What is the variance gamma characteristic function?

phi_VG(u) = (1 - i*u*theta*nu + sigma^2*nu*u^2/2)^(-T/nu), which can be inverted via FFT to get option prices. The VG process is a Brownian motion with drift subordinated to a gamma time change.

How does theta control skewness in VG?

Negative theta produces negative skewness (left-skewed returns), consistent with observed equity market skew. Setting theta=0 gives a symmetric process with only excess kurtosis.

Variance Gamma Process Skewness and Kurtosis Calculator

Price options under the Variance Gamma (VG) process. Three parameters: sigma (volatility), nu (variance rate of gamma time change), theta (skewness). Captures fat tails and skew.

Principal ($)

Annual Rate (%)

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Compounding / Year

$ Finance Disclaimer: These calculators are for educational and illustrative purposes only. Results do not constitute financial advice. Consult a licensed financial advisor before making investment or borrowing decisions.

How to Use

Enter the values for the scenario you are assessing. Price options under the Variance Gamma (VG) process. Three parameters: sigma (volatility), nu (variance rate of gamma time change), theta (skewness). Captures fat tails and skew. Use the variance gamma process result to inform your calculation.

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Variance Gamma Process Skewness and Kurtosis Calculator

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Frequently Asked Questions

What is the variance gamma characteristic function?

How does theta control skewness in VG?