Practical References for FX Local Volatility and Smile Calibration
Summary
The document asks how to move from FX vanilla and barrier option quotes to a local volatility model. The author describes fitting smiles at quoted maturities with Vanna–Volga, then interpolating total variance across maturities using a flat-forward approach. They ask whether a smooth, arbitrage-free implied volatility surface is needed before estimating local volatility from call-price derivatives, and whether the resulting model can price options with backward equations or Monte Carlo.
The response offers a reading path rather than an implementation recipe: it recommends practical books and papers covering non-constant volatility, FX smile construction, and comparisons of smile calibration procedures. The cited sources are presented as accessible guides to calibration and interpolation. The response does not explain how to construct the surface, calculate its derivatives, or validate a local volatility implementation; it also notes that newer references may exist. Thus, the document is useful for locating foundational FX volatility material, but leaves the technical questions open.
Key ideas
- Vanna–Volga is described as a way to construct a smile at a fixed maturity from liquid option prices.
- The author uses linear interpolation in total variance to extend smiles across maturities.
- The central implementation question is how to obtain an arbitrage-free implied volatility surface suitable for local volatility calculations.
- The answer recommends practical references on FX option pricing, smile construction, and calibration comparisons.
- The response supplies a reading list rather than a step-by-step calibration method.
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Full text
# Implementing Local Volatility model in FX
# Implementing Local Volatility model in FX
Goal: initial goal is to calibrate to Bloomberg's OVML prices for Vanillas and Barriers in OVML/DLIB
History: My approach has been a bit ad-hoc so far and I've confused about how to proceed with implementation. I previously wrote code to mostly match Bloomberg's pricing for Vanillas, Barriers and Touches under Vanna-Volga. From what I understand: VV is essentially just for building a smile at a fixed maturity T in a manner consistent with observed liquid option prices while incorporating hedging costs for the three volatility related Greeks. To go from the smile at a number of given tenors to a full implied volatility surface, you need temporal interpolation: I used flat-forward time interpolation (linear in total variance) as the Clark book ("Foreign Exchange Option Pricing: A Practitioner's Guide") suggested this prevents calendar arbitrage in your model. I've so far read the Derman-Kani paper and the Dupire one but the actual implementation remains quite unclear to me. Is the idea that you extract a smooth arbitrage free surface from selected quotes, then estimate the derivatives of the call prices via this implied vol surface via finite differences and that gives you the local volatility surface/function?Presumably the twice continuously differentiable/arbitrage requirements rule out the Vanna Volga surface. If so, is there some baseline way for implied vol surface calibration in FX? Or is there some method that goes from quotes to local vol directly? From what I understand, after you have calibrated the local vol surface; actually pricing options with it itself can be done via solving backward equations or via MonteCarlo?
Essentially,all I want right now is to figure out where I can learn this stuff or what the sequencing is? Are there industry-standard papers for implementing this - do not need the most computationally sophisticated work in so much as figuring out the basics?
## Answer by Dimitri Vulis (score 0, accepted)
https://quant.stackexchange.com/a/85692
It's been a while since I looked at FX, so there are likely to be newer better books available now. Nevertheless, I will suggest a few that are easy to find and I have a reasonably detailed practical discussions of vol surface calibration and interpolation:
- Alexander Lipton. Mathematical Methods for Foreign Exchange: A Financial Engineer's Approach (2001) , particularly Chapter 10: Non-constant volatility
- Antonio Castagna. FX Options and Smile Risk-Wiley (2010)
- Dimitri Reiswich, Uwe Wystup. FX Volatility Smile Construction (2010) also https://onlinelibrary.wiley.com/doi/abs/10.1002/wilm.10132
- Dimitri Reiswich. An empirical comparative analysis of foreign exchange smile calibration procedures (2011) (risk.net paywall)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.