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References for the Vanna-Volga Method in FX Volatility Smile Construction

Article Quant Q&A · Author: Mahi
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Summary

The document gathers references for readers seeking to understand vanna, volga, and vega approximations in implied-volatility modeling. It points particularly to the vanna-volga method for constructing foreign-exchange volatility smiles and notes a formulation based on at-the-money volatility together with 25-delta call and put volatilities.

Suggested sources include a dissertation on the foreign-exchange volatility surface, a book on FX options and structured products, and papers covering implied and normal volatilities. These citations indicate where to study market conventions and derivations; the document itself does not explain the approximation, develop its equations, or compare its performance. The references therefore serve as a reading guide rather than a standalone account, and readers should check each source for its assumptions, scope, and treatment of volatility conventions.

Key ideas

  • The vanna-volga method is presented as a reference point for FX volatility smile construction.
  • One cited approach expresses smile volatility using at-the-money volatility and 25-delta call and put volatilities.
  • The recommended materials include a dissertation, a textbook, and papers on implied and normal volatility.
  • The document provides citations but does not derive or evaluate the method.

Tags

ForexOptionsVolatilityDerivatives pricing
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# Reference: Vanna, volga, vega approximations


# Reference: Vanna, volga, vega approximations












I am looking for a reference on how to approximate implied volatility in a stochastic model vis-a-vis vanna, volga, vega, and other model parameters, in particular the derivation of such equations and the underlying intuition.

Any good articles/books out there?

## Answer by LocalVolatility (score 1)

https://quant.stackexchange.com/a/33213

I find Dimitri Reiswich's Ph.D. thesis quite useful when it comes to FX smile construction and market conventions. Section 3.3 is on vanna/volga method.

Also have a look at Uwe Wystup's book, especially Section 3.1 "The Trader's Rule of Thump".

References

Reiswich, Dimitri (2010) "The Foreign Exchange Volatility Surface", Ph.D. Dissertation, Frankfurt School of Finance & Management

Wystup, Uwe (2006) "FX Options and Structured Products", John Wiley & Sons

## Answer by Randor (score -1)

https://quant.stackexchange.com/a/33212

perhaps this is what you're looking for? - lookup Mercurio Vanna VOlga "Consistent Pricing of FX Options " this paper derives a formula for the vol smile in terms of atm vol and 25 delta call and put vols

## Answer by jaehyukchoi49 (score -1)

https://quant.stackexchange.com/a/42369

Here's more references to the vanna-volga method:

- Castagna, Mercurio (2007), The vanna-volga method for implied volatilities, Risk [ Download ]

- Perederiy (2018), Vanna-Volga Method for Normal Volatilities, arXiv. `Note: As the title indicates, this paper is about the normal volatility`

- Wikipedia `Note: also see the references there`

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.