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Robust Numerical Calibration for Implied Volatility Expansion Models

Radu Baltean-Lugojan (rb2309***at***imperial.ac.uk)
Panos Parpas (p.parpas***at***imperial.ac.uk)

Abstract: Implied volatility expansions allow calibration of sophisticated volatility models. They provide an accurate fit and parametrization of implied volatility surfaces that is consistent with empirical observations. Fine-grained higher order expansions offer a better fit but pose the challenge of finding a robust, stable and computationally tractable calibration procedure due to a large number of market parameters and nonlinearities. We propose calibration schemes for second order expansions that take advantage of the model's structure via exact parameter reductions and recoveries, reuse and scaling between expansion orders where permitted by the model asymptotic regime and numerical iteration over bounded significant parameters. We perform a numerical analysis over 12 years of real S&P 500 index options data for both multiscale stochastic and general local-stochastic volatility models. Our methods are validated empirically by obtaining stable market parameters that meet the qualitative and numerical constraints imposed by their functional forms and model asymptotic assumptions.

Keywords: implied volatility expansions, numerical calibration, parameter reduction, nonlinear least squares

Category 1: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Category 2: Applications -- OR and Management Sciences (Finance and Economics )

Category 3: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Citation: Preprint, August 2016

Download: [PDF]

Entry Submitted: 10/20/2015
Entry Accepted: 10/20/2015
Entry Last Modified: 09/26/2016

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