### Citations

569 |
A method for the solution of certain non-linear problems in least squares
- Levenberg
- 1944
(Show Context)
Citation Context ...problem, of finding θ such that d(θ) = dmin, has no unique solution in general. Some (local) minimum of a function over its parameter space may be detected by a standard Levenberg-Marquardt algorithm =-=[8, 9]-=- or some modification involving Tikhonov regularization [10]. This requires to compare at any point θ in parameter space not only the state Q(θ), but also its Jacobi matrix ∇T θ Q(θ). The correspondin... |

291 |
Pricing interest rate derivative securities
- Hull, White
- 1990
(Show Context)
Citation Context ...n interest rate models The most widely used classes of valuation models for interest rate derivatives are either short rate models, with the (normally distributed) Hull White (extended Vasicek) model =-=[1]-=- and the (log-normal) Black Karasinski model [2] as their most prominent representatives, or forward rate models, such as the LIBOR market (rate) model [3, 4]. In both classes, calibration of the mode... |

273 |
Solution of incorrectly formulated problems and the regularization method
- Tikhonov
- 1963
(Show Context)
Citation Context ...ution in general. Some (local) minimum of a function over its parameter space may be detected by a standard Levenberg-Marquardt algorithm [8, 9] or some modification involving Tikhonov regularization =-=[10]-=-. This requires to compare at any point θ in parameter space not only the state Q(θ), but also its Jacobi matrix ∇T θ Q(θ). The corresponding Sobolev norm might then be considered instead of the dista... |

264 |
Matrix Computations. third edition
- Golub, Loan
- 1996
(Show Context)
Citation Context ...s components, Qmodel,i(θ),Qtarget,i ∈ Vi, i = 1,... ,n. A standard choice on finite-dimensional real vector spaces is the Euclidean distance, specified by setting f := || · ||2, the Euclidean l2-norm =-=[7]-=- on V ⊂ R n , and correspondingly also fi := | · |, the Euclidean norm on Vi ⊂ R. In some cases (Example 1 and 2), particular state components corresponds to particular individual benchmark instrument... |

238 |
The market model of interest rate dynamics.
- Brace, Gatarek, et al.
- 1997
(Show Context)
Citation Context ...ributed) Hull White (extended Vasicek) model [1] and the (log-normal) Black Karasinski model [2] as their most prominent representatives, or forward rate models, such as the LIBOR market (rate) model =-=[3, 4]-=-. In both classes, calibration of the model parameters to specific market data is required. Typical financial instruments that are priced by short rate models are Bermudan swaptions or bond options. T... |

102 | Complete search in continuous global optimization and constraint satisfaction. In: Iserles,
- Neumaier
- 2004
(Show Context)
Citation Context ...ssibility of getting trapped within a wrong local minimum. In order to solve this problem, a simulated annealing algorithm has been proposed in [11]. Further deterministic approaches are described in =-=[12]-=-. Below we will present another algorithm, which is based on an adaptive refinement of a lattice L ⊂ S. This algorithm is particularly useful in the case when p := dimS is not too large. The method is... |

30 |
Modern pricing of interest-rate derivatives: The LIBOR market model and beyond
- REBONATO
- 2002
(Show Context)
Citation Context ...ributed) Hull White (extended Vasicek) model [1] and the (log-normal) Black Karasinski model [2] as their most prominent representatives, or forward rate models, such as the LIBOR market (rate) model =-=[3, 4]-=-. In both classes, calibration of the model parameters to specific market data is required. Typical financial instruments that are priced by short rate models are Bermudan swaptions or bond options. T... |

3 |
On the fundamental length of quantum geometry and the black hole entropy
- Rainer
(Show Context)
Citation Context ...ts” really take their actually observed values. E.g. a recent problem, in the context of quantum gravity models, is the appropriate calibration of the fundamental length of quantum geometry (see e.g. =-=[5]-=-). In general, all models have to be calibrated, in order to be consistent with the relevant fundamental constants of nature. This fine-tuning of fundamental theories (like the standard model of parti... |

3 |
Closed-form solutions for option pricing in the presence of volatility smiles: A density-function approach
- Mirfendereski, Rebonato
- 2001
(Show Context)
Citation Context ...dmissible probability distributions is required (within in the range of Levy processes), in order to calibrate to options prices quoted at different strike values. One possible extension (proposed by =-=[13]-=-) enlarges the space of probability density distributions from the log-normal density to the generalized beta density of the second kind, defined as the following 4-parameter family on R + : x ↦→ ρa,b... |

1 |
Bond and option pricing when when short rates are lognormal. Financial Analyst Journal,47
- Black, Karasinski
- 1991
(Show Context)
Citation Context ...ses of valuation models for interest rate derivatives are either short rate models, with the (normally distributed) Hull White (extended Vasicek) model [1] and the (log-normal) Black Karasinski model =-=[2]-=- as their most prominent representatives, or forward rate models, such as the LIBOR market (rate) model [3, 4]. In both classes, calibration of the model parameters to specific market data is required... |

1 |
Volatility and Correlation. Second Edition
- Rebonato
- 2004
(Show Context)
Citation Context ...he very functional relation of time dependence which then provides a relation to past and/or future. The prominent example for calibration of time dependence in finance is the volatility surface (see =-=[6]-=-). The afore mentioned situation of practitioners requiring time-stability of the volatility surface is in fact very close to the fundamental view, although in finance applications often a compromise ... |

1 |
Simulated Annealing Algorithmus. Sect. 33.2.3 in: Derivate und Interne Modelle (3rd edn
- Deutsch
(Show Context)
Citation Context ...n problem with the search for a global minimum is the possibility of getting trapped within a wrong local minimum. In order to solve this problem, a simulated annealing algorithm has been proposed in =-=[11]-=-. Further deterministic approaches are described in [12]. Below we will present another algorithm, which is based on an adaptive refinement of a lattice L ⊂ S. This algorithm is particularly useful in... |

1 |
Calibration on the Two Dimensional Lattice. Sect. 7.5.2.2
- Value, AG
- 2002
(Show Context)
Citation Context ...algorithm of Section 3 have been implemented and tested for both, C++ and Java, within several applications. The Java implementation is part of the current commercial software library of Value & Risk =-=[14]-=-. It is applied both, within the Value & Risk Valuation Engine (for pricing), and at the heart of further other applications using the same pricing kernel. The Value & Risk applications are used produ... |

1 | V& R Calibration Engine
- Rainer
- 2007
(Show Context)
Citation Context ...ppropriately combining different algorithms of both types. For this purpose however, a strict modularization of the calibration engine is a necessary condition. Currently a modular calibration engine =-=[15]-=- is developed at Value & Risk as a separate commercial application, which is extending its calibration functionality both, to new interest rate models, and from interest rate derivatives to other asse... |