Basics of Option Pricing Theory &
Applications in Business Decision Making
Purpose:
• Provide background on the basics of Option
Pricing Theory (OPT)
pp
• Examine some recent applications
What are options?
• Options are financial contracts whose value is
contingent upon the value of some underlying
asset
• Such arrangements are also known as contingent
claims
– because equilibrium market value of an option moves in
direct association with the market value of its
underlying asset.
• OPT measures this linkage
The basics of options
Calls and puts defined
• Call: privilege of buying the underlying
asset at a specified price and time
• Put: privilege of selling the underlying
p
price
p
and time
asset at a specified
The basics of options
American and European options defined
• American options can be exercised anytime
before expiration date
• European options can be exercised only on
the expiration
p
date
• Asian options are settled based on average
price of underlying asset
The basics of options
• Options may be allowed to expire without
exercising them
• Options game has a long history
– at least as old as the “premium game” of 17th
century Amsterdam
– developed from an even older “time game”
• which evolved into modern futures markets
• and spawned modern central banks
Put-Call Parity
C id two
Consider
t portfolios
tf li
• Portfolio A contains a call
and a bond:
C(S,X,t) + B(X,t)
• Portfolio B contains stock
plus put:
S + P(S,X,t)
Put-Call Parity
Consider
C
id two
t
portfolios
• Portfolio A contains a
call and a bond:
VA
C(S,X,t) + B(X,t)
• Portfolio B contains
stock plus put:
S + P(S,X,t)
VB
S*<X
0
+X
=X
X-S
+S
=X
S*>X
S-X
+X
=S
0
+S
=S
Put-Call Parity
• If S* < X,
X Payoff for either portfolio is X
dollars
• If S* > X, Payoff for either portfolio is S*
• Therefore
C(S X t) + B(X,t)
C(S,X,t)
B(X t) = S + P(S,X,t)
P(S X t)
Boundaries on call values
C(S,X,t) + B(X,t) = S + P(S,X,t)
• Upper Bound:
Call
C(S,X,t) < S
Stock
Boundaries on call values
C(S,X,t) = S - B(X,t) + P(S,X,t)
• Upper Bound:
• Lower bound:
Call
C(S,X,t) < S
C(S,X,t) > S – B(X,t)
B(X,t)
Stock
Call values
Call
C(S,X,t) = S - B(X,t) + P(S,X,t)
B(X,t)
Stock
Call values
Call
C(S,X,t) = S - B(X,t) + P(S,X,t)
B(X,t)
Stock
Call values
Call
C(S,X,t) = S - B(X,t) + P(S,X,t)
B(X,t)
Stock
Call values
Call
C(S,X,t) = S - B(X,t) + P(S,X,t)
B(X,t)
Stock
Call values
Call
C(S,X,t) = S - B(X,t) + P(S,X,t)
B(X,t)
Stock
Call values
Call
C(S,X,t) = S - B(X,t) + P(S,X,t)
B(X,t)
Stock
Call values
Call
C(S,X,t) = S - B(X,t) + P(S,X,t)
B(X,t)
Stock
Call values
Call
C(S,X,t) = S - B(X,t) + P(S,X,t)
B(X,t)
Stock
Call values
Call
C(S,X,t) = S - B(X,t) + P(S,X,t)
B(X,t)
Stock
Call values
Call
C(S,X,t) = S - B(X,t) + P(S,X,t)
B(X,t)
Stock
Call values
Call
C(S,X,t) = S - B(X,t) + P(S,X,t)
Stock
B(X,t)
Keys for using OPT as an analytical
tool
C(S,X,t) = S - B(X,t) + P(S,X,t)
C
Call
S
B(X,t)
Stock
S
C
X
C
Call
Keys for using OPT as an analytical
tool
C(S,X,t) = S - B(X,t) + P(S,X,t)
B(X,t)
Stock
S
C
X
C
R
C
Call
Keys for using OPT as an analytical
tool
C(S,X,t) = S - B(X,t) + P(S,X,t)
B(X,t)
Stock
S
C
X
C
R
C
t
C
Call
Keys for using OPT as an analytical
tool
C(S,X,t) = S - B(X,t) + P(S,X,t)
B(X,t)
Stock
S
C
X
C
R
C
t
C
σ
C
Call
Keys for using OPT as an analytical
tool
C(S,X,t) = S - B(X,t) + P(S,X,t)
B(X,t)
Stock
S
C
P
X
C
P
R
C
P
t
C
P
σ
C
P
Call
Keys for using OPT as an analytical
tool
C(S,X,t) + B(X,t) = S + P(S,X,t)
B(X,t)
Basic Option Strategies
•
•
•
•
•
•
Long Call
Long Put
Short Call
Short Put
L
Long
Straddle
St ddle
Short Straddle
Stock
Long Call
$
0
-C
X
S
X+C
