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I have read in the literature of Levy processes that the only complete market models are pure Brownian motion andpure Poisson processes.Is anyone familiar with any references for explicitly creating the hedge in the case of Poisson processes?Might it follow the same procedure as in the Brownian motion case (the lack of continuity makes it feel less intuitive)?Many thanksTom

I haven't looked at it in a while, but Cox and Ross, "The Valuation of Options for Alternative Stochastic Processes"should have what you want. The basic idea is similar to the binomial model, and gives the intuition.regards,

QuotetwIs anyone familiar with any references for explicitly creating the hedge in the case of Poisson processes?Isn't the pure poisson process the simple binomial tree?Quotecrowlogic This is true because the Poisson process has no memory and its mean and variance are equalCan you elaborate a bit on that? I cannot see why this can be the reason.thxKyriakos

Thanks for the responses. I am trying to get hold of a copy of the paper (anyone have one to hand?) - I seem to remember reading this a long time ago, but mainly being interested in the novelty of thebinomial tree method and glossed over the application to alternative stochastic processes.I was interested in Merton's jump diffusion paper, particularly where he contrasts two option traders who agree on the value of atm options but one of whom believes in jumps and the other does not.This naturally leads to a smile.However Merton's CAPM based method seems to basically average over the jumps to derive a weighted sumof BS option values in the event of a jump. Hedging is not discussed in significant detail.I was interested in exactly known cases (Brownian & Poisson) how the two hypothetical option traders would hedge.

Here is another paper which might be of interest http://xxx.lanl.gov/abs/cond-mat/0108137Regards