When Higher-Order Greeks Matter for Options Risk

Summary

The discussion asks why higher-order Greeks are not seen more often in practice. The answer distinguishes Black–Scholes use for quoting implied volatility from more complex models used to price products and measure their risks. Exotic options may require richer models, which can produce higher-order sensitivities as well as stress-test results and other risk measures.

The answer cites vanna and volga as sensitivities that may be useful in risk analysis or profit-and-loss attribution. It says these measures are generally calculated when they provide practical value, though some teams decide the effort is not justified. The exchange gives no specific product examples, calculation methods, or empirical comparison of risk outcomes. Its central point is that the usefulness of higher-order Greeks depends on the pricing model and whether the added detail improves risk monitoring enough to justify the work.

Key ideas

• Black–Scholes may be used to quote implied volatility even when a more complex model is used for pricing and risk.
• Complex option models can provide higher-order Greeks and outputs for stress testing.
• Vanna and volga may help with risk measurement and profit-and-loss attribution.
• Teams may omit higher-order measures when their expected benefit does not justify the effort.

Tags

# the need for utilising high order greeks


# the need for utilising high order greeks












In theory, there are high order greeks that can be used to monitor the BS model sensitivities. However, barely seems them in practical. Anyone can share if you use them frequently and shout out some reasons for using them if available?

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/81683

Black-Scholes model is used a lot in practice in certain contexts, such as quoting implied volatilities.

But more complicated models are used to actually price and to calculate various risk measures of products, such as various exotic options, where Black-Scholes, used for quoting, would have been too simplistic for pricing and risk. The more complicated models can calculate higher-order greeks, as well as the results of various market stress tests, and other risk measures.

Usually, but not always, in a situation where it would be helpful to calculate higher order risk measures like vanna and volga and to use them, for example, in P&L explain - this gets done. Sometimes people just assume or do some analysis and conclude that the benefits would not be worth the effort.

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