# Option models This article's tone or style may not reflect the encyclopedic tone used on Wikipedia.

American Exercise - price given smile These functions take as their starting point an implied volatility smile. Whereas the Black-Scholes model assumes that the volatility is constant, the market-observed behavior is that it generally varies both with strike price and with maturity.

Option models can be accounted for through the theory of Local Volatility, by assuming that the volatility of the underlying stochastic process is a function both of asset price and of time. To price an American option from the implied volatility smile, the local volatility function is first computed, and then used in conjunction with finite difference methods on the underlying no-arbitrage partial differential equation.

In addition to standard vanilla options, these functions can also be used to price option trading strategies, portfolios of vanilla options, and options with arbitrary piecewise linear payoffs.

### Option Pricing Models and Volatility Using Excel-VBA

The function uses local volatility in conjunction with finite difference methods on the underlying no-arbitrage PDE, and handles European and American exercise features as well as forward valuation. European Exercise — price given process These functions depart from the Black-Scholes assumption in that they allow for non-lognormal underlying stochastic processes. Whereas the volatility in the Black-Scholes model is constant, here it is a function option models the underlying asset price. Hence the name Local Volatility.

### A Real-World Way to Manage Real Options

The supported local volatility functions are those which define the lognormal, normal, CEV and shifted lognormal stochastic processes. In addition to standard vanilla options, these functions can also be used to price option trading strategies, portfolios of vanilla options, and options with arbitrary piecewise linear payoffs, for any of these processes. The function uses closed-form solutions for standard processes. European Exercise - price given smile These functions take as their starting point an implied volatility smile.

### 7. Value At Risk (VAR) Models

To price a European option from the implied volatility smile, the relevant values of the implied volatility are first computed by interpolation from the smile data points. These values are then used in the Black-Scholes formula. The function interpolates implied volatilities from the smile to use in the Black-Scholes formula.