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It might be a naive question but I'm new to finance. I've been trying to get my head around this question from a long time and still totally clueless about this.

Suppose that the observed jumps in three consecutive months are 0, 1, 2 times. How to find the estimated parameters λ̂ of the Black-Scholes-Merton model using maximum likelihood estimate method.

Thanks for your time !

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The jumps are modeled as an independent Compound Poisson Process. Here's a paper (Leopold Simar: Maximum Likelihood Estimation of a Compound Poisson Process in The Annals of Statistics 4(6) November 1976) that describes how to get MLE for such process

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