Evaluating Option Greeks Through Empirical Hedging Performance
Summary
The response addresses how to compare option-pricing models when their Greeks imply different hedge positions. It points to empirical studies that evaluate alternative pricing models and implied-volatility functions, using delta hedging of equity options as the relevant test. The cited work offers a way to assess models through hedge performance rather than choosing solely from theoretical assumptions.
For plain-vanilla equity options, the answer emphasizes the volatility skew and the tendency for implied and realized volatility to move inversely with the underlying. This relationship can make a model’s delta differ from Black–Scholes delta; the response says a trader may hedge volatility with another option or adjust the underlying hedge. It offers no study results, sample design, or model ranking, so it identifies a practical evaluation focus rather than providing a definitive choice of model.
Key ideas
- Option models can imply different Greeks and therefore different hedge sizes.
- Empirical delta-hedging performance is one way to compare models.
- Equity option skew and the inverse relationship between volatility and the underlying matter for hedging.
- Volatility exposure can be hedged with options or reflected in an adjusted underlying delta.
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Full text
# evaluation of option pricing models based on Greeks empirical hedging effectiveness
# evaluation of option pricing models based on Greeks empirical hedging effectiveness
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?
## Answer by Enrico Schumann (score 2, accepted)
https://quant.stackexchange.com/a/47139
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).Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.