Option Pricing. An option is a contract entitling the holder to buy or sell designated security at or within a certain period of time at a particular price. Options contracts are characterized by a nonlinear payoff because the price depends on a nonlinear function of the underlying. Thus, it is impossible to price without a model for the underlying but the assumptions of mathematical finance (not moving the market; liquidity, jumps; shorting; fractional quantities; no transaction costs) substantially make difficult to determine a single model always valid with the changing market conditions.