BLACK-SCHOLES OPTION PRICING MODEL
The Black-Scholes model prices the "fair value"
of an option. Current "appropriate" value of an option is calculated
on the basis of historical data and calculated probabilities of
future stock prices. The basic formula is presented below:
Call Premium = Expected Future Stock Price - Expected Cost
of Exercising Option
The Black-Scholes model adds
the following adjustments to this formula:
· for the possibility of a range of future stock prices,
· for the net present value of the exercising cost,
· for the possibility that the exercise price may become higher
than the underlying stock price, etc.
The option
always costs more than the differential between the exercise price
and current stock price. The difference exists because the future
underlying stock value may be more or less than $100. If the underlying
stock rises to $104, the call premium rises to more than $8. The
cost of the option above and beyond the difference between the
strike and the underlying stock price is what you pay for the
possibility of a higher price. The Black-Scholes model quantifies
the possible future underlying stock prices.
No one knows
the future value of a stock with certainty. The Black-Scholes
model assumes a standard normalized distribution curve for future
stock prices. The sigma calculation for this curve, which determines
the height or width of the standard curve, is derived from historical
stock data. The more volatile a stock has been, the higher probability
it has of being far from today's price on expiration date. To
be compensated for this, the seller needs to receive more for
the option, and the buyer needs to pay more for the possibility.
Historical data is used to predict future stock prices. In this
respect, Black-Scholes modeling has the same problems as technical
analysis: the past doesn't always predict the future.
The Black-Scholes
option model is primarily used to search for underpriced option
to buy, or overpriced option to sell and to hedge a portfolio
to reduce risk (lower volatility). Options can be sold to offset
losses in the underlying stocks.
The Black-Scholes model does have weak points.
The model uses normal standardized probability curves for future
stock price approximations. While they can be considered accurate
at any given time of pricing, the model discounts prices with
low probabilities. But the lower future price with a low probability
may still turn out to be the future price.
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