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I need someone to explain me the importance sampling method. There are several topics but the drift parameter $\theta$ when adjusting is never discussed.

I read publications where $\theta$ was used to optimize the linear part of the payoff variance, and stratified sampling was used to improve the quadratic part.

I'm talking about publications such as Glasserman, Heidelberger and Shahabuddin

https://www0.gsb.columbia.edu/faculty/pglasserman/Other/asym_opt_is.pdf

And

https://pdfs.semanticscholar.org/4fe5/94e3c7667c762cf1f7d841fcd0a4bf30f255.pdf

So far what I understood is, you adjust the drift by $\sigma$$\theta$ and you multiply each path at each time step and simulation by

$$L(\theta, t)=exp(-\theta W^{Q_\theta}_t - \dfrac{1}{2}\theta^2t)$$

1\ Is that first step correct ?

2\ The important part is to set a routine so that the optimal $\theta$ is found while using stratified sampling. Is someone able to understand and tell me how that method works (links above) ?

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  • $\begingroup$ I haven't seen this specific application of importance sampling, but may I ask if you are aware of the purpose of importance sampling in a general application? That may help people focus a response.. $\endgroup$ – Attack68 Aug 29 '18 at 18:33
  • $\begingroup$ Yes. To be more clear, I'm dealing with Down and In Put with barriers that can be as low as -50% from Spot. By changing the measure I hope it will improve the convergence speed of my Monte Carlo simulations. The point is I'd like to fully automatize the search of the optimal drift adjutment, and as far as I understood these papers are dealing with this topic. I guess the drift adjustment is not done manually product by product on trading floors ? Hope this can help. $\endgroup$ – Cedric_W Aug 30 '18 at 6:29

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