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I’ve studied many different pricing models (B&S, Vasicek, CIR, Merton jump, Heston, ecc), each of them gives as output a different price and different values for the Greeks.

So, for example, if a trader manage option risk using greeks arising from B&S he would probably hedge his portfolio trading different amounts than the one Who manage his risk using Heston.

How can I choose between different models not in terms of theory but based on empirical accuracy of its greeks?

Is there any academic paper about this topic?

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    $\begingroup$ Excellent question I think. However, I don't think there is one correct answer and I believe the answer to this question is more of discussion rather than pure math/equation based solution. Try to look for paper on the topic "Model Risk". If you hav't already. You're basically asking how to handle Model Risk $\endgroup$ – Sanjay Aug 15 '19 at 13:44
  • $\begingroup$ I have suggested a new tag: model-risk! $\endgroup$ – Sanjay Aug 15 '19 at 14:02
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These papers study delta-hedging of equity options with different models.

@Article{,
  author  = {Gurdip Bakshi and Charles Cao and Zhiwu Chen},
  title   = {Empirical Performance of Alternative Option Pricing Models},
  journal = {Journal of Finance},
  year    = 1997,
  volume  = 52,
  number  = 5,
  pages   = {2003--2049},
}

@Article{,
  author  = {Bernard Dumas and Jeff Fleming and Robert E. Whaley},
  title   = {Implied Volatility Functions: Empirical Tests},
  journal = {Journal of Finance},
  year    = 1998,
  volume  = 3,
  number  = 6,
  pages   = {2059--2106},
}

In plain-vanilla equity options, the key empirical property to handle is the skew, i.e. the correlation between vol (both implied and realised) and the underlier. That is, when the underlier goes up, vol typically goes down. So, to "earn" the delta in an upmove, you either need to hedge vol (with another option), or simply hold a little more Black-Scholes delta (e.g. with a negative correlation between underlier and vol, the Heston delta will usually be higher than the Black-Scholes delta).

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