Dr. Scott Brown
Stock Options
Introduction
 Call & Put prices are highly inter-dependent and are
not arbitrarily chosen.
 Put Call Parity is a strong mathematical relationship
that describes the connection between calls and puts.
Critical for understanding the mechanics of the
options market and how options are priced.
 “Parity” – means equivalence.
 Parity Relationships simply shows the connections
between two or more variables.
Put-Call Parity Equation
 Formula: S + P – C = Pv (E)
 S – Stock Price
 P – Put Price
 C – Call Price
 Pv(E) – Present Value of the Exercise Price.
 This formula says that values of long stock + long put +
short call are equal to the present value of the exercise.
Put-Call Parity Equation (Cont.)
Example:
Portfolio
Strike Price
Stock
$50 Put
$50 Call
Total Value
35
35
15
0
50
40
40
10
0
50
45
45
5
0
50
50
50
0
0
50
55
55
0
5
50
60
60
0
10
50
65
65
0
15
50
• The “total value” column shows this portfolio always
sums to $50 no matter what happens to the stock’s
price at expiration.
Put-Call Parity Equation (Cont.)
 Formula: S + P = C + Pv (E)
 Left-hand side of equation: represents an investor who
owns stocks plus a protective put.
 Right-Hand side of equation: represents an investor who
owns a call option plus a deposit of cash, Pv (E).
 Formula tells us that an investor who buys stock and a
put is financially doing the same thing as someone
who buys a call and deposits sufficient cash to grow
the value to the exercise price at expiration by earning
the risk-free rate.
Put-Call Parity Equation (Cont.)
 Formula: C = S – Pv(E) + P
 Shows us that a long call option is the same thing as
owning stock (+S), borrowing money, -Pv (E), and also
owning a put (+P)
 When you buy a call, you are borrowing money to buy
stock and also buying a put option.
Put-Call Parity Equation (Cont.)
Example:
Portfolio A
Stock Price
$50 Call
Stock
Pay $50
Exercise
Total Value
35
0
35
50
-15
40
0
40
50
-10
45
0
45
50
-5
50
0
50
50
0
55
5
55
50
5
60
10
60
50
10
65
15 call performs better
65
50 A if the stock15is
• The $50
than Portfolio
below $50 at expiration since it doesn’t lose dollar-for-dollar with
the stock, but both perform equally if the stock is at $50 or
higher.
Synthetic Options
 Not a type of option such as calls or puts.
 Are ways of creating positions that look, feel, and
behave like one asset but are constructed from entirely
different assets.
 The benefit of this is that one form may be more liquid
or more efficient than another.
 To create a synthetic option all we need to do is refer to
any of the put-call parity formulas and algebraically
solve for the call option.
Synthetic Options (Cont.)
 Example:
 Original Formula: S + P – C = Pv (E)
 Synthetic Long Call Option: C = S – Pv (E) + P

If you borrow the present value of the exercise price and buy
stock plus buy a put, you have created a synthetic call option.
All Synthetic Combinations
Asset
Synthetic Equivalent
Long Stock
Long Call + Short Put
Short Stock
Short Call + Long Put
Long Call
Long Stock + Long Put
Short Call
Short Stock + Short Put
Long Put
Short Stock + Long Call
Short Put
Long Stock + Short Call
Real Applications for Synthetics
 When you are long the call, rather than exercising it,
you could, instead, sell the same strike put.
 While the synthetic long stock position does not allow
you to collect the dividend of the stock, it does let you
collect the premium of the put.
 This put premium will be of greater value than the
dividend on the stock while either choice exposes you
to the same downside risk.
Creating a Call Option
 Assume you wish to buy a stock but are afraid to because of




the recent volatility or because you don’t have enough
money.
So rather than buy stock, you decide to buy a call option.
Once your order is received, the market maker must create
a call option.
In order to create that call, the market maker must buy
stock and buy a put, which is a synthetic long call. He can
then transfer that over to you by selling the call.
When he sells you the call, he has effectively transferred
the long stock plus long put positions over to you.
Are Options Bad for the Market?
 Many investors adamantly refuse to buy or sell options
because they hear how “speculative” they are. They
insist on holding only stocks.
 If you refuse to use options, you are speculating. By
buying stocks, you are speculating that nothing will go
wrong with your long stock position.
 It can be argued that investors who don’t use options
are among the most speculative of investors.
Valuing Corporate Securities as
Options
 Securities:
 Consider a firm that has issued a zero-coupon bond that
matures to a value of $1,000,000 in five years.
 Payoffs for stockholders and bondholders at maturity:


If value of the firm is less than $1M, say, $800k:
 Bondholders get: $800,000
 Stockholders get: $0
 Total Value of Firm: $800,000
If value of the firm is greater than $1M, say, $1.2M at maturity:
 Bondholders get: $1,000,000
 Stockholders get: $200,000
 Total Value of Firm: $1,200,000
Valuing Corporate Securities as
Options
 Options: (Cont.)
 Assume you own 100 shares of stock and have sold, or
written, a $100 call option against it.


