Chapter 21 Options and Corporate Finance: Basic Concepts

1
Chapter 21 Options and Corporate Finance Basic
Concepts

• Derivatives
• Types of Traders
• Calls, Puts and Shares
• Financial Alchemy with Options
• Option Valuation
• What Determines Option Value
• Implicit Option feature in Corporate Finance

2
Derivatives

• Forward contract - an agreement to buy or sell as
  asset at a certain future time for a certain
  price
• Futures contract - same concept as forward, but
  mark-to-market, uncertainty over exact delivery
  date, product quality and location for commodity,
  etc.
• Options - holder of options has rights to buy
  (call) or sell (put)
• Swaps - agreement between two parties to exchange
  cash flow in the future according to prearranged
  formula

3
Types of traders

• Hedgers to reduce a risk by eliminating an
  exposure to movements in the price of an asset
• Speculators - take a position in the market
  without holding an asset
• Arbitrageurs lock in a riskless profit by
  entering simultaneously into transactions in two
  or more markets

4
Option Terminology
Call Option Right to buy an asset at a specified
exercise price on or before the exercise date.

• Put Option
• Right to sell an asset at a specified exercise
  price on or before the exercise date.

5
Option Obligations
6
Option Value

• The value of an call option at expiration is a
  function of the stock price and the exercise
  price.
• Example - Option values given a exercise price of
  85

7
Option Value
Stock Price
Upper Limit
Lower Limit
(Stock price - exercise price) or 0 whichever
is higher
8
Option Value
Call option Intrinsic value (graphic) given a 85
exercise price.
Call option value
20
85 105
Share Price
9
Option Value
Put option Intrinsic value (graphic) given a 85
exercise price.
Put option value
5
80 85
Share Price
10
Option Value
Call option payoff (to seller) given a 85
exercise price.
Call option payoff
85
Share Price
11
Option Value
Put option payoff (to seller) given a 85
exercise price.
Put option payoff
85
Share Price
12
Financial Alchemy with Options

• Protective Put - Long stock and long put

Long Stock
Position Value
Share Price
13
Financial Alchemy with Options

• Protective Put - Long stock and long put

Long Put
Position Value
Share Price
14
Financial Alchemy with Options

• Protective Put - Long stock and long put

Long Stock
Protective Put
Position Value
Long Put
Share Price
15
Financial Alchemy with Options

• Protective Put - Long stock and long put

Protective Put
Position Value
Share Price
16
Valuation of Call Options

• Binomial model for European Option
• One-year call options on Intel stock (X85)
• S 85, Call is at the money
• Risk-free interest rate 2.5
• Expected return for Stock 11.5
• Stock price at expiration
• S106.25 (? by 25, probability of 70)
• S 68 (? by 20, probability of 30)

17
Black-Scholes Option Pricing Model
OC PsN(d1) - SN(d2)e-rt
OC- Call Option Price Ps - Stock Price N(d1) -
Cumulative normal density function of (d1) S -
Strike or Exercise price N(d2) - Cumulative
normal density function of (d2) r - discount rate
(90 day comm paper rate or risk free rate) t -
time to maturity of option (as of year) v -
volatility - annualized standard deviation of
daily returns
18
Example of the Black-Scholes Option Pricing Model

• S 27
• E 25
• t 120 days / 365
• rF 7
• s2 0.0576
• d1 ln(27/25) (.07 .5 x .0576) 120/365
  (.0576 x 120/365)(-1/2) .7953
• d2 .7953 - (.0576 x 120/365)(1/2) .6577
• N(d1) .7868
• N(d2) .7446
• C (27)(.7868) - (25)(e-(.07)(120/365))(.7466)
  3.05

19
Determinants of Option Pricing

• Determinants of Relation to Relation to
• Option Pricing Call Option Put Option
• Stock price Positive Negative
• Strike price Negative Positive
• Risk-free rate Positive Negative
• Volatility of the stock Positive Positive
• Time to expiration date Positive Usually
• Positive

20
Put-Call Parity

• Purchase the Intel stock, one-year 85 put
  option, and sell one-year 85 call option.
• Investment Payoffs Stock _at_ 106.25 Stock _at_
  68
• Stock 106.25 68
• Put 0 17
• Call -21.25 0
• Net Total Payoffs 85 85

21
Put-Call Parity

• Stock - Call Put Strike Price e -(T)(Rf)
• Continuous compounding
• or
• Stock - Call Put Strike Price / (1 Rf) -T
• Simple interest
• Purchase the Intel stock, one-year 85 put
  option, and sell one-year 85 call option.

22
Payoff to Stockholders
Cash flowto stockholders ()
45o
0
Cash flowto firm ()
Face value of debt
23
Payoff to Bondholders
Cash flowto stockholders ()
800
0
Cash flowto firm ()
Face value of debt