Choosing Option Greeks That Match the Pricing Model
Summary
The document discusses why Black-Scholes Greeks remain common in vanilla option risk management despite the availability of stochastic-volatility models. One response favors using hedge sensitivities consistent with the model used to price trades, noting that practitioners use SABR-based sensitivities in interest-rate markets. Another emphasizes the closed-form Greeks’ speed and simplicity for large portfolios, treating them as a convenient approximation when deeper modeling is impractical.
The discussion highlights a tradeoff rather than establishing one universally best approach. Black-Scholes Greeks are easy to compute and can serve as a model-independent reference, but sensitivities derived separately across strikes may not be mutually consistent with a volatility surface or capture risks such as volatility-of-volatility and spot-volatility correlation. More complex models may better align pricing and hedging, yet they also remain imperfect and can cost more to run. The appropriate choice depends on the pricing framework, portfolio scale, and how the firm manages volatility-related exposures.
Key ideas
- Hedge sensitivities are generally most coherent when they come from the model used to price the options.
- Black-Scholes Greeks are popular because they are simple, closed-form, and computationally inexpensive.
- A single Black-Scholes framework may not capture volatility dynamics or consistent risks across strikes.
- Stochastic-volatility models can provide richer sensitivities but also introduce complexity and remain imperfect.
- The choice of Greeks depends on pricing practice, computational needs, and the risks being managed.
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Full text
# Why are Black-Scholes derived greeks used for risk management when alternatives exist? # Why are Black-Scholes derived greeks used for risk management when alternatives exist? To my understanding, it is still quite common for market makers of vanilla options to use Black-Scholes greeks. My concern with this is best expressed by Pat Hagan in the original SABR model paper: " Since different models are being used for different strikes, it is not clear that the delta and vega risks calculated at one strike are consistent with the same risks calculated at other strikes" Additionally, it seems theoretically ludicrous to derive risk exposures to vol-of-vol or spot vol correlation (volga and vanna) from a model that says nothing about these. Since we do have alternatives that account for the issues of Black-Scholes (take your pick of a stochastic volatility model), why would anyone relegate themselves to the theoretical inconsistencies involved with using Black-Scholes greeks? ## Answer by Hasek (score 3) https://quant.stackexchange.com/a/78836 I do not agree with the answer by @river_rat. SABR greeks (the so-called Bartlett delta and vega) are used by practitioners in Interest Rates trading from my own experience. In general you want your hedges to be consistent with your pricing model, so it really makes sense to use the hedges provided by a "better" (whatever that means) model than a standard Black-Scholes if you use it for pricing your deals. The Black-Scholes greeks are popular as a cheap and dirty model independent approach when you don't want to or can't go to into a depth of things but generally your greeks should be consistent with your pricing model and barely anyone are using a textbook Black-Scholes for pricing nowadays. ## Answer by river_rat (score 2) https://quant.stackexchange.com/a/78831 Pick your poison, what is better? A simple model that is wrong or a complicated model that is also wrong. Add to that computation time on large portfolios and the simplicity of a closed form Black-Scholes greek sensitivity number makes a lot of sense. The nuance is then on the implied volatilities feeding that model and the external factors driving correlation between those implied volatilities and the market.
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