TY - THES A1 - Müller, Stefanie T1 - The Binomial Approach to Option Valuation: Getting Binomial Trees into Shape N2 - This thesis deals with the application of binomial option pricing in a single-asset Black-Scholes market and its extension to multi-dimensional situations. Although the binomial approach is, in principle, an efficient method for lower dimensional valuation problems, there are at least two main problems regarding its application: Firstly, traded options often exhibit discontinuities, so that the Berry- Esséen inequality is in general tight; i.e. conventional tree methods converge no faster than with order 1/sqrt(N). Furthermore, they suffer from an irregular convergence behaviour that impedes the possibility to achieve a higher order of convergence via extrapolation methods. Secondly, in multi-asset markets conventional tree construction methods cannot ensure well-defined transition probabilities for arbitrary correlation structures between the assets. As a major aim of this thesis, we present two approaches to get binomial trees into shape in order to overcome the main problems in applications; the optimal drift model for the valuation of single-asset options and the decoupling approach to multi-dimensional option pricing. The new valuation methods are embedded into a self-contained survey of binomial option pricing, which focuses on the convergence behaviour of binomial trees. The optimal drift model is a new one-dimensional binomial scheme that can lead to convergence of order o(1/N) by exploiting the specific structure of the valuation problem under consideration. As a consequence, it has the potential to outperform benchmark algorithms. The decoupling approach is presented as a universal construction method for multi-dimensional trees. The corresponding trees are well-defined for an arbitrary correlation structure of the underlying assets. In addition, they yield a more regular convergence behaviour. In fact, the sawtooth effect can even vanish completely, so that extrapolation can be applied. KW - Finanzmathematik KW - Option KW - Derivat KW - Bewertung KW - Binomialbaum KW - Approximationsalgorithmus KW - Finanznumerik KW - Multi-Asset Option KW - Konvergenzrate KW - Konvergenzverhalten KW - Sägezahneffekt KW - monotone Konvergenz KW - Extrapolation KW - computational finance KW - multi-asset option KW - option valuation KW - binomial tree KW - rate of convergence KW - convergence behaviour KW - sawtooth effect Y1 - 2009 UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2166 UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-24627 ER -