Derivative pricing is based on the hedge portfolio concept: combination of a derivative and underlying such that risk is eliminated. The hedge portfolio should earn the risk-free rate. A derivative’s value is the price of the derivative that forces the hedge portfolio to earn the risk-free rate. It is also important to understand the concepts of storage and arbitrage.
Certain kinds of derivatives like forward/future contracts where the underlying is a commodity like food grain, gold, or oil require storage. Storage incurs costs and consequently the forward/future price must be adjusted upwards.
Arbitrage is the condition that if two equivalent assets or derivatives or combinations of assets and derivatives sell for different prices, then this leads to an opportunity to buy at a low price and sell at a high price, thereby earning a risk-free profit without committing any capital.
Let us consider an example of a stock selling in two markets A and B. The stock is selling in market A for $51 and in market B for $52. An arbitrage opportunity exists here as an investor can buy the stock at a lower price in market A and sell it at a higher price in market B.
The combined actions of arbitrageurs bring about a convergence of prices. Hence, arbitrage leads to the law of one price: transactions that produce equivalent results must sell for equivalent prices. If more people buy the stock in market A, and more people sell the stock in market B, the stock’s price will converge in both the markets.