Recovery of the time-dependent implied volatility of time fractional Black–Scholes equation using linearization technique

Autor:	Yujie Wei, Sajad Iqbal
Rok vydání:	2021
Předmět:	Applied Mathematics 010102 general mathematics Black–Scholes model Implied volatility 01 natural sciences Regularization (mathematics) Volterra integral equation 010101 applied mathematics symbols.namesake Linearization symbols Applied mathematics 0101 mathematics Mathematics
Zdroj:	Journal of Inverse and Ill-posed Problems. 29:599-610
ISSN:	1569-3945 0928-0219
DOI:	10.1515/jiip-2020-0105
Popis:	This paper tries to examine the recovery of the time-dependent implied volatility coefficient from market prices of options for the time fractional Black–Scholes equation (TFBSM) with double barriers option. We apply the linearization technique and transform the direct problem into an inverse source problem. Resultantly, we get a Volterra integral equation for the unknown linear functional, which is then solved by the regularization method. We use L 1 {L_{1}} -forward difference implicit approximation for the forward problem. Numerical results using L 1 {L_{1}} -forward difference implicit approximation ( L 1 {L_{1}} -FDIA) for the inverse problem are also discussed briefly.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::74d2ed14eb7ea493067f484a1e29068d https://doi.org/10.1515/jiip-2020-0105 Zobrazit plný text záznamu