How Euler Time Steps Affect Heston Option Pricing

Summary

The document raises a numerical question about estimating an option price under the Heston stochastic volatility model with Euler discretization. It compares simulated prices obtained using different numbers of time intervals with a cited benchmark price, and observes that the estimates generally fall as the grid becomes coarser. The simulation uses 100,000 paths, but the document does not specify enough setup details to diagnose the pattern or establish a reliable convergence trend.

Its value is in highlighting the need to examine discretization error when pricing options by simulation. The listed estimates fluctuate rather than changing smoothly, so sampling variation may also matter alongside time-step bias. The document poses the question but supplies no answer, validation, or comparison with alternative schemes. Readers would need details such as the variance process treatment, parameter values, payoff, and confidence intervals before drawing conclusions about the cause or magnitude of the bias.

Key ideas

• Euler discretization can affect simulated option prices under the Heston model.
• The example compares estimates across time grids with a cited benchmark.
• The reported estimates fluctuate, so sampling error may complicate comparisons.
• The document does not identify the cause or provide a resolved pricing method.

Tags

# Euler discretization bias, heston model


# Euler discretization bias, heston model












I am performing option pricing using Heston model and Euler discretization. I'm getting the following result:

```
1000    6.81982     
500     6.85281  
250     6.81557     
200     6.78875     
150     6.79469     
100     6.77717     
50      6.72955 
30      6.68981     
10      6.42615 
10      6.41056
```

Where the first column denotes the number of discretization intervals, and the second one is an option price. Number of simulation paths is equal to 100000 and true option price is 6.8061 as in the following link:

https://www.quantstart.com/articles/Heston-Stochastic-Volatility-Model-with-Euler-Discretisation-in-C

What can be the reason for the decreasing option price when the number of discretization intervals is decreasing as well?

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