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TRANSCRIPT
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Black- Scholes Model
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Introduction
The Black-Scholes option pricing model
(BSOPM) has been one of the mostimportant developments in finance in the
last 50 years Has provided a good understanding of what
options should sell for Has made options more attractive to individual
and institutional investors
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The Model
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The Model (contd)
Variable definitions:S = current stock price
K = option strike price
e = base of natural logarithms
R = riskless interest rate
T = time until option expiration
= standard deviation (sigma) of returns onthe underlying security
ln = natural logarithm
N(d1) and
N(d2) = cumulative standard normal distributionunctions
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Development and Assumptions
of the Model
Derivation from:
Physics Mathematical short cuts
Arbitrage arguments
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Determinants of the Option
Premium
Striking price
Time until expiration Stock price
Volatility
DividendsRisk-free interest rate
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Time Until Expiration
The longer the time until expiration, the
more the option is worth The option premium increases for more distant
expirations for puts and calls
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Striking Price
The lower the striking price for a given
stock, the more the option should be worth Because a call option lets you buy at a
predetermined striking price
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Stock Price
The higher the stock price, the more a given
call option is worth A call option holder benefits from a rise in the
stock price
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Volatility
The greater the price volatility, the more the
option is worth.
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Dividends
A company that pays a large dividend will
have a smaller option premium than acompany with a lower dividend, everything
else being equal
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Risk-Free Interest Rate
The higher the risk-free interest rate, the
higher the option premium, everything elsebeing equal.
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Assumptions of the Black-
Scholes Model
The stock pays no dividends during the
options life European exercise style
Markets are efficient
No transaction costs
Interest rates remain constant
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European Exercise Style
A European option can only be exercised
on the expiration date American options are more valuable than
European options
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Markets Are Efficient
The BSOPM assumes informational
efficiency People cannot predict the direction of the market
or of an individual stock
Put/call parity implies that you and everyone else
will agree on the option premium, regardless ofwhether you are bullish or bearish
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No Transaction Costs
There are no commissions and bid-ask
spreads.
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Interest Rates Remain Constant
There is no real riskfree interest rate
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Problems Using the Black-
Scholes Model
Does not work well with options that are
deep-in-the-money or substantially out-of-the-money
Produces biased values for very low or
very high volatility stocks
Increases as the time until expiration increases
May yield unreasonable values when an
option has only a few days of life remaining