I want to price a down and out call, barrier option, with the underlying asset following a Levy process. I am interest on the Kou double exponential model or the NIG process, to capture asymmetric behavior of jumps. Due to high mathematical complexity of semi-analytical approaches provided in the literature, I am leaning towards a raw monte carlo simulation. However, would the estimate of the price be biased, even after a large number of Iterations (e.g N=100.000)?

  • $\begingroup$ There isn't enough information in your question to answer it. Sample size, generally, impacts consistency, not bias. There are a couple of issues here. First, it depends on what you do next. The method of maximum likelihood is, generally, the most efficient estimator and is generally biased. The MVUE will tend to be relatively inefficient. The larger issue is how you are getting your parameter estimates. I haven't sat down to do the math, but I don't think there are point sufficient statistics, so there will be information loss. $\endgroup$ – Dave Harris Jun 27 '19 at 15:30
  • $\begingroup$ The pivot is probably sufficient, but I am not sure that would be useful. Other than for social reasons, why are you concerned with bias? Have you considered a Bayesian construction to avoid the information loss? You also can avoid the simulation, though you will still may end up doing MC to calculate the denominator of Bayes theorem. $\endgroup$ – Dave Harris Jun 27 '19 at 15:32

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