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Heston Stochastic Volatility and Vanna–Volga for FX Options

Article Quant Q&A · Author: Charly Sandoval Cuenca
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Summary

The document compares Heston stochastic volatility with Vanna–Volga (VV), an interpolation approach used to construct an FX implied volatility smile. It describes VV as requiring a small set of market volatility quotes, commonly at-the-money and 25-delta risk reversal and butterfly quotes. The discussion raises whether adding 10-delta quotes can be accommodated and summarizes concerns that VV may not match quoted wing volatilities or price first-generation exotic options correctly.

Heston is presented as a model with a semi-closed-form vanilla option price that can support calibration, while allowing non-lognormal return distributions and capturing skewness and kurtosis. The text also notes a calibration difficulty for short maturities. It offers no quantitative comparison or detailed calibration evidence, and it cautions that Heston can also misprice first-generation exotics. Its stated advantage is that it can serve as a base for more sophisticated models designed to match those products.

Key ideas

  • Vanna–Volga interpolates an FX volatility smile from a limited set of quoted volatilities.
  • The document says Vanna–Volga may struggle to match wing quotes and price first-generation exotics accurately.
  • Heston permits non-lognormal distributions and has a semi-closed-form vanilla option pricing formula.
  • The document notes that short-maturity Heston calibration can be difficult.
  • Both approaches have limitations when pricing first-generation exotic options.

Tags

ForexOptionsVolatilityDerivatives pricing
Full text
# Stochastic Volatility vs Vanna-Volga


# Stochastic Volatility vs Vanna-Volga












I'm working on the calibration of the Heston Stochastic Volatility Model for some FX option data for my bachelor thesis and I was asked "Why should people use Heston instead of other simple approach like Vanna-Volga (VV)?".

According to my research, the greatest point in favor of stochastic volatility models is that volatility seems to behave stochastic, also it may be useful in iliquid markets where only few data is availabe. The pros of the Heston model is that it contains a semi-closed formula for vanilla options, which makes calibration easier, and it doesn't assume log-normality, so it captures better the asymmetry and kurtosis. The cons are that for short maturities it may be impossible to calibrate the model.

On the other hand, VV is an interpolation method which is arbitrage-free and needs only 3 volatility quotes (commonly 25$\Delta$ BFY, 25$\Delta$ RR, ATM). The first point that comes to my mind is that maybe when we also have the 10$\Delta$ BFY and 10$\Delta$ RR, VV may not be able to fit the 5 points.

In summary:

- What are the disadvantages of the Vanna-Volga method?

- What are the advantages of Heston model (or stochastic volatility models in general) over Vanna-Volga?

Any paper, book or other source is welcome. I also share some of my sources.

- https://www.coursehero.com/file/42365761/calibrating-hestonpdf/

- https://mathfinance.com/wp-content/uploads/2017/06/FXOptionsVannaVolga.pdf

- https://papers.ssrn.com/sol3/papers.cfm?abstract_id=873788

- Antonio Castagna - FX Options and Smile Risk-Wiley (2010)

- Jim Gatheral, Nassim Nicholas Taleb - The Volatility Surface - A Practitioner's Guide (Wiley Finance)-Wiley (2006)

## Answer by river_rat (score 2)

https://quant.stackexchange.com/a/61492

Vanna-Vega-Volga is a cute way of interpolating the fx implied volatility surface. The problem is that the vols coming from that interpolation do not match the interbank quoted volatilities, you can't match the 10 delta wings without some weird contortions and using that methodology for first generation exotics results in the incorrect market price. To be fair the same is true for Heston but it has the added benefit of being the base model for a lot of the more sophisticated models you do need to match first generation fx exotics.

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