129 The Concepts underlying Black-scholes The option price and the stock price depend on the same underlying source of uncertainty We can form a portfolio consisting of the stock and the option which eliminates this source of uncertainty The portfolio is instantaneously riskless and must instantaneously earn the risk-free rate This leads to the black-Scholes differential equation Options, Futures, and Other Derivatives, Sth Edition C 2002 by John C. Hull12.9 Options, Futures, and Other Derivatives, 5th Edition © 2002 by John C. Hull 9 The Concepts Underlying Black-Scholes • The option price and the stock price depend on the same underlying source of uncertainty • We can form a portfolio consisting of the stock and the option which eliminates this source of uncertainty • The portfolio is instantaneously riskless and must instantaneously earn the risk-free rate • This leads to the Black-Scholes differential equation