The calibration of stochastic local-volatility modelsan inverse problem perspective

Resumo

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.

Ficha do documento

Tipo

Artigo científico

Ano

2019

Instituição

Elsevier

Fonte

Repositório da FGV

Idioma

Português

Acesso

Acesso restrito

Identificador

oai:repositorio.fgv.br:10438/32410

Palavras-chave

Stochastic local-volatilityInverse problemsLocal volatilityCalibrationFinancial mathematicsMatemáticaMatemática financeiraVolatilidade (Finanças)