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 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:hbz:386-kluedo-24627
ER -