Merton model is a mathematical model for the dynamics of a financial market containing derivative investment instruments. The key idea behind the model is to hedge the forex online option trading calculator currency exchange11 by buying and selling the underlying asset in just the right way and, as a consequence, to eliminate risk. The model’s assumptions have been relaxed and generalized in many directions, leading to a plethora of models that are currently used in derivative pricing and risk management. Scholes formula, that are frequently used by market participants, as distinguished from the actual prices.

Scholes formula has only one parameter that cannot be directly observed in the market: the average future volatility of the underlying asset, though it can be found from the price of other options. Scholes model assumes that the market consists of at least one risky asset, usually called the stock, and one riskless asset, usually called the money market, cash, or bond. The rate of return on the riskless asset is constant and thus called the risk-free interest rate. The stock does not pay a dividend.

It is possible to borrow and lend any amount, even fractional, of cash at the riskless rate. With these assumptions holding, suppose there is a derivative security also trading in this market. It is a surprising fact that the derivative’s price is completely determined at the current time, even though we do not know what path the stock price will take in the future. Several of these assumptions of the original model have been removed in subsequent extensions of the model.