The Pricing of Options and Corporate Liabilities

Fischer Black/ University of Chicago
Myron Scholes/ MIT

The Valuation Assumption
a) The short-term interest rate is known and is constant through time.
b) The stock price follows a random walk in continuous time with a variance rate proportional to the square of the stock price. Thus the distribution of possible stock prices at the end of any finite interval is lognormal. The variance rate of the return on the stock is constant.
c) The stock pays no dividends or other distribution.
d) The option is "European", that is, it can only be exercised at maturity.
e) There are no transaction cost in buying or selling the stock or option.
f) It is possible to borrow any fraction of the price of a security to buy it or to hold it, at the short-term interest rate.
g) There are no penalties to short selling.

幹後面的數學我看不懂...........