At expiration, if the value of the stock is less than $100, say
$80:
 You get: $80
 Call buyer: $0
 Total value of your position is: $80
If the value of the stock is greater than $100, say $120 at
expiration:
 You get: $100
 Call buyer gets: $20
 Total Value of positions is: $120
Using
Black-Scholes
Model
 Recall thethe
put-call
parity formula:
 Stock + Put – Call = Present value of the exercise price.
 Rewritten for above corporation at maturity as:
 Stock + Put – Call = Total Value of Debt.
 Stock – Call = Total value of Debt – Put.
 So the Black-Scholes Option Pricing Model tells us the
value of the covered call position (left side) is equal to the
debt at maturity with a put written against it (right side).
 Options allow you to do what stockholders have always
done – but for a lot less money. Why? Because they have
strike prices. They allow you to partition the unlimited
range of possible stock prices into segments that you wish
to control.
Summary
 Stock + Put – Present value of the exercise price =




Risk-free position (Conversion).
The opposite of a Conversion is a Reversal (Short – Put
+ Present Value of exercise price).
The value of a put option equals the time value of the
call (above the cost-of-carry).
Any synthetic position can be found by solving the
formula S+P-C = Present value of E for a single
variable.
Buying calls is synthetically equivalent to buying stock
on margin and buying a put for insurance.
Disclaimer

DISCLAIMER: THE DATA CONTAINED HEREIN IS BELIEVED TO BE RELIABLE BUT CANNOT BE GUARANTEED
AS TO RELIABILITY, ACCURACY, OR COMPLETENESS; AND, AS SUCH ARE SUBJECT TO CHANGE WITHOUT
NOTICE. WE WILL NOT BE RESPONSIBLE FOR ANYTHING, WHICH MAY RESULT FROM RELIANCE ON THIS
DATA OR THE OPINIONS EXPRESSED HERE IN. DISCLOSURE OF RISK: THE RISK OF LOSS IN TRADING
FUTURES, FOREX AND OPTIONS CAN BE SUBSTANTIAL; THEREFORE, ONLY GENUINE RISK FUNDS SHOULD
BE USED. FUTURES, FOREX AND OPTIONS MAY NOT BE SUITABLE INVESTMENTS FOR ALL INDIVIDUALS,
AND INDIVIDUALS SHOULD CAREFULLY CONSIDER THEIR FINANCIAL CONDITION IN DECIDING WHETHER
TO TRADE. OPTION TRADERS SHOULD BE AWARE THAT THE EXERCISE OF A LONG OPTION WOULD RESULT
IN A FUTURES OR FOREX POSITION.HYPOTHETICAL PERFORMANCE RESULTS HAVE MANY INHERENT
LIMITATIONS, SOME OF WHICH ARE DESCRIBED BELOW. NO REPRESENTATION IS BEING MADE THAT ANY
ACCOUNT WILL, OR IS LIKELY TO, ACHIEVE PROFITS OR LOSSES SIMILAR TO THOSE SHOWN. IN FACT,
THERE ARE FREQUENTLY SHARP DIFFERENCES BETWEEN HYPOTHETICAL PERFORMANCE RESULTS AND
THE ACTUAL RESULTS SUBSEQUENTLY ACHIEVED BY ANY PARTICULAR TRADING PROGRAM. ONE OF THE
LIMITATIONS OF HYPOTHETICAL PERFORMANCE RESULTS IS THAT THEY ARE GENERALLY PREPARED WITH
THE BENEFIT OF HINDSIGHT. IN ADDITION, HYPOTHETICAL TRADING DOES NOT INVOLVE FINANCIAL
RISK, AND NO HYPOTHETICAL TRADING RECORD CAN COMPLETELY ACCOUNT FOR THE IMPACT OF
FINANCIAL RISK IN ACTUAL TRADING. FOR EXAMPLE, THE ABILITY TO WITHSTAND LOSSES OR TO ADHERE
TO A PARTICULAR TRADING PROGRAM, IN SPITE OF TRADING LOSSES, ARE MATERIAL POINTS WHICH CAN
ALSO ADVERSELY AFFECT ACTUAL TRADING RESULTS. THERE ARE NUMEROUS OTHER FACTORS RELATED
TO THE MARKETS, IN GENERAL, OR TO THE IMPLEMENTATION OF ANY SPECIFIC TRADING PROGRAM
WHICH CANNOT BE FULLY ACCOUNTED FOR IN THE PREPARATION OF HYPOTHETICAL PERFORMANCE
RESULTS AND ALL OF WHICH CAN ADVERSELY AFFECT ACTUAL TRADING RESULTS. PS. In our opinion, we
believe, it may be possible, that heavy smoking and drinking may be hazardous to your health. If you choose to smoke
and drink while trading, The Delano Max Wealth Institute nor Dr. Scott Brown is liable for any damage it may cause. If
you slip and fall on the ice, we're not liable for that either.