Valuation models

Main article: Valuation of options

The value of an option can be estimated using a variety of quantitative techniques based on the concept of risk neutral pricing and using stochastic calculus. The most basic model is the Black-Scholesmodel. More sophisticated models are used to model the volatility smile. These models are implemented using a variety of numerical techniques.^[7] In general, standard option valuation models depend on the following factors:

• The current market price of the underlying security,
• the strike price of the option, particularly in relation to the current market price of the underlier (in the money vs. out of the money),
• the cost of holding a position in the underlying security, including interest and dividends,
• the time to expiration together with any restrictions on when exercise may occur, and
• an estimate of the future volatility of the underlying security's price over the life of the option.

More advanced models can require additional factors, such as an estimate of how volatility changes over time and for various underlying price levels, or the dynamics of stochastic interest rates.

The following are some of the principal valuation techniques used in practice to evaluate option contracts.