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Calibrating Local-Stochastic Volatility Models from Sparse FX Quotes

Article Quant Q&A · Author: opt
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Summary

The document raises the practical problem of calibrating local-stochastic volatility models when an FX volatility surface has only a few quoted strikes per maturity. It notes that standard FX quotes may be expressed through at-the-money straddles and 25-delta risk reversals and butterflies, with some markets also quoting 10-delta structures. The question is whether this limited set of observations can support a successful calibration, including for a Heston local volatility model.

The response points to a comprehensive paper that reviews nine LSV model specifications and discusses their calibration and pricing, including PDE and PIDE approaches and the question of whether jumps are needed. It offers the paper as a reference rather than explaining a calibration algorithm or demonstrating a fit. The document therefore identifies relevant model and data constraints but does not establish how sparse quotes alone determine a unique or robust surface.

Key ideas

  • FX volatility quotes may provide only a small number of strike observations at each maturity.
  • At-the-money, risk reversal, and butterfly quotes encode market information about the volatility smile.
  • LSV calibration practice involves both model choice and option pricing methodology.
  • The cited review covers multiple LSV models but the document itself gives no calibration example.

Tags

ForexOptionsVolatilityDerivatives pricing
Full text
# LSV model calibration with only few quotes per maturity


# LSV model calibration with only few quotes per maturity












At this link I have asked what is the market standard when pricing options in different asset classes. Based on the answers, the standard for FX and equities seems to be the local-stochastic volatility models. My question is how can such a model be calibrated in practice for FX. The reason why I mention FX specifically is that I can see that only 3 strikes are quoted in the market (those embedded in the ATM straddle and in the 25 delta risk reversal and butterfly). If also the 10 delta are quoted, there are 5 quotes. But how can that be enough to successfully calibrate on a FX surface? Is there any example that shows how to calibrate, for example, Heston local volatility model?

## Answer by JejeBelfort (score 2, accepted)

https://quant.stackexchange.com/a/44704

Have a look at this paper.

This is a rather exhaustive paper summarizing 9 models to be used as Local-Stochastic Volatility (LSV) models.

It describes various aspects of Calibration and Pricing of LSV models with the associated references, so that you can dig deeper in the topic should you find a suitable model for your needs.

The beginning of the abstract goes as follows:

> We analyze in detail calibration and pricing performed within the framework of local stochastic volatility LSV models, which have become the industry market standard for FX and equity markets. We present the main arguments for the need of having such models, and address the question whether jumps have to be included. We include a comprehensive literature overview, and focus our exposition on important details related to calibration procedures and option pricing using PDEs or PIDEs derived from LSV models.

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.