Using Fixed Random Seeds in Monte Carlo Calibration

Summary

The document considers whether to reuse the same random numbers for each objective-function evaluation when calibrating a stochastic model to option prices by Monte Carlo. Keeping the seed fixed makes successive evaluations comparable by reducing simulation noise in the difference between parameter settings. This can make optimization and finite-difference gradient estimates more stable, and it also makes prices and calibrated parameters reproducible.

The answer cautions that a fixed seed can conceal sensitivity to the simulation sample: a calibration may look stable under one draw while producing different results with another. The proposed practical check is to increase the number of simulations to reduce estimator variance and assess whether the outcome remains dependable. The document offers this guidance conceptually, without a worked example, convergence analysis, or details about seed management and gradient methods. Its central caveat is that reproducibility for one fixed sample does not by itself establish that Monte Carlo estimates have converged.

Key ideas

• Reusing random numbers across parameter evaluations can reduce noise in objective comparisons.
• A fixed seed makes simulated prices and calibrated parameters reproducible.
• Finite-difference optimization can benefit from reduced simulation noise.
• A single seed can mask sensitivity to the Monte Carlo sample.
• More simulations can reduce estimator variance and help assess stability.

Tags

# Calibration by monte carlo, should I fix my seed?


# Calibration by monte carlo, should I fix my seed?












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?)

## Answer by Quantuple (score 7, accepted)

https://quant.stackexchange.com/a/35818

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.