文档介绍：Theory of rational option pricing
Robert C. Merton
Assistant Professor of Finance
Sloan School of Management
Massachusetts Institute of Technology
The long history of the theory of option pricing began in 1900 when the
French mathematician Louis Bachelier deduced an option pricing
formula based on the assumption that stock prices follow a Brownian
motion with zero drift. Since that time, numerous researchers have
contributed to the theory. The present paper begins by deducing a set of
restrictions on option pricing formulas from the assumption that in-
vestors prefer more to less. These restrictions are necessary conditions
for a formula to be consistent with a rational pricing theory. Attention
is given to the problems created when dividends are paid on the under-
mon stock and when the terms of the option contract can be
changed explicitly by a change in exercise price or implicitly by a shift
in the investment or capital structure policy of the firm. Since the de-
duced restrictions are not suficient to uniquely determine an option
pricing formula, additional assumptions are introduced to examine and
extend the seminal Black-Scholes theory of option pricing. Explicit
formulas for pricing both call and put options as well warrants
and the new "down-and-out" option are derived. The effects of dividends
and call provisions on the warrant price are examined. The possibilities
for further extension of the theory to the pricing of corporate liabilities
are discussed.
The theory of warrant and option pricing has been studied ex- 1. Introduction
tensively in both the academic and trade literature.' The approaches
taken range from sophisticated general equilibrium models to ad hoc
statistical fits. Because options are specialized and relatively unim-
portant financial securities, the amount of time and space devoted
to the development of a pricing theory might be questioned. One
justification is that, s