OPTIONS Black-Scholes
The OptionsBS function in FinTools XL utilizes the Black-Scholes model to calculate the theoretical price and risk sensitivities of European options.
Inputs
Model: The variant of the Black-Scholes model to use.
- European model: This model assumes that the option can only be exercised at expiration, not before.
- Quasi-American model: This model is particularly useful for underlying assets that yield discrete cash flows, such as dividend-paying equities. It allows the option holder to exercise the option early, but only at specific dates.
Underlying Price: The current price of the underlying asset.
Exercise Price: The price at which the asset can be bought (call) or sold (put) at.
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.
MarketOptionPrice: The traded price of the option in the market for calculating Implied Volatility.
Outputs
Theoretical Value The calculated market Theoretical value of the option based on the Black-Scholes 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.
Gamma 1% Gamma sensitivity to a 1% change 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 Black-Scholes model.
Intrinsic Value The intrinsic value of the option, calculated as the difference between the underlying asset's price and the exercise price.
Time Value The part of the option price that exceeds the intrinsic value, representing the potential for further gains in the option’s value over time.
Zero Volatility The value of the option if the underlying asset's volatility were to approach zero.
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.