The OptionsCEV function in FinTools XL utilizes the Constant Elasticity of Variance model, an extension of the Black-Scholes framework in which the instantaneous volatility of the underlying asset is a function of its price. By choosing the elasticity parameter, the model can replicate the leverage effect commonly observed in equity markets and capture skew in implied volatility.

Inputs

Model: The variant of the CEV model to use for the valuation.

Underlying Price: The current price of the underlying asset.

Exercise Price: The price at which the asset can be bought (call) or sold (put).

Time: The time to expiration of the option, expressed in years, between the Value Date and the Expiration Date.

Interest Rate: The risk-free interest rate.

Yield Rate: The annual dividend yield expressed as a percentage of the underlying asset price.

Volatility: The annualized volatility of the underlying asset's returns, expressed as a decimal.

Rho Elasticity: The elasticity parameter of the CEV model. A value of 1 reduces the model to standard lognormal Black-Scholes; a value of 0 corresponds to the absolute (Bachelier) diffusion. Values between 0 and 1 capture the leverage effect for equities.

Max Term Count: The maximum number of terms used in the CEV series expansion. Higher values increase accuracy at the cost of computation time.

Market Option Price: The traded price of the option in the market for calculating implied volatility.

Outputs

Theoretical Value The calculated theoretical value of the option based on the CEV model parameters.

Delta Measures the rate of change of the option price with respect to changes in the underlying asset's price.

Gamma Measures the rate of change in Delta with respect to changes in the underlying asset's price.

Theta Measures the sensitivity of the option price to the passage of time (time decay).

Vega Measures the sensitivity of the option price to changes in the volatility of the underlying asset.

Implied Volatility The volatility implied by the market price of the option, based on the CEV model.

Intrinsic Value The intrinsic value of the option, calculated as the difference between the underlying asset's price and the exercise price.

Delta 100's The delta of the option multiplied by 100.

Lambda Measures the percentage change in option value per percentage change in the underlying asset price.

Theta (-7 Days) Theta calculated over a shorter timeframe of 7 days, providing a more immediate view of time decay.

Rho Measures the sensitivity of the option price to changes in the risk-free interest rate.

Psi Measures the sensitivity of the option price to changes in the dividend yield of the underlying asset.

Strike Sensitivity Measures how sensitive the option price is to changes in the strike price.