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Estimating Monte Carlo Option Pricing Error with Standard Error

Article Quant Q&A · Author: Pietro Scaglione
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Summary

The document explains how to estimate simulation error when pricing an option with Monte Carlo. It identifies the relevant quantity as the standard error of the estimated price, calculated by dividing the estimated standard deviation of simulated outcomes by the square root of the number of simulations. The variance first needs to be converted to a standard deviation before applying this relationship.

This gives the general sampling-error estimate for a simulation run, rather than a guarantee about the accuracy of the model or the correctness of the option price. The prompt supplies a simulation count and variance, but the answer states the formula without calculating a numerical result. The estimate relies on the usual interpretation of independent simulation draws and describes sampling uncertainty, not other sources of pricing error.

Key ideas

  • Monte Carlo sampling error is commonly measured by the standard error of the estimated price.
  • Compute the standard deviation from the estimated simulation variance before applying the formula.
  • The standard error scales inversely with the square root of the simulation count.
  • This estimate measures simulation noise and does not capture model misspecification.

Tags

OptionsStatisticsDerivatives pricing
Full text
# MonteCarlo option pricing error estimate


# MonteCarlo option pricing error estimate












Consider the problem of pricing an option via MonteCarlo with 10000 simulations. If the variance of the simulation is 100, which is the MC estimate of the error on the price?

## Answer by wanna_be_quant (score 0, accepted)

https://quant.stackexchange.com/a/51322

If you are referring to the standard error, i.e. the simulation error, then this can be defined as:

$\frac{\hat{\sigma(M)}}{\sqrt{M}}$

where M is the number of simulations and $\sigma$ is the estimated standard deviation $(\sqrt{\hat{\sigma^2}})$ of the specific simulation run. The “ $\hat{}$” denotes that it is the estimate.

I hope that this will help you.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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