A twostate jump model

We introduce a pricing model for equity options in which sample paths follow a variance-gamma (VG) jump model whose parameters evolve according to a two-state Markov chain process. As in GARCH type models, jump sizes are positively correlated to volatility. The model is capable of justifying the observed implied volatility skews for options at all maturities. Furthermore, the term structure of implied VG kurtosis is an increasing function of the time to maturity, in agreement with empirical evidence. Explicit pricing formulae, extending the known VG formulae, for European options are derived. In addition, a resummation algorithm, based on the method of lines, which greatly reduces the algorithmic complexity of the pricing formulae, is introduced. This algorithm is also the basis of approximate numerical schemes for American and Bermudan options, for which a state dependent exercise boundary can be computed