Computational Reconstruction of the Volatility Term Structure in the General Hull–White Model
Volatility recovery is of paramount importance in contemporary finance. Volatility levels are heavily used in risk and portfolio management. We employ the Hull–White one- and two-factor models to describe the market condition. We computationally recover the volatility term structure as a piecewise-l...
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MDPI AG
2025-01-01
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| author | Slavi G. Georgiev Lubin G. Vulkov |
| author_facet | Slavi G. Georgiev Lubin G. Vulkov |
| author_sort | Slavi G. Georgiev |
| collection | DOAJ |
| description | Volatility recovery is of paramount importance in contemporary finance. Volatility levels are heavily used in risk and portfolio management. We employ the Hull–White one- and two-factor models to describe the market condition. We computationally recover the volatility term structure as a piecewise-linear function of time. For every maturity, a cost functional, defined as the squared differences between theoretical and market prices, is minimized and the respective linear part is reconstructed. On the last time steps, before each maturity, the derivative price is decomposed in order to make the minimization problem analytically solvable. The procedure works fast since only scalar values are obtained on each minimization. However, the predictor–corrector nature of the algorithm allows for the precise recovery of very complex volatility functions. An implicit scheme is used to solve the PDEs on bounded domains. The computational simulations with artificial and real data show that the proposed algorithm is stable, accurate and efficient. |
| format | Article |
| id | doaj-art-5be5f1e15ee446bda0be6642ec387773 |
| institution | Kabale University |
| issn | 2079-3197 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj-art-5be5f1e15ee446bda0be6642ec3877732025-01-24T13:27:48ZengMDPI AGComputation2079-31972025-01-011311610.3390/computation13010016Computational Reconstruction of the Volatility Term Structure in the General Hull–White ModelSlavi G. Georgiev0Lubin G. Vulkov1Department of Informational Modeling, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. Georgi Bonchev Str., 1113 Sofia, BulgariaDepartment of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse, 8 Studentska Str., 7004 Ruse, BulgariaVolatility recovery is of paramount importance in contemporary finance. Volatility levels are heavily used in risk and portfolio management. We employ the Hull–White one- and two-factor models to describe the market condition. We computationally recover the volatility term structure as a piecewise-linear function of time. For every maturity, a cost functional, defined as the squared differences between theoretical and market prices, is minimized and the respective linear part is reconstructed. On the last time steps, before each maturity, the derivative price is decomposed in order to make the minimization problem analytically solvable. The procedure works fast since only scalar values are obtained on each minimization. However, the predictor–corrector nature of the algorithm allows for the precise recovery of very complex volatility functions. An implicit scheme is used to solve the PDEs on bounded domains. The computational simulations with artificial and real data show that the proposed algorithm is stable, accurate and efficient.https://www.mdpi.com/2079-3197/13/1/16Hull–White modelimplied volatilityinverse problemcomputational reconstructionmarket measurements |
| spellingShingle | Slavi G. Georgiev Lubin G. Vulkov Computational Reconstruction of the Volatility Term Structure in the General Hull–White Model Computation Hull–White model implied volatility inverse problem computational reconstruction market measurements |
| title | Computational Reconstruction of the Volatility Term Structure in the General Hull–White Model |
| title_full | Computational Reconstruction of the Volatility Term Structure in the General Hull–White Model |
| title_fullStr | Computational Reconstruction of the Volatility Term Structure in the General Hull–White Model |
| title_full_unstemmed | Computational Reconstruction of the Volatility Term Structure in the General Hull–White Model |
| title_short | Computational Reconstruction of the Volatility Term Structure in the General Hull–White Model |
| title_sort | computational reconstruction of the volatility term structure in the general hull white model |
| topic | Hull–White model implied volatility inverse problem computational reconstruction market measurements |
| url | https://www.mdpi.com/2079-3197/13/1/16 |
| work_keys_str_mv | AT slaviggeorgiev computationalreconstructionofthevolatilitytermstructureinthegeneralhullwhitemodel AT lubingvulkov computationalreconstructionofthevolatilitytermstructureinthegeneralhullwhitemodel |