OPTIONS Jump-Diffusion
This calculator uses the Merton jump-diffusion option pricing model to compute the theoretical value and greeks of European-style call and put options. The model extends Black-Scholes by adding a Poisson jump process to capture sudden, discontinuous moves in the underlying asset price.
| 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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The OptionsJump function in FinTools XL prices European options using the Merton jump-diffusion model. In this framework, the underlying asset price follows geometric Brownian motion with an additional Poisson-driven jump component. This combination produces fatter tails and a more realistic implied volatility smile than the lognormal Black-Scholes model.
Inputs
Model: The variant of the 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 diffusion component of the underlying asset's returns.
Jump Size: The mean log-jump size in the Merton jump-diffusion model. Negative values represent average downward jumps, common in equity markets.
Num Jumps: The average number of jumps per year (the Poisson intensity).
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 jump-diffusion model.
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.