Long C
Call
Short Call
$
$
C
0
0
-C
X
S
X+C
X C
X+C
X
S
$
0
-C
S
X
$
X+C
Short C
Call
Long C
Call
Long Put
$
C
0
X C
X+C
S
X
X-P
0
X
-P
S
Lo
ong Put
$
0
-C
$
0
-P
S
X
X+C
$
C
0
X C
X+C
S
X
$
P
X-P
X
Short C
Call
Long C
Call
Short Put
S
0
X
X-P
S
0
-C
S
X
X+C
$
X-P
0
X
-P
$
S
Short C
Call
$
Sh
hort Put
Lo
ong Put
Long C
Call
Long Straddle
$
C
X C
X+C
0
S
X
$
P
0
X
S
X-P
X-P-C
0
S
X
-(P+C)
X+P+C
S
X
X+C
$
X-P
0
X
-P
$
0
-(P+C)
S
$
C
0
X C
X+C
S
X
$
P
0
X
S
X+P+C
S
X-P
$
P+C
X-P-C
X
Short C
Call
0
-C
Sh
hort Put
$
Long
Straddle
Lo
ong Put
Long C
Call
Short Straddle
X+P+C
0
X
X-P-C
S
Impact of Limited Liability
• Equity = C(V,D,t)
• Debt = V - C(V,D,t)
Equity
C(V,D,t) = V - B(D,t) + P(V,D,t)
B(D,t)
V
Applications
) Options
to abandon
– See Kensinger (1982), Myers & Majd (1984)
) Options
to shut down temporarily
– See McDonald and Siegel (1985).
Applications
) Options
to add new products
– See Majd and Pindyck (1987)
) Options
to choose the most profitable of
several activities
– See Chen,, Conover,, and Kensinger
g ((1998))
) Strategic
Options
– See Titman (1997)
– See Luerhman (1998)
Lessons
The discounted cash flow NPV,
NPV using expected
prices of the input and output commodities at
future dates, represents only the lower bound of
the project’s true NPV.
) The true NPV may be significantly higher than the
DCF estimate.
)
Lessons
) The
more volatile the relationship between
the prices of input and output commodities,
the greater the difference between the true
project NPV and the discounted cash flow
NPV.
Lessons
) The
difference between the true project
NPV and the discounted cash flow NPV is
greater:
– the more innovative the project, and
– the stronger the barriers to entry for potential
competitors.
Lessons
• A company with the same potential uses for a
system as another company, plus one or more
additional uses, will gain a higher NPV by
purchasing the system.
– Thus, the NPV of a project may differ from one
company to another,
– And companies with more flexibility have an advantage
in generating positive net present value.
Box Spread
• Long call, short put, exercise = X
• Same as buying a futures contract at X
$
0
X
S
Box Spread
• Long call, short put, exercise = X
• Short call, long put, exercise = Z
$
0
Z
X
S
Box Spread
• You have bought a futures contract at X
• And sold a futures contract at Z
$
0
Z
X
S
Box Spread
• Regardless of stock price at expiration
– you’ll buy for X, sell for Z
– net outcome is Z - X
$
0
Z-X
Z
X
S
Box Spread
• How much did you receive at the outset?
+ C(S,Z,t) - P(S,Z,t)
- C(S,X,t) + P(S,X,t)
$
0
Z
X
S
Z-X
Box Spread
• Because of Put/Call Parity, we know:
C(S,Z,t) + B(Z,t) = S + P(S,Z,t)
$
0
Z-X
Z
X
S
Box Spread
• C(S,Z,t) + B(Z,t) = S + P(S,Z,t)
Now, let’s subtract the bond from each side:
• C(S,Z,t) = S + P(S,Z,t) - B(Z,t)
$
0
Z
X
S
Z-X
Box Spread
• C(S,Z,t) = S + P(S,Z,t) - B(Z,t)
Next, let’s subtract the pput from each side:
• C(S,Z,t) - P(S,Z,t) = S - B(Z,t)
$
0
Z-X
Z
X
S
Box Spread
• So, because of Put/Call Parity, we know:
C(S,Z,t) - P(S,Z,t) = S - B(Z,t)
$
0
Z
X
S
Z-X
Box Spread
• C(S,Z,t) - P(S,Z,t) = S - B(Z,t)
Given this, we also know:
- C(S,X,t) +P(S,X,t) = - S + B(X,t)
$
0
Z-X
Z
X
S
Box Spread
So, because of Put/Call Parity, we know:
C(S,Z,t) - P(S,Z,t) = S - B(Z,t)
- C(S,X,t) + P(S,X,t) = B(X,t) - S
$
0
Z
X
S
Z-X
Box Spread
• So, building the box brings you
S - B(Z,t) + B(X,t) - S
= B(X,t) - B(Z,t)
$
0
Z-X
Z
X
S
Assessment of the Box Spread
• At time zero, receive PV of X-Z
• At expiration, cash flow is Z-X
• You have borrowed at the T-bill rate.
$
0
Z-X
Z
X
S