NDLI: Robustness for path-dependent volatility models

Content Provider	Springer Nature Link
Author	Rosestolato, Mauro Vargiolu, Tizia Villani, Giovanna
Copyright Year	2012
Abstract	In this paper, we consider a generalisation of the Hobson–Rogers model proposed by Foschi and Pascucci (Decis Eocon Finance 31(1):1–20, 2008) for financial markets where the evolution of the prices of the assets depends not only on the current value but also on past values. Using differentiability of stochastic processes with respect to the initial condition, we analyse the robustness of such a model with respect to the so-called offset function, which generally depends on the entire past of the risky asset and is thus not fully observable. In doing this, we extend previous results of Blaka Hallulli and Vargiolu (2007) to contingent claims, which are globally Lipschitz with respect to the price of the underlying asset, and we improve the dependence of the necessary observation window on the maturity of the contingent claim, which now becomes of linear type, while in Blaka Hallulli and Vargiolu (2007), it was quadratic. Finally, in this framework, we give a characterisation of the stationarity assumption used in Blaka Hallulli and Vargiolu (2007), and prove that this model is stationary if and only if it is reduced to the original Hobson–Rogers model. We conclude by calibrating the model to the prices of two indexes using two different volatility shapes.
Starting Page	137
Ending Page	167
Page Count	31
File Format	PDF
ISSN	15938883
Journal	Decisions in Economics and Finance
Volume Number	36
Issue Number	2
e-ISSN	11296569
Language	English
Publisher	Springer Milan
Publisher Date	2012-03-18
Publisher Place	Milan
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Path-dependent volatility models Hobson–Rogers model Differential of stochastic processes Lagrange theorem Economic Theory Econometrics Public Finance & Economics Finance/Investment/Banking Management/Business for Professionals Operations Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Finance

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