Transcript Corporate Financial Theory

CORPORATE
FINANCIAL
THEORY
Lecture 10
Derivatives
Insurance
Risk Management
Lloyds
Ship Building
Jet Fuel
Cost Predictability
Revenue Certainty
Underlying Assets








Stocks (example)
Bonds
Indices
Commodities (examples for metal and ag.)
Currencies
Weather
Carbon emissions
Radio bandwidth
Derivative Uses



Arbitrage
Speculation
Hedging
Derivatives Definition


Derivatives are financial instruments whose price
and value derive from the value of the underlying
assets or other variables (ISDA)
Derivatives are a “zero sum game”
 Example:
Insurance
Derivatives & Options
Historical Topics (Internal to the Corp)
1 - Capital Budgeting (Investment)
2 - Capital Structure (Financing)
Today
We are leaving Internal Corporate Finance
We are going to Wall St & “Capital Markets”
Options - financial and corporate
Options are a type of derivative
Options
Long
Short
Call option Right tobuy asset Obligation to sell asset
Put option Right tosell asset Obligation to buy asset
Options
Terminology
 Derivatives - Any financial instrument that is derived from another.
(e.g.. options, warrants, futures, swaps, etc.)
 Option - Gives the holder the right to buy or sell a security at a
specified price during a specified period of time.
 Call Option - The right to buy a security at a specified price within a
specified time.
 Put Option - The right to sell a security at a specified price within a
specified time.
 Option Premium - The price paid for the option, above the price of
the underlying security.
 Intrinsic Value - Diff between the strike price and the stock price
 Time Premium - Value of option above the intrinsic value
Options
Terminology
Exercise Price - (Striking Price) The price at which you buy or sell the
security.
Expiration Date - The last date on which the option can be exercised.
American Option - Can be exercised at any time prior to and including
the expiration date.
European Option - Can be exercised only on the expiration date.
All options “usually” act like European options because you make more
money if you sell the option before expiration (vs. exercising it).
3 vs. 70-68=2
Option Value
The value of an option at expiration is a function of the stock price and the
exercise price.
Option Value
The value of an option at expiration is a function of the stock price and the
exercise price.
Example - Option values given a exercise price of $85
Stock P rice $60
Call Value
0
Put Value
25
70
0
15
80
0
5
90
5
0
100 110
15
25
0
0
Options
CBOE Success
1 - Creation of a central options market place.
2 - Creation of Clearing Corp - the guarantor of all
trades.
3 - Standardized expiration dates - 3rd Friday
4 - Created a secondary market
Option Value
Components of the Option Price
1 - Underlying stock price
2 - Striking or Exercise price
3 - Volatility of the stock returns (standard deviation of annual
returns)
4 - Time to option expiration
5 - Time value of money (discount rate)
Option Value
Black-Scholes Option Pricing Model
OC  N (d1 )  P  N (d2 )  PV ( EX )
Black-Scholes Option Pricing Model
OC  N (d1 )  P  N (d2 )  PV ( EX )
OC- Call Option Price
P - Stock Price
N(d1) - Cumulative normal density function of (d1)
PV(EX) - Present Value of 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
Black-Scholes Option Pricing Model
OC  N (d1 )  P  N (d2 )  PV ( EX )
PV ( EX )  EX  e rt 
e
 rt
1
 rt  continuous compoundin g discount factor
e
Black-Scholes Option Pricing Model
ln( )  ( r  )t
d1 
v t
P
EX
v2
2
N(d1)=
Cumulative Normal Density Function
ln( )  ( r  )t
d1 
v t
P
EX
v2
2
d2  d1  v t
Call Option
Example
What is the price of a call option given the following?
P = 36
r = 10%
v = .40
EX = 40
t = 90 days / 365
ln( )  ( r  )t
d1 
v t
P
EX
d1  .3070
v2
2
N (d1 )  1  .6206 .3794
.3070
= .3
= .00
= .007
Call Option
Example
What is the price of a call option given the following?
P = 36
r = 10%
v = .40
EX = 40
t = 90 days / 365
d 2  d1  v t
d 2  .5056
N ( d 2 )  1  .6935 .3065
Call Option
Example
What is the price of a call option given the following?
P = 36
r = 10%
v = .40
EX = 40
t = 90 days / 365



 .3794 36  .3065 ( 40)e
OC  N (d1 )  P   N ( d 2 )  ( EX )e  rt
OC
OC  $1.70
(.10 )(.2466 )
Put - Call Parity
Put Price = Call + EX - P - Carrying Cost + Div.
or
Put = Call + EX(e-rt)– Ps - Carrying Cost + Div.
Carrying cost = r x EX x t
Put - Call Parity
Example
ABC is selling at $41 a share. A six month May 40 Call is
selling for $4.00. If a May $ .50 dividend is expected and
r=10%, what is the put price?
OP = OC + EX - P - Carrying Cost + Div.
OP = 4 + 40 - 41 - (.10x 40 x .50) + .50
OP = 3 - 2 + .5
Op = $1.50
Warrants & Convertibles




Review Topics (not going over in class)
Warrant - a call option with a longer time to expiration.
Value a warrant as an option, plus factor in dividends
and dilution.
Convertible - Bond with the option to exchange it for
stock. Value as a regular bond + a call option.
Won’t require detailed valuation - general concept on
valuation + new option calc and old bond calc.
Option Strategies

Option Strategies are viewed via charts.

How do you chart an option?
Profit
Loss
Stock Price
Option Strategies
• Long Stock Bought stock @ Ps = 100
+10
P/L
Ps
90
-10
100
110
Option Strategies

Long Call Bought Call @ Oc = 3 S=27 Ps=30
+6
P/L
Ps
-3
27
30
36
Option Strategies

Short Call Sold Call @ Oc = 3 S=27 Ps=30
+3
P/L
Ps
27
-6
30
36
Option Strategies

Long Put = Buy Put @ Op = 2 S=15 Ps=13
+3
P/L
Ps
10
-2
13
15
Option Strategies

Short Put = Sell Put @ Op = 2 S=15 Ps=13
+2
P/L
Ps
10
-3
13
15
Option Strategies
•
•
Synthetic Stock = Short Put & Long Call @
Oc = 1.50 Op=1.50 S=27 Ps=27
+1.50
P/L
-1.50
Ps
24
27
30
Option Strategies
•
•
Synthetic Stock = Short Put & Long Call @
Oc = 1.50 Op=1.50 S=27 Ps=27
+1.50
P/L
-1.50
Ps
24
27
30
Option Strategies
•
•
Synthetic Stock = Short Put & Long Call @
Oc = 1.50 Op=1.50 S=27 Ps=27
+1.50
P/L
-1.50
Ps
24
27
30
Option Strategies
Why?
 1 - Reduce risk - butterfly spread
 2 - Gamble - reverse straddle
 3 - Arbitrage - as in synthetics


Arbitrage - If the price of a synthetic stock is different
than the price of the actual stock, an opportunity for
profit exists.
Recall discussion on Real Options
Dilution
V  NqEX
Share priceafterexercise
N  Nq
Dilutionfactor
1
of new shares
1  # of#outstandin
g shares
Binomial vs. Black Scholes
Expanding the binomial model to allow more possible price changes
1 step
(2 outcomes)
2 steps
(3 outcomes)
etc. etc.
4 steps
(5 outcomes)