Practical Limits of Lévy Processes in Derivative Pricing

Summary

The document considers whether Lévy processes and related academic techniques are used on options market-making desks. Its answer argues that Lévy models are a poor practical choice for pricing derivatives under the risk-neutral measure, warning that using them in this role may create dangerous results. It also groups entropy-based pricing measures and Fourier transform techniques with methods the respondent views as impractical for that purpose.

For risk management under the statistical measure, the answer allows that a carefully implemented Lévy model could have a role, particularly as a benchmark. The respondent nevertheless says they would not use one for risk management either. The discussion offers no examples, data, or comparison with desk practice, so its claims reflect one practitioner's opinion rather than a demonstrated industry consensus. It distinguishes pricing from risk analysis but does not explain the circumstances in which Lévy models might be suitable or how to implement them.

Key ideas

• The answer argues against using Lévy processes to price derivatives under the risk-neutral measure.
• It warns that inappropriate pricing-model use can be hazardous in practice.
• A properly implemented Lévy model might serve as a risk-management benchmark under the statistical measure.
• The response gives a practitioner's view without supporting data or broader evidence about market-making desks.

Tags

# To what extent are Lévy processes used in financial engineering?


# To what extent are Lévy processes used in financial engineering?












I know that (time changed) Lévy processes are actively researched in the academic world, including tools such as minimal entropy martingale pricing measures and fast Fourier transforms. To what extent are such topics used in financial engineering, i.e. in trading desks of options market makers?

## Answer by AXH (score 1, accepted)

https://quant.stackexchange.com/a/42764

Levy processes are not used for pricing derivatives and are useless in practice. When the task at hand is to price a derivative, i.e., working in the risk neutral measure, then using Levy processes is worse than useless, it is dangerous and should actively be avoided. You can add entropy risk measures, FFTs and other (practically) useless concepts from academia to that list.

If implemented properly, and there is a big emphasis on "properly", then they may be useful for risk management, i.e., working in the statistical measure. I would not use them for risk management either, but they could be used in this context for benchmarking purposes.

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