The methodologies which they introduced have been expanded for use in pricing a wide variety of derivative instruments and contingent claims. A breakthrough of this work was the realization that the price of an option is not dependent on investor risk preferences. This means that investors can agree upon a fair value for an option without regard for their respective aversions to risk. This realization lead to the methodology of risk neutral valuation for derivative instruments. There are no transaction costs or taxes .
Markets trade continuously i.e. there are no sudden jumps in prices .
The risk-free rate is constant and the same for all maturities.