Computational recovery of time-dependent volatility from integral observations in option pricing

Abstract In this paper robust algorithms for numerical identification of time dependent volatility by integral observations of one- and two-asset Black–Scholes models are developed. An average linearization in time of diffusion terms of the discrete initial boundary value problems is used. Then, a decomposition with respect to the volatility of the approximate solution is applied so that the transition to a new time layer is carried out by solving standard discrete elliptic problems. Numerical experiments using simulated as well as real data confirm the effectiveness of the present approach.

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