eprintid: 6549
rev_number: 8
eprint_status: archive
userid: 1
dir: disk0/00/00/65/49
datestamp: 2006-05-29 13:55:47
lastmod: 2015-04-21 16:11:38
status_changed: 2012-08-14 15:18:40
type: preprint
metadata_visibility: show
creators_name: Jäger, Simon
creators_name: Kostina, Ekaterina
title: An Inverse Problem for a Nonlinear Stochastic Differential Equation Modeling  Price Dynamics
ispublished: pub
subjects: ddc-510
divisions: i-708000
cterms_swd: Nichtlineares inverses Problem
cterms_swd: Numerisches Verfahren
cterms_swd: Wechselkurs
abstract: Diffusion processes are widely used for mathematical modeling in finance e.g. in modeling foreign exchange rates. This paper presents a non-linear stochastic continuous time model that captures the main characteristics of price dynamics. The generalized mean reversion process discloses various features of observed price movements such as multi-modality of the distributions, multiple equilibria, and regime switching. The attractors depend substantially on the economic environment. The model reveals a significant connection between exchange rates and its fundamentals. Furthermore, it is consistent with traditional flexible exchange rate models. Stochastic differential equations describing diffusion processes are directly linked to the forward Kolmogorov equation. In order to calibrate the models, efficient algorithms identifying the system parameters are in demand. Taking into account nonlinear effects in volatility and drift and dependence on observed economic data, which are not directly modeled, one obtains problems which cannot be treated by standard numerical methods. The coefficients are rapidly oscillatory and strong instabilities may arise. To handle these problems we develop numerical methods, which are used to simulate the nonlinear dynamics of exchange rates depending on economic data.
abstract_translated_lang: eng
class_scheme: msc
class_labels: 91B24, 90C55, 93C20
date: 2006
date_type: published
id_scheme: DOI
id_number: 10.11588/heidok.00006549
ppn_swb: 1646175875
own_urn: urn:nbn:de:bsz:16-heidok-65496
language: eng
bibsort: JAGERSIMONANINVERSEP2006
full_text_status: public
citation:   Jäger, Simon ; Kostina, Ekaterina  (2006) An Inverse Problem for a Nonlinear Stochastic Differential Equation Modeling Price Dynamics.  [Preprint]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/6549/1/price_dynamics.pdf