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) / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal.

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Subject of the submitted thesis is the issue of currency options. The aim is the detailed analysis of currency options forcefully on dealing, characteristics, methods of pricing and their use for hedging strategies. The first part of the thesis presents an introduction into the option theory. The second part is about dealing, pricing and arbitrage relationships of currency options. In this part are two option pricing model extracted -- the binomial options pricing model for pricing currency options and the Garman-Kohlhagen model for pricing European currency options. In the third part is an example for a currency put option hedging strategy.