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I am calibrating a 3-parameter stochastic model to options market data via Monte Carlo simulation. Let the parameter set be denoted by $\bar{\theta}$. (this is not a simple Black-Scholes type model, so MC calibration is the only possible way of calibrating this model)

Now, my question is whether I should have a fixed seed for my objective function evaluation, with the objective function being the mean squared error between the simulated options value and the market implied options value. Meaning that every time my optimizer makes a call to the objective function with a perturbed parameter set $\theta+\delta$, I am using the same random numbers. Effectively eliminating Monte Carlo noise. But is this 'cheating', if so the use of finite difference gradients for this type of problems are useless (or?)

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It is not cheating. It allows you to make your results (e.g. prices, calibrated parameters) 'reproducible' which is good. However, fixing the seed can hide convergence issues. When the variance of your Monte Carlo estimator is large, picking different seeds could yield drastically different results. So be careful. In practice you can obviously solve this by increasing the number of simulations (hence decreasing the estimator's variance).

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  • $\begingroup$ okey, thanks! I have reduced the variance of the MC estimator significantly through variance reduction techniques. So that should be fine. $\endgroup$ – vgdev Aug 28 '17 at 18:21
  • $\begingroup$ Yes. As a sanity check just try using another seed and assess whether your results change significantly. Sometimes variance reduction techniques are not that effective depending on your exact implementation or the problem at hand. Good luck. $\endgroup$ – Quantuple Aug 28 '17 at 18:23
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    $\begingroup$ Depending on how you're calculating the greeks, fixing the seed can be useful here too - if you're just going down the "bump market data, recalculate prices" route, then fixing the seed really reduces noise a lot. $\endgroup$ – will Aug 29 '17 at 6:51

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