Comparing Pricing Models Beyond Calibration Error

Summary

The document outlines how to compare models used to price European, American, and exotic options, including the accuracy of prices and hedging Greeks. For options included in calibration, calibration error is a direct comparison; for other products or uses, the evaluation target must be specified clearly. A model’s suitability depends on more than fit, and the document offers practical criteria: numerical robustness, speed, stable risk estimates, calibration difficulty, interpretability, parameter identifiability, and how readily the desk can understand it.

It also raises whether one model should serve every product, noting that practice may call for different models. The key question is whether a model captures the risks relevant to the products it targets. The discussion is a qualitative checklist rather than a formal testing protocol: it provides no empirical comparison, quantitative acceptance thresholds, or specific validation method for exotic prices or Greeks.

Key ideas

• Calibration error can compare models on the instruments used for calibration, but other use cases require a clearly defined target.
• Model assessment should include numerical robustness, speed, risk stability, calibration effort, and interpretability.
• Parameter identifiability matters because poorly distinguished parameters make model outputs harder to understand.
• A single model may not suit every product in practice.
• A model should capture the risks relevant to its intended products.

Tags

# How to compare pricing models?


# How to compare pricing models?












Say there is model A and model B to price vanilla European and American options. Both are calibrated against market prices

- How to determine what model provides more accurate prices for either European/American/Exotic options?

- How to determine what model provides more accurate greeks for hedging?

- How new models are being assesed in real world when deciding whether new model shall be used instead of the one being used now?

## Answer by Andrea (score 0, accepted)

https://quant.stackexchange.com/a/81233

- You have to be more clear. Prices for what? If it is for the same options it is calibrated to, then the calibration error is an obvious answer. Otherwise you need to explain exactly what you want to do.



- What makes a good model? Not an easy answer.

In my opinion, these are some of the key features of a good / better model (in no particular order)

- Does it have a robust numerical implementation?

- Is it fast enough for its target usage?

- Does it produce stable risks?

- How hard is it to calibrate it to market prices?

- Do I understand its output?

- Are the parameters well identified (so orthogonal or with a clear meaning)?

- How long will it take to explain it to the desk? Anything that needs more than 5 minutes is too complicated and likely to have already failed some point above



- Do we need a single model for al products? Another very difficult question. In theory yes, but in practice, things are very different.

- Does it capture the relevant risks of the target products?

I am sure there are plenty mode which I have forgotten.

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