TABLE OF CONTENTS The celebrated Black Scholes option pricing formula depends fundamentally on the assumption that stock prices are log-normally distributed. While it is not possible to develop an option pricing formula without making a distributional assumption, a number of distribution-free properties can still be identified. Several of these basic properties of options have already been developed in previous chapters. For example, the max [ ] function associated with the expiration date value of an option describes one distribution-free property of options. Put call parity is another property. For completeness, even those properties already derived will be listed here.
Given the notation provided in Chapter 1, Section I, unless otherwise stated, the following properties are stated for the case of a non-dividend-paying stock (or deliverable commodity that does not earn a carry return). This case is examined for traditional reasons, as early statements of the distribution-free properties of options (e.g., Merton, 1973) used this case. Extensions to other cases, such as options on dividend-paying stocks, spot commodities, and futures contracts, are provided when appropriate, either in this section or elsewhere (e.g., in the discussion of early exercise of American currency options in Chapter 8, Section IV). The distribution-free properties rely on conventional perfect markets assumptions: no transaction costs, no taxes, and riskless lending and borrowing at the constant riskless interest rate.
Property 1: Non-Negative Prices
This property holds for every t ? T.
Property 2: Expiration Date Value
As with other properties...
