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We investigate a specific ill-posed nonlinear inverse problem that arise on the financial markets. Precisely, as a benchmark problem, we consider the simultaneous recovery of implied volatility and interest rate functions over a finite interval corresponding to call and put prices for idealized continuous European vanilla options over the same maturity. In order to find these time-dependent functions, we minimize the cost functional which is the sum of the squared error between the market values and the computed values, obtained by implicit difference scheme for the Black–Scholes model. Furthermore, results of numerical experiments are discussed. [ABSTRACT FROM AUTHOR]

This paper is devoted to develop a robust numerical algorithm to solve inverse problems of determining the right boundary conditions according to measurements inside a truncated domain for regime-switching models of European options. Difference schemes on Tavella-Randall grids are derived. We propose and discuss results of computational experiments for a several European options. [ABSTRACT FROM AUTHOR]

In this work we report the development of an algorithm to solve inverse problems of determining the right boundary condition according to a measurement inside a truncated domain for the Black-Scholes equation. The difference schemes for the direct and inverse problems are derived on non-uniform Tavella-Randall grids. We propose and discuss results of computational experiments for several European options. [ABSTRACT FROM AUTHOR]