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When does convergence of asset price processes imply convergence of option prices?

Hubalek, Friedrich and Schachermayer, Walter (1998) When does convergence of asset price processes imply convergence of option prices? Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science", 13. SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, Vienna.

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Abstract

We consider weak convergence of a sequence of asset price models (Sn) to a limiting asset price model S. A typical case for this situation is the convergence of a sequence of binomial models to the Black-Scholes model, as studied by Cox, Ross, and Rubinstein. We put emphasis on two different aspects of this convergence: firstly we consider convergence with respect to the given "physical" probability measures (Pn) and secondly with respect to the "risk-neutral" measures (Qn) for the asset price processes (Sn). (In the case of non-uniqueness of the risk-neutral measures also the question of the "good choice" of (Qn) arises.) In particular we investigate under which conditions the weak convergence of (Pn) to P implies the weak convergence of (Qn) to Q and thus the convergence of prices of derivative securities. The main theorem of the present paper exhibits an intimate relation of this question with contiguity properties of the sequences of measures (Pn) with respect to (Qn) which in turn is closely connected to asymptotic arbitrage properties of the sequence (Sn) of security price processes. We illustrate these results with general homogeneous binomial and some special trinomial models. (author's abstract)

Item Type: Paper
Keywords: weak convergence / option prices / asymptotic arbitrage / contiguity / binomial models
Divisions: Departments > Informationsverarbeitung u Prozessmanag. > Produktionsmanagement > Taudes
Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Departments > Marketing > Service Marketing und Tourismus
Departments > Informationsverarbeitung u Prozessmanag. > Informationswirtschaft
Depositing User: Repository Administrator
Date Deposited: 07 Mar 2002 17:17
Last Modified: 24 Oct 2014 03:21
URI: http://epub.wu.ac.at/id/eprint/1768

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