Simultaneous identification of time-dependent volatility and interest rate for European options

Georgiev, Slavi G.; Vulkov, Lubin G.

doi:10.1063/5.0041788

Cited by 6 publications

(2 citation statements)

References 12 publications

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“…A simple approximate solution of the bond pricing equation is useful in many applications, where an evaluation of the bond prices is necessary. We plan to focus our future work on using these approximations in inverse problems, similar to those in [24][25][26]. In particular, we are interested in estimating the implied correlation from the market data.…”

Section: Discussionmentioning

confidence: 99%

New Approximations to Bond Prices in the Cox–Ingersoll–Ross Convergence Model with Dynamic Correlation

Stehlíková

2021

Mathematics

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We study a particular case of a convergence model of interest rates. The bond prices are given as solutions of a parabolic partial differential equation and we consider different possibilities of approximating them, using approximate analytical solutions. We consider an approximation already suggested in the literature and compare it with a newly suggested one for which we derive the order of accuracy. Since the two formulae use different approaches and the resulting leading terms of the error depend on different parameter sets of the model, we propose their combination, which has a higher order of accuracy. Finally, we propose one more approach, which leads to higher accuracy of the resulting approximation formula.

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Section: Discussionmentioning

confidence: 99%

New Approximations to Bond Prices in the Cox–Ingersoll–Ross Convergence Model with Dynamic Correlation

Stehlíková

2021

Mathematics

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“…Hofmann et al [26] used a two-parameter Tikhonov regularization with heuristic parameter choice rules to settle the ill-posed nonlinear inverse problem which is the simultaneous recovery of implied volatility and interest rate functions from market data. Georgiev and Vulkov [27] considered an algorithm of predictor-corrector type to recover the piecewise linear time-dependent volatility and risk-free interest rate functions. In this paper, we try to reconstruct the volatility function and parameter γ from market option prices by alternating direction method of multiplier (ADMM) and Euler-Lagrange iterative method [22], then present the empirical analysis of Shanghai Stock Exchange (SSE) 50ETF.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous Identification of Volatility and Mean-Reverting Parameter for European Option under Fractional CKLS Model

Zhao

2022

Fractal Fract

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In this paper, we reconstruct the time-dependent volatility function of the underlying asset and the mean-reverting parameter γ of the interest rate for European options under the fractional Chan–Karolyi–Longstaff–Sanders (CKLS) stochastic interest rate model. Tikhonov regularization is used to solve the ill-posedness of the inverse problem. The existence and stability of the solution of the regularization problem are given. We employ the alternating direction method of multipliers (ADMM) to iteratively optimize the volatility function and the parameter γ. Finally, numerical simulations and the empirical analysis are presented to illustrate the efficiency of the proposed method.

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Recovering the Time-Dependent Volatility and Interest Rate in European Options from Nonlocal Price Measurements by Adjoint Equation Optimization

Georgiev

Vulkov

2023

Advanced Computing in Industrial Mathematics

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Simultaneous identification of time-dependent volatility and interest rate for European options

Cited by 6 publications

References 12 publications

New Approximations to Bond Prices in the Cox–Ingersoll–Ross Convergence Model with Dynamic Correlation

New Approximations to Bond Prices in the Cox–Ingersoll–Ross Convergence Model with Dynamic Correlation

Simultaneous Identification of Volatility and Mean-Reverting Parameter for European Option under Fractional CKLS Model

Recovering the Time-Dependent Volatility and Interest Rate in European Options from Nonlocal Price Measurements by Adjoint Equation Optimization

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