OPTIONS Method of Lines
This calculator uses the Method of Lines with Richardson extrapolation to compute the theoretical value and greeks of American-style call and put options. The Method of Lines provides a fast and accurate approach to valuing American options with continuous early exercise.
| Output | Call | Put |
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| Theoretical Value |
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| Delta |
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| Gamma |
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| Theta |
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| Vega |
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| Intrinsic Value |
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| Delta 100's |
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| Lambda |
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| Theta (-7 Days) |
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| Rho |
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| Psi |
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| Strike Sensitivity |
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| Implied Volatility |
%
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%
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The OptionsLines calculator prices American options using the Method of Lines with Richardson extrapolation. The Method of Lines discretizes the option pricing partial differential equation along the time dimension and applies Richardson extrapolation across multiple grid resolutions to achieve high accuracy with relatively few grid points. The result is a fast, accurate quasi-analytic alternative to lattice methods for American options.
Inputs
Richardson Point Count: The number of Richardson extrapolation points used in the Method of Lines. Higher values increase accuracy at the cost of computation time. Typical values are between 3 and 8.
Underlying Price: The current price of the underlying asset.
Exercise Price: The price at which the asset can be bought (call) or sold (put).
Years to Expiration: 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.
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 American option based on the Method of Lines.
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.
Intrinsic Value The intrinsic value of the option.
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.
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.
Strike Sensitivity Measures how sensitive the option price is to changes in the strike price.
