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Reconstructing FX Option Volatility Surfaces from Delta Quotes

Article Quant Q&A · Author: Michael Mark
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Summary

The document explains why foreign exchange option data may arrive as volatility quotes and delta-based smile points rather than as a ready-made table of implied volatilities by strike and maturity. In much of the over-the-counter market, options are quoted using conventions such as at-the-money volatility, risk reversals, and flies at specified deltas. To obtain strikes, a practitioner can use the Black–Scholes delta relationship together with the at-the-money volatility and other required model inputs for the relevant tenor.

The answer recommends calibrating to standard benchmark points, including at-the-money levels and risk-reversal or fly quotes at commonly used deltas. It also notes that exchange-listed FX options provide another source of data, though liquidity is concentrated in a limited number of currency pairs. The discussion is a concise outline rather than a full conversion recipe: it does not specify all quoting conventions, market inputs, or implementation choices needed to transform a particular vendor dataset. Those details must be checked for the instrument and data source being used.

Key ideas

  • Over-the-counter FX options are commonly quoted in volatility and delta terms rather than as strike grids.
  • Delta-based smile quotes can be translated into strikes using the relevant Black–Scholes relationship and market inputs.
  • At-the-money volatility, risk reversals, and flies provide standard calibration points across a smile tenor.
  • Listed FX options offer an alternative data source, but liquidity is concentrated in a limited set of pairs.
  • The quote conventions and model inputs must be verified before constructing a strike-based surface.

Tags

ForexOptionsVolatilityDerivatives pricing
Full text
# FX volatility quotation


# FX volatility quotation












I am attempting to calibrate my SV(heston) model to market data. My intention is to minimize the difference between market IVs and my model's IVs. I use Bloomberg to get the data, however fx options are quoted in different way than equities and I can't arrive to recover volatility surface in needed format from these data.

I can download the data in following format: RR/BF or Put/Call and Bid/Ask or Mid/Spread

What I want is to get set of strikes, maturities and IVs for them.

Thanks for ideas

## Answer by wchyk-cyw (score 2, accepted)

https://quant.stackexchange.com/a/29588

Due to the nature of OTC trading of FX Options for the majority of the market, they are traded in volatility prices and strikes in delta space. You can derive the specific decimal strikes based on the Black-Scholes delta using the at-the-money volatility for a particular smile tenor, given you know the values of the other parameters in the BS formula as well. However there is a listed FX Options market too, and CME is the largest of all, but it is only liquid for a limited number of pairs.

The typical benchmark spreads are 25D RR/FLY, 10D RR/FLY, together with atm those are the points you want to calibrate to.

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.