# Closed form european option prices for a variance gamma process with a randomly distributed drift, volatility, and variance rate

Does an option pricing model with a closed form European option price exist that takes into account randomly distributed drift, volatility, and variance rate?

I prefer a modification to the variance gamma model, but a modification to any other model is welcome.

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What about Peter Carrs FFT option pricing? – pyCthon Nov 19 '13 at 22:20
@pyCthon Please bear with me as this isn't my specialty. I think that paper shows how to calculate VG with FFT instead of the current closed form that involves a quadrature. I am asking that the VG factors be assumed to be randomly distributed as well as prices. Should I edit? Thank you! – user6500 Nov 20 '13 at 17:36
your right sorry was late and i miss read the question – pyCthon Nov 21 '13 at 4:02

In general, there cannot be a closed-form solution of a random coefficients VG model. The reason is the drift-restriction that needs to be imposed to ensure that the discounted price process is a martingale under the risk-neutral measure. Using the bank account as numeraire, the restriction is $$\frac{1}{\beta} > \theta + \frac{\sigma^2}{2}$$ where $\beta$ is the variance rate of the gamma subordinator, and $\theta$ and $\sigma$ are the drift and diffusion coefficient of the driving Brownian motion.