313 research outputs found
A mathematical proof of the existence of trends in financial time series
We are settling a longstanding quarrel in quantitative finance by proving the
existence of trends in financial time series thanks to a theorem due to P.
Cartier and Y. Perrin, which is expressed in the language of nonstandard
analysis (Integration over finite sets, F. & M. Diener (Eds): Nonstandard
Analysis in Practice, Springer, 1995, pp. 195--204). Those trends, which might
coexist with some altered random walk paradigm and efficient market hypothesis,
seem nevertheless difficult to reconcile with the celebrated Black-Scholes
model. They are estimated via recent techniques stemming from control and
signal theory. Several quite convincing computer simulations on the forecast of
various financial quantities are depicted. We conclude by discussing the r\^ole
of probability theory
Delta Hedging in Financial Engineering: Towards a Model-Free Approach
Delta hedging, which plays a crucial r\^ole in modern financial engineering,
is a tracking control design for a "risk-free" management. We utilize the
existence of trends in financial time series (Fliess M., Join C.: A
mathematical proof of the existence of trends in financial time series, Proc.
Int. Conf. Systems Theory: Modelling, Analysis and Control, Fes, 2009. Online:
http://hal.inria.fr/inria-00352834/en/) in order to propose a model-free
setting for delta hedging. It avoids most of the shortcomings encountered with
the now classic Black-Scholes-Merton framework. Several convincing computer
simulations are presented. Some of them are dealing with abrupt changes, i.e.,
jumps.Comment: 18th Mediterranean Conference on Control and Automation, Marrakech :
Morocco (2010
Stability margins and model-free control: A first look
We show that the open-loop transfer functions and the stability margins may
be defined within the recent model-free control setting. Several convincing
computer experiments are presented including one which studies the robustness
with respect to delays.Comment: 13th European Control Conference, Strasbourg : France (2014
Systematic and multifactor risk models revisited
Systematic and multifactor risk models are revisited via methods which were
already successfully developed in signal processing and in automatic control.
The results, which bypass the usual criticisms on those risk modeling, are
illustrated by several successful computer experiments.Comment: First Paris Financial Management Conference, Paris : France (2013
Preliminary remarks on option pricing and dynamic hedging
An elementary arbitrage principle and the existence of trends in financial
time series, which is based on a theorem published in 1995 by P. Cartier and Y.
Perrin, lead to a new understanding of option pricing and dynamic hedging.
Intricate problems related to violent behaviors of the underlying, like the
existence of jumps, become then quite straightforward by incorporating them
into the trends. Several convincing computer experiments are reported.Comment: 1st International Conference on Systems and Computer Science,
Villeneuve d'Ascq : France (2012
Towards New Technical Indicators for Trading Systems and Risk Management
We derive two new technical indicators for trading systems and risk management. They stem from trends in time series, the existence of which has been recently mathematically demonstrated by the same authors (A mathematical proof of the existence of trends in financial time series, Proc. Int. Conf. Systems Theory: Modelling, Analysis and Control, Fes, 2009), and from higher order quantities which replace the familiar statistical tools. Recent fast estimation techniques of algebraic flavor are utilized. The first indicator tells us if the future price will be above or below the forecasted trendline. The second one predicts abrupt changes. Several promising numerical experiments are detailed and commented.Quantitative Finance, technical analysis, trading systems, risk management, trends, technical indicators, time series
Delta Hedging in Financial Engineering: Towards a Model-Free Approach
Delta hedging, which plays a crucial rôle in modern financial engineering, is a tracking control design for a "risk-free" management. We utilize the existence of trends in financial time series (Fliess M., Join C.: A mathematical proof of the existence of trends in financial time series, Proc. Int. Conf. Systems Theory: Modelling, Analysis and Control, Fes, 2009. Online: http://hal.inria.fr/inria-00352834/en/) in order to propose a model-free setting for delta hedging. It avoids most of the shortcomings encountered with the now classic Black-Scholes-Merton framework. Several convincing computer simulations are presented. Some of them are dealing with abrupt changes, i.e., jumps.Financial engineering; delta hedging; dynamic hedging; trends; quick fluctuations; abrupt changes; jumps; tracking control; model-free control
A model-free approach to delta hedging
See http://hal.inria.fr/inria-00479824/en/ for a slightly more elaborate version.Delta hedging; trends; quick fluctuations; abrupt changes; jumps; tracking control; model-free control
Systematic risk analysis: first steps towards a new definition of beta
We suggest a new model-free definition of the beta coefficient, which plays an important rôle in systematic risk management. This setting, which is based on the existence of trends for financial time series via nonstandard analysis (Fliess M., Join C.: A mathematical proof of the existence of trends in financial time series, Proc. Int. Conf. Systems Theory: Modelling, Analysis and Control, Fes, 2009, online: http://hal.inria.fr/inria-00352834/en/) leads to convincing computer experiments which are easily implementable.Quantitative finance; risk analysis; beta; alpha; trends; technical analysis; estimation techniques; forecasting; abrupt changes; nonstandard analysis.
A mathematical proof of the existence of trends in financial time series
We are settling a longstanding quarrel in quantitative finance by proving the existence of trends in financial time series thanks to a theorem due to P. Cartier and Y. Perrin, which is expressed in the language of nonstandard analysis (Integration over finite sets, F. & M. Diener (Eds): Nonstandard Analysis in Practice, Springer, 1995, pp. 195--204). Those trends, which might coexist with some altered random walk paradigm and efficient market hypothesis, seem nevertheless difficult to reconcile with the celebrated Black-Scholes model. They are estimated via recent techniques stemming from control and signal theory. Several quite convincing computer simulations on the forecast of various financial quantities are depicted. We conclude by discussing the rôle of probability theory.Financial time series; mathematical finance; technical analysis; trends; random walks; efficient markets; forecasting; volatility; heteroscedasticity; quickly fluctuating functions; low-pass filters; nonstandard analysis; operational calculus.
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