Finite Difference Benchmarks for American Options under Heston Volatility

Summary

The document asks how to obtain a reliable benchmark for American option values under the Heston stochastic-volatility model, with the goal of assessing bias in least-squares Monte Carlo (LSM). It considers a stochastic-volatility binomial model but asks for alternatives that are easier or faster to use.

The response recommends finite difference methods. It describes them as efficient and capable of high numerical accuracy for validating LSM, while acknowledging that implementation for Heston is not entirely straightforward. The stated accuracy is an estimate from the respondent, not a reported experiment or universal guarantee. No scheme, grid design, boundary conditions, or benchmark prices are provided, so the document offers a method direction rather than a reproducible comparison.

Key ideas

• Finite difference methods are suggested as benchmarks for American options under Heston volatility.
• The proposed use is to evaluate bias in least-squares Monte Carlo prices.
• Implementation is described as manageable but not trivial.
• The accuracy claim is not supported by a worked example in the document.

Tags

# Benchmark value for American Options under stochastic volatility


# Benchmark value for American Options under stochastic volatility












Does anyone know any kind of method that produces reasonably well results for American Options under Heston Model setting that could be used as benchmark value? Since right now my goal is to investigate the biasedness of the Least-Square Monte Carlo(LSM) More details on LSMunder different conditions, I want some methods known to produce better results than LSM. I presume the binomial model under stochastic volatility might be a good choice but maybe a bit hard to implement and time-consuming. So just wondering if anyone knows something better than sv binomial model that could serve as a benchmark? Thanks!

## Answer by Yian Pap (score 1)

https://quant.stackexchange.com/a/37141

Well, I guess the OP is done with this by now, but the answer is finite difference methods. Not that easy to implement for Heston, but not terribly difficult either. Those are so efficient that they can give 7-8 digits of accuracy easily (a lot more than you'd need to validate LSM, which could give you maybe 3 correct digits if you're lucky). If anyone needs some benchmarks I can provide them.

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