Calibration of the Local Volatility in a Generalized Black-Scholes Model Using Tikhonov Regularization

Calibration of the local volatility in a trinomial tree using Tikhonov regularization

Following an approach introduced by Lagnado and Osher (Lagnado R and Osher S 1997 J. Comput. Finance 1 13–25), we study the application of Tikhonov regularization to the financial inverse problem of calibrating a local volatility function from observed vanilla option prices. Moreover, we provide a unified treatment for this problem in two different settings: first, the generalized Black–Scholes...

Non-parametric calibration of the local volatility surface for European options

In this paper, we explore a robust method for calibration of the local volatility surface for European options. Assuming the the volatility surface is smooth, we apply a second order Tikhonov regularization to the calibration problem. Additionally we propose a new approach for choosing the Tikhonov regularization parameter. Using the TAPENADE automatic differentiation tool in order to obtain ad...

Tikhonov Regularization Applied to the Inverse Problem of Option Pricing: Convergence Analysis and Rates‡

This paper investigates the stable identification of local volatility surfaces σ(S, t) in the Black-Scholes/Dupire equation from market prices of European Vanilla options. Based on the properties of the parameter-to-solution mapping, which assigns option prices to given volatilities, we show stability and convergence of approximations gained by Tikhonov regularization. In case of a known term-s...

Regularization Applied to the Inverse Problem of Option Pricing : Convergence Analysis and Rates

This paper investigates the stable identification of local volatility surfaces σ(S, t) in the Black-Scholes/Dupire equation from market prices of European Vanilla options. Based on the properties of the parameter-to-solution mapping, which assigns option prices to given volatilities, we show stability and convergence of approximations gained by Tikhonov regularization. In case of a known term-s...

THE FLORIDA STATE UNIVERSITY COLLEGE OF ARTS AND SCIENCES Calibration of a Local Volatility Surface using Tikhonov Regularization