OPTIONS Forward Start Black-Scholes
This calculator uses the Forward-Start variant of the Black-Scholes option pricing model to compute the theoretical value and greeks of forward-start European-style call and put options. A forward-start option is purchased today but its strike price is set on a future issue date as a ratio of the underlying price at that date. To generate results, enter the Inputs and click Calculate.
| Output | Call | Put |
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| Theoretical Value |
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| Delta |
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| Gamma |
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The ForwardStartBS function in FinTools XL prices forward-start European options. The strike price of a forward-start option is determined at a specified issue date in the future as a ratio of the underlying asset price at that date. These options are commonly embedded in employee compensation plans, cliquet structures, and reset features in structured products.
Inputs
Underlying Price: The current price of the underlying asset.
Exercise Ratio: The ratio of the future exercise price to the underlying price at the issue date. A ratio of 1.0 corresponds to an at-the-money strike at issue.
Time to Expiration: The time to expiration from today (decimal fraction of a year)
Years to Start The time to the start of the option from today (decimal fraction of a year)
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.
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 forward-start option.
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.
