Option Pricing
The VG process can be advantageous to use when pricing options since it allows for a wider modeling of skewness and kurtosis than the Brownian motion does. As such the variance gamma model allows to consistently price options with different strikes and maturities using a single set of parameters. Madan and Seneta present a symmetric version of the variance gamma process. Madan, Carr and Chang extend the model to allow for an asymmetric form and present a formula to price European options under the variance gamma process.
Hirsa and Madan show how to price American options under variance gamma. Fiorani presents numerical solutions for European and American barrier options under variance gamma process. He also provides computer programming code to price vanilla and barrier European and American barrier options under variance gamma process.
Lemmens et al. construct bounds for arithmetic Asian options for several Lévy models including the variance gamma model.
Read more about this topic: Variance Gamma Process
Famous quotes containing the word option:
“Our passional nature not only lawfully may, but must, decide an option between propositions, whenever it is a genuine option that cannot by its nature be decided on intellectual grounds; for to say, under such circumstances, “Do not decide, but leave the question open,” is itself a passional decision—just like deciding yes or no—and is attended with the same risk of losing the truth.”
—William James (1842–1910)