Transcript Option Contracts - Villanova University

Chapter 24
Option Contracts
Innovative Financial Instruments
Dr. A. DeMaskey
Derivatives

Forwards
–

fix the price or rate of an underlying asset
Options
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allow holders to decide at a later date whether
such fixing is in their best interest
Option Market Convention
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Private transactions (OTC)
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–
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–

asset illiquid
credit risk is one-sided
created in response to needs
associations of broker-dealers
Chicago Board Options Exchange (CBOE)
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Options Clearing Corporation (OCC)
Price Quotations for
Exchange-Traded Options

Equity options
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CBOE, AMEX, PHLX, PSE
typical contract for 100 shares
require secondary transaction if exercised
time premium affects pricing
Price Quotations for
Exchange-Traded Options
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Stock index options
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
Foreign currency options
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
only settle in cash
allow sale or purchase of a set amount of non-USD
currency at a fixed exchange rate
quotes in USD
Options on futures contracts (futures options)
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right, but not the obligation, to enter into a futures
contract at a later date at a predetermined price
The Fundamentals of Option
Valuation

Risk reduction tools when used as a hedge
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Theoretical value of option depends on combining it
with its underlying security to create a synthetic
riskfree portfolio.
Theoretically, it is always possible to use the option as a
perfect hedge against fluctuations in the value of the
underlying asset.
Put-Call Parity versus Option
Valuation
The portfolio implied by the put-call parity
transaction does not require special
calibration.
 Put-call parity paradigm does not require a
forecast of the future price level of the
underlying asset.

Basic Approach

Create a riskless hedge portfolio by combining options
with the underlying security.
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
Hold one share of stock long and some number of call options so
that the position is riskless.
Number of call options (h) needed is established by ensuring
portfolio has same value at expiration regardless of forecasted
stock values.
Solve for hedge ratio, h, which has both direction and
magnitude.
Assume no arbitrage opportunities exit, so that the value of
the hedge portfolio should grow at the riskfree rate.
Improving Forecast Accuracy
Subdivide interval into subintervals, and
form a stock price tree
 Work backward on each pair of possible
outcomes from the future

The Binomial Option Pricing
Model
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Two-State Option Pricing Model
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up movement or down movement
forecast stock price changes from one subperiod to
the next
•
•
•
up change (u)
down change(d)
number of subperiods
Cj 
 p C ju  1  p C jd
r
where:
rd
p
ud
The Binomial Option Pricing
Model
N
 n
N!
N j
j
j N j
Co  
p 1  p  max 0, u d
S  X r
 j 0 N  j ! j!

 

N
 n
N!
N j
j
j N j
Co  
p 1  p 
u d
S  X r
 j m  N  j ! j!


hj 
u  d S j
C
jd
 C ju 



The Black-Scholes Valuation
Model

For a European call option on a nondividend paying stock, Black and Scholes
developed the following:

C0  SNd1   X e


 RFRT
d1  lnS X   RFR  0.5
d2  d1   T 
12
N d 
2
2
T   T  
12
The Black-Scholes Valuation
Model
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Value is a function of five variables:
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Current security price
Exercise price
Time to expiration
Riskfree rate
Security price volatility
C = f(S, X, T, RFR, s)
Estimating Volatility

Mean and standard deviation of a series of
price relatives:
1N
R    Rt
 N  t 1
2
 1 
 
 Rt  R 
 N  1  t 1
N
2
Problems With
Black-Scholes Valuation
Stock prices do not change continuously.
 Arbitrageable differences between option
values and prices (due to brokerage fees,
bid-ask spreads, and inflexible position
sizes).
 Riskfree rate and volatility levels do not
remain constant until the expiration date.

Option Valuation:
Extensions and Advanced
Topics
Valuing European-style put options
 Valuing options on dividend bearing
securities
 Valuing American-style options
 Stock index options
 Foreign currency options
 Futures options
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Exotic Options
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Asian options
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Lookback options
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Terminal payoff determined by the average price of the
underlying security during the life of the contract.
Payoff = max [0, Average(S) - X]
Terminal payoff based on the maximum price of the
underlying security achieved during the life of the
contract.
Payoff = max [0, max(S) - X]
Digital options
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Terminal payoff is fixed.
Payoff = $Q if ST > 0 or $0 if ST < 0
Option Trading Strategies
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Protective put options
Covered call options
Straddles, strips, and
straps
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Strangle
Chooser options
Spreads
Range forwards
Protective Put Options

Purchase at-the-money put to hedge against
a fall in the price of a stock already held
(Long Stock) + (Long Put) = (Long Call) + (Long T-Bill)
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Insures position in equity
Preserves potential for capital gains if stock
price rises, but limits loss if stock price falls
Covered Call Option

Sale of a call option while owning the stock
(Long Stock) + (Short Call) = (Long T-Bill) + (Short Put)
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Generates income from premiums
Risks:
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Stock may be called away if price rises
Price of stock my decline by more then premium
received
Straddles, Strips, and Straps
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Straddle
– Simultaneous purchase (or sale) of a call and a put with the same
underlying asset, exercise price, and expiration date
– Buyer expects price to move a lot up or down
– Seller expects price to remain fairly stable
Long Strap
– Purchase of two calls and one put with the same exercise price
– Buyer expects price increase is more likely
Long Strip
– Purchase of two puts and one call with the same exercise price
– Buyer expects price decrease is more likely
Strangle

Simultaneous purchase or sale of a call and
a put on the same underlying security with
the same expiration date, but whose
exercise prices are both out-of-the money.
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Reduces initial cost
Price will have to move more for a profit
Modest risk-reward structure
Chooser Options
Investor selects exercise price and
expiration date, but decides after the
purchase whether the option is a put or a
call.
 This is an option with an embedded option
that is more expensive.
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Spreads
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Purchase of one contract and the sale of another,
in which the options are alike in all respects except
for one distinguishing characteristic.
Money Spread
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Sell an out-of-the money call and buy an in-the-money
call on the same stock with the same expiration date.
Calendar Spread
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Purchase and sale of two calls (or two puts) with the
same exercise price but different expiration dates.
Spreads
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Bull Spread
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Bear Spread
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Buy an in-the-money call and sell an out-of-the money call
Profitable when stock prices rise
Buy and out-of-the-money call and sell an in-the-money call
Profitable when stock prices fall
Butterfly Spread
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Combining a bull money spread and a bear money spread
Buy one in-the-money call, sell two at-the-money calls, and buy
one out-of-the-money call
Range Forward
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Combination of two option positions
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Buy an out-of-the money put and sell an out-ofthe money call of the same size
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Purchase of put is financed by sale of call
Sell upside potential with call
Obtain downside risk protection with put
Cost of hedging is reduced
Known as cylinder
The Internet
Investments Online
www.cboe.com/products
www.cboe.com//institutional/flex.html
www.finance.wat.ch/cbt/options
www.optionmax.com