Pricing of Financial Derivatives

A financial derivative, for example an option, is an instrument (contract) whose value depends on the values of some underlying variables, where the underlying can be a commodity, an interest rate, stock, a stock index, a currency, to mention just a few examples. The financial derivatives market is enormous and is regularly reported to be worth $500 trillion. Derivatives provide an efficient way to reduce risk related to changes in the value of the underlying variable. Once a financial derivative is defined the first question is the following: “what is the fair price that the seller of the derivative should charge to the buyer?” Eventually this question is answered, at least for options, by the so-called Black and Scholes formula. The purpose of this short note is to display in very simplified contexts the main underlying argument leading up to the fair price of a derivative, namely that markets eliminate any opportunity for risk-free profits (the principle of no arbitrage).