Monte Carlo Error for Calls at Higher Volatility

Summary

The document considers Monte Carlo estimates of a vanilla European call compared with the Black–Scholes value, asking why the estimates diverge as volatility rises. Each simulated path depends on volatility and random draws; greater volatility spreads terminal outcomes across a wider range, increasing the dispersion that the simulation must average over.

The suggested response is to increase the number of simulated paths as volatility or the time horizon grows, targeting a tolerable standard error for terminal values. This is a qualitative explanation rather than a numerical study. It does not give a convergence rate, confidence interval, or variance-reduction technique, and the size of pricing error also depends on the estimator and simulation setup.

Key ideas

• Higher volatility increases the dispersion of simulated paths and terminal outcomes.
• Longer simulation horizons can also increase path dispersion.
• More paths can reduce Monte Carlo uncertainty to a chosen tolerance.
• The explanation gives no quantitative error bound or variance-reduction method.

Tags

# why does monte carlo simulation become less accurate as volatility increases?


# why does monte carlo simulation become less accurate as volatility increases?












I simulated sample paths to approximate the price of a vanilla European call and then plotted a graph comparing this to the value achieved from the Black Scholes. Why do these values diverge as the option volatility increases?

## Answer by Judo (score 1)

https://quant.stackexchange.com/a/51703

Each path is evolved based on the vol and a random number. The higher the vol the more the paths will diverge.

Paths will diverge if you increase time as well.

The solution is to increase the number of paths as vol or time increases to get a standard deviation of terminal values that you are comfortable with.

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