Use Strike-Specific Implied Volatility for Option Greeks

Summary

The document answers whether to use an underlying asset's volatility or each option's implied volatility when calculating delta or vega across strikes. It recommends using the implied volatility associated with the option's strike and expiry, reflecting the volatility surface rather than applying one volatility value to every contract.

The rationale is that option prices are set in the options market, and implied volatility is inferred from those observed prices. An option model used to represent market prices should therefore use the corresponding implied volatility input. The excerpt addresses this input choice but does not explain how to construct a volatility surface, how to handle interpolation between quoted strikes or expiries, or which model to use for a particular trading or backtesting task. It also leaves the question about practical implementations in R or Python unanswered.

Key ideas

• Option Greeks across strikes should use implied volatility for the specific strike and expiry.
• Implied volatility reflects the option's market price.
• Using strike- and expiry-specific volatility helps a model represent observed option prices.
• The excerpt does not cover volatility-surface construction or practical model implementation.

Tags

# Implied volatility and greeks of options


# Implied volatility and greeks of options












When we are calculating deltas or vegas for different strikes should we use the underlying asset's volatility or should we use the implied volatility for the specific strikes at a fixed maturity?

Is there a book or blog where I can learn about the actual models used in option backtesting or trading platforms( in R / python) instead of the normal theoretical ones ?

## Answer by Kermittfrog (score 0, accepted)

https://quant.stackexchange.com/a/52913

Re your first question: Use the implied volatility $\sigma_{imp}(X,\tau)$ for strike $X$ and expiry $\tau$.

The option price, and hence the implied volatility, is driven by the options markets. Your option model should first and foremost be able to replicate observed option prices (hence, you plug in implied vols).

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.