35 lines
2.3 KiB
Plaintext
35 lines
2.3 KiB
Plaintext
32 • The Intelligent Option Investor
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This example illustrates precisely the process on which the BSM and
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all other statistically based option pricing formulas work. The BSM has a
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fixed number of inputs regarding the underlying asset and the contract itself.
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Inputting these variables into the BSM generates a range of likely future values
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for the price of the underlying security and for the statistical probability of the
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security reaching each price. The statistical probability of the security reach-
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ing a certain price (that certain price being a strike price at which we are inter-
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ested in buying or selling an option) is directly tied to the value of the option.
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Now that you have a feel for the BSM on a conceptual dining-
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reservation level, let’s dig into a specific stock-related example.
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Step-by-Step Method for Predicting Future Stock
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Price Ranges—BSM-Style
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In order to understand the process by which the BSM generates stock price
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predictions, we should first look at the assumptions underlying the model.
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We will investigate the assumptions, their tested veracity, and their impli-
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cations in Chapter 3, but first let us just accept at face value what Messrs.
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Black, Scholes, and Merton take as axiomatic.
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According to the BSM,
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• Securities markets are “efficient” in that market prices perfectly
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reflect all publicly available information about the securities. This
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implies that the current market price of a stock represents its fair
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value. New information regarding the securities is equally likely to
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be positive as negative; as such, asset prices are as likely to move up
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as they are to move down.
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• Stock prices drift upward over time. This drift cannot exceed the
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risk-free rate of return or arbitrage opportunities will be available.
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• Asset price movements are random and their percentage returns
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follow a normal (Gaussian) distribution.
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• There are no restrictions on short selling, and all hedgers can bor -
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row at the risk-free rate. There are no transaction costs or taxes.
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Trading never closes (24/7), and stock prices are mathematically
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continuous (i.e., they never gap up or down), arbitrage opportuni-
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ties cannot persist, and you can trade infinitely small increments of
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shares at infinitely small increments of prices. |