Data driven recovery of local volatility surfaces

Vinicius Albani, Uri M. Ascher, Xu Yang, Jorge P. Zubelli

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


This paper examines issues of data completion and location uncertainty, popular in many practical PDE-based inverse problems, in the context of option calibration via recovery of local volatility surfaces. While real data is usually more accessible for this application than for many others, the data is often given only at a restricted set of locations. We show that attempts to “complete missing data” by approximation or interpolation, proposed and applied in the literature, may produce results that are inferior to treating the data as scarce. Furthermore, model uncertainties may arise which translate to uncertainty in data locations, and we show how a model-based adjustment of the asset price may prove advantageous in such situations. We further compare a carefully calibrated Tikhonov-type regularization approach against a similarly adapted EnKF method, in an attempt to fine-tune the data assimilation process. The EnKF method offers reassurance as a different method for assessing the solution in a problem where information about the true solution is difficult to come by. However, additional advantage in the latter approach turns out to be limited in our context.

Original languageBritish English
Pages (from-to)799-823
Number of pages25
JournalInverse Problems and Imaging
Issue number5
StatePublished - Oct 2017


  • Data science
  • Ensemble Kalman filter
  • Inverse problem
  • Local volatility calibration
  • Tikhonov-type regularization


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