Options

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Options
Professor Dr. Rainer Stachuletz Corporate
Finance Berlin School of Economics
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Economic Benefits Provided by Options
Derivative securities are instruments that derive
their value from the value of other assets.
Derivatives include options, futures, and swaps.
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Options Vocabulary
Strike price or exercise price the price
specified for purchase or sale in an option
contract
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Options Vocabulary
Neither trade usually has any connection to the
underlying firm.
Can trade options on an exchange (such as CBOE)
or in the over-the-counter market.
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Moneyness of Options
S current stock price X strike price
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Option Quotations
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Intrinsic and TimeValue of Options
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Payoff Diagrams
Shows value of an option on the expiration date
Y-axis plots exercise value or intrinsic value
X-axis plots price of underlying asset
Payoff the price of the option at expiration date
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Long Call Option Payoffs
x 75, premium 8
10
Short Call Option Payoffs
75
83
x 75, premium 8
8
stock price
Payoff
Payoff at expiration
Net payoff
slope -1

• Both long and short positions have zero net
  payoff at a price of 83
• On net basis, buyer of the call makes a profit
  when the price exceeds 83 seller of the call
  makes a profit when price is below 83

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Long Put Option Payoffs
x 75, premium 7
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Short Put Option Payoffs
Net payoff
7
68
Stock price
75
Payoff at expiration
Payoff
-75
x 75, premium 7
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Portfolios of Options
Look at payoff diagrams for combinations of
options rather than just one
Shows the range of potential strategies made
possible by options
Some positions can be a form of portfolio
insurance.
Some strategies allow investor to speculate on
the volatility (or lack thereof) of a stock
rather than betting on which direction it will
move.
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Portfolio Containing 1 Call and 1 Put (Long
Straddle)
Call x 30, premium 4.5, Put x 30,
premium 3.5

• Buy a put and a call on the same stock at the
  same strike price and the same expiration date
• Profits come with large price changes in either
  direction.
• Positive net payoff if the price rises above 38
  or falls below 22

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Option Strategies (Long Straddle)
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Option Strategies (Long Strangle)

• - Long call and long put (different exercise
  prices)
• - Strategy for profiting from high volatility

Strangle
Position Value
Share Price
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Option StrategiesSynthetic Long Future
Synthetic Long Future(Long Call Short Put)
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Option StrategiesSynthetic Short Future
Synthetic Short Future(Short Call Long Put)
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Option Strategies (Short Butterfly)
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Other Option Portfolio Payoffs
Now look at portfolios containing options,
stocks, and bonds
Looking at these payoffs will help lead us to an
important option pricing relationship put-call
parity.
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Gross Payoff of Stock Put

• Position allows investor to profit if stock price
  rises above X.
• If stock price falls below X, portfolio provides
  protection put option allows investor to sell
  at a price no lower than X.

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Gross Payoff of Bond Call
X strike price of call and face value of bond
x
Payoff at expiration
x
stock price

• The bond assures a minimum payoff of X
• The call allows for a higher payoff if the stock
  price rises

This payoff diagram and the preceding one are
identical!
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Put-Call Parity
Future payoffs of stockput are identical to
payoffs of bondcall provided

• Put and call have same exercise price and
  expiration date
• Underlying stock pays no dividends during life of
  options
• Put and call are European options
• Bond is risk-free, zero-coupon, price at maturity
  strike (X),
• Bond matures when options expire.

If two assets A and B, have same future payoffs
with certainty, then they should sell for the
same price now

• Price of put price of stock Price of call
  price of bond

Put S Call B
Put Call B - S
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Factors Affecting Option Prices(holding other
factors equal)
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EvaluationFramework
Assume that a stock is currently quoted at 150 .
If nothing happens over the coming year, the
stocks price will also be at 150 in one year.
The one-year risk free rate is at 10. Under this
assumptions, a Call Option, maturing one year
from now with a strike of 120 is easy to value
The Intrinsic Value of the Call (S-X) is 41,42
!!
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EvaluationFramework
Under this conditions, the Call Option Pricing
Model is like
This price is a fair price, as it does not allow
to gain risk-free profits from arbitrage-trading

• One could also borrow money to buy the stock now.
  At a risk free rate of 10 p.a. the cost of
  borrowing over one year will add to ((150 x
  (2,7184 0,10) - 1)) 15.7764 .
• The other way round borrowing money to buy the
  option - and one year later the stock leads to
  the same borrowing costs Borrowing of 41,42 at
  10 means to pay back 41,42 x 2,7184 0,10
  45,7764 after one year. Netted with the profit
  from the options exercise at a strike of 120
  (150 - 120 30 ), the costs add to 15.7764
  .

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Determinantsof Option Prices
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Price Value Chart
Greeks show the sensitivity of the option price
referring to
D DeltaCall Price and Spot Price
G GammaDelta
? ThetaCall Price and Time to Expiration
K Kappa / VegaCall Price and Volatility
R RhoCall Price and Int. Rate
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Factors Affecting Option PricesVolatility
The 2nd call option is more valuableupside is
better, downside the same as the 1st option.