The calibration of stochastic local-volatility models: An inverse problem perspective

Yuri F. Saporito, Xu Yang, Jorge P. Zubelli

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We tackle the calibration of the Stochastic Local-Volatility (SLV) model. This is the class of financial models that combines the local volatility and stochastic volatility features and has been subject of the attention by many researchers and practitioners recently. The corresponding inverse problem consists in finding certain (functional) coefficients in a class of parabolic partial differential equations from observed values of the solutions. More precisely, given a calibrated local volatility surface and a choice of stochastic volatility parameters, we calibrate the corresponding leverage function. Our approach makes use of regularization techniques from inverse-problem theory, respecting the integrity of the data and thus avoiding data interpolation. The result is a stable and efficient algorithm which is resilient to instabilities in the regions of low probability density of the spot price and of the instantaneous variance. We substantiate our claims with numerical experiments using synthetic and real data.

Original languageBritish English
Pages (from-to)3054-3067
Number of pages14
JournalComputers and Mathematics with Applications
Volume77
Issue number12
DOIs
StatePublished - 15 Jun 2019

Keywords

  • Calibration
  • Financial mathematics
  • Inverse problems
  • Local volatility
  • Stochastic local-volatility

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