Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Calibration of stochastic models for interest rate derivatives
Date
2009-01-01
Author
Rainer, Martin
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
84
views
0
downloads
Cite This
For the pricing of interest rate derivatives various stochastic interest rate models are used. The shape of such a model can take very different forms, such as direct modelling of the probability distribution (e.g. a generalized beta function of second kind), a short-rate model (e.g. a Hull-White model) or a forward rate model (e.g. a LIBOR market model). This article describes the general structure of optimization in the context of interest rate derivatives. Optimization in finance finds its particular application within the context of calibration problems. In this case, calibration of the (vector-valued) state of a given stochastic model to some target state, which is determined by available relevant market data, implies a continuous optimization of the model parameters such that a global minimum of the distance between the target state and the model state is achieved. In this article, a novel numerical algorithm for the optimization of parameters of stochastic interest rate models is presented. The optimization algorithm operates within the model parameter space on an adaptive lattice with a number of lattice points per dimension which is both low and fixed. In this way, a considerable performance gain is achieved, as compared to algorithms working with non-adaptive lattices requiring increasing and/or large numbers of lattice points. As compared to standard algorithms, e.g. those of the Levenberg-Marquardt type, the presented adaptive lattice algorithm also reduces the danger of getting trapped near a wrong local minimum. As a numerical example, its application is demonstrated by optimizing volatility and mean reversion parameters of the Hull-White model, such that the latter becomes calibrated to the swaption volatility market relevant for a given OTC (over-the-counter, i.e. not exchange traded) bond option.
Subject Keywords
Management Science and Operations Research
,
Control and Optimization
,
Applied Mathematics
URI
https://hdl.handle.net/11511/63351
Journal
OPTIMIZATION
DOI
https://doi.org/10.1080/02331930902741796
Collections
Graduate School of Applied Mathematics, Article
Suggestions
OpenMETU
Core
Optimal pricing and ordering policy for non-instantaneous deteriorating items under inflation and customer returns
Ghoreishi, M.; Mirzazadeh, A.; Weber, Gerhard Wilhelm (Informa UK Limited, 2014-01-01)
This paper deals with an economic production quantity inventory model for non-instantaneous deteriorating items under inflationary conditions considering customer returns. We adopt a price-and time-dependent demand function. Also, the customer returns are considered as a function of both price and demand. The effects of time value of money are studied using the Discounted Cash Flow approach. The main objective is to determine the optimal selling price, the optimal replenishment cycles, and the optimal produ...
Solving optimal investment problems with structured products under CVaR constraints
Korn, Ralf; Zeytun, Serkan (Informa UK Limited, 2009-01-01)
We consider a simple investment problem where besides stocks and bonds the investor can also include options (or structured products) into the investment portfolio. The aim of the investor is to maximize the expected return under a conditional value-at-risk (CVaR) constraint. Due to possible intermediate payments, we have to deal with a re-investment problem which turns the original one-period problem into a multi-period one. For solving this problem, an iterative scheme based on linear optimization is deve...
Effective optimization with weighted automata on decomposable trees
Ravve, E. V.; Volkovich, Z.; Weber, Gerhard Wilhelm (Informa UK Limited, 2014-01-02)
In this paper, we consider quantitative optimization problems on decomposable discrete systems. We restrict ourselves to labeled trees as the description of the systems and we use weighted automata on them as our computational model. We introduce a new kind of labeled decomposable trees, sum-like weighted labeled trees, and propose a method, which allows us to reduce the solution of an optimization problem, defined in a fragment of Weighted Monadic Second Order Logic, on such a tree to the solution of effec...
Analysis of volatility feedback and leverage effects on the ISE30 index using high frequency data
Inkaya, A.; Okur, Y. Yolcu (Elsevier BV, 2014-03-15)
In this study, we employ the techniques of Malliavin calculus to analyze the volatility feedback and leverage effects for a better understanding of financial market dynamics. We estimate both effects for a general semimartingale model applying Fourier analysis developed in Malliavin and Mancino (2002) [10]. We further investigate their joint behaviour using 5 min data of the ISE30 index. On the basis of these estimations, we look for the evidence that volatility feedback effect rate can be employed in the s...
JOINT PRICING AND REPLENISHMENT DECISIONS FOR NON-INSTANTANEOUS DETERIORATING ITEMS WITH PARTIAL BACKLOGGING, INFLATION- AND SELLING PRICE-DEPENDENT DEMAND AND CUSTOMER RETURNS
Ghoreishi, Maryam; Mirzazadeh, Abolfazl; Weber, Gerhard Wilhelm; Nakhai-Kamalabadi, Isa (American Institute of Mathematical Sciences (AIMS), 2015-07-01)
This paper develops an Economic Order Quantity (EOQ) model for non-instantaneous deteriorating items with selling price- and inflation-induced demand under the effect of inflation and customer returns. The customer returns are assumed as a function of demand and price. Shortages are allowed and partially backlogged. The effects of time value of money are studied using the Discounted Cash Flow approach. The main objective is to determine the optimal selling price, the optimal length of time in which there is...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
M. Rainer, “Calibration of stochastic models for interest rate derivatives,”
OPTIMIZATION
, pp. 373–388, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63351.