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

Friedrich Hubalek, Walter Schachermayer

Publikation: Working/Discussion PaperWU Working Paper

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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)
OriginalspracheEnglisch
ErscheinungsortVienna
HerausgeberSFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business
PublikationsstatusVeröffentlicht - 1998

Publikationsreihe

NameReport Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
Nr.13

WU Working Paper Reihe

  • Report Series SFB \Adaptive Information Systems and Modelling in Economics and Management Science\

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