
• Greater than exercise price Stock price
  exercise price
• Less than exercise price Zero
• Payoffs to the put buyer at expiration
• Stock Price at Expiration Put Payoff at
  Expiration
• Greater than exercise price Zero
• Less than exercise price Exercise price stock
  price

7
Selling Calls and Puts

• Options traded on organized exchanges are issued
  by the call and put writers. If one investor
  buys an option, some other investor must be on
  the other side of the bargain. In general, the
  buyers gain is the sellers loss, and vice
  versa.
• The payoffs to sellers of call and put options
  are (exercise price 8.00)

Payoff
Payoff
8
8
Stock Price
Stock Price
Call Option
Put Option
8
Payoffs at Expiration

• Payoff to the call seller at expiration
• Stock Price at Expiration Call Payoff at
  Expiration
• Greater than exercise price Exercise price
  share price
• Less than exercise price Zero
• Payoffs to the put seller at expiration
• Stock Price at Expiration Put Payoff at
  Expiration
• Greater than exercise price Zero
• Less than exercise price Stock price exercise
  price

9
Examples on Call and Option Payoffs

• Mixing options and securities can often create
  interesting payoffs. For each of the following
  combinations show what the payoff would be when
  the option expires if (1) stock price is below
  the exercise price, and (2) stock price is above
  the exercise price. Assume that each option has
  the same exercise price of 100 and expiration
  date.
• (a) Buy a call and invest the present value of
  the exercise price in a bank deposit
• (b) Buy a share and a put option on the share
• (c) Buy a share, buy a put option on the share,
  and sell a call option on the share
• (d) Buy a call option and a put option on the
  share

10

11

12
Example B

• Suppose you buy
• a call option with exercise price 10
• a call option with exercise price 20
• Assuming both have the same expiry date, draw the
  payoff profile.

13
(No Transcript)
14
(No Transcript)
15
Example B

• Suppose you buy
• a call option with exercise price 10
• a call option with exercise price 30
• and sell
• a put option with exercise price of 5
• a call option with exercise price of 35
• Assuming all have the same expiry date, draw the
  payoff profile.

16
(No Transcript)
17
(No Transcript)
18
Bounds on Call Option Values

19
Determinants of Option Value

• Stock Price the higher the stock price (S0) is,
  the more the call is worth
• Exercise Price the higher the exercise price (E)
  is, the less the call is worth
• Time to Expiration the longer the time to
  expiration is (the bigger t is), the more the
  option is worth
• Risk-free Rate the higher the risk-free rate
  (Rf), the more the call is worth
• Volatility of Stock Price the greater the
  variance of the return on the underlying stock
  is, the more the option is worth