Das Suchergebnis hat sich seit Ihrer Suchanfrage verändert. Eventuell werden Dokumente in anderer Reihenfolge angezeigt.
  • Treffer 58 von 226
Zurück zur Trefferliste

Edgeworth Expansions for Binomial Trees

  • In the theory of option pricing one is usually concerned with evaluating expectations under the risk-neutral measure in a continuous-time model. However, very often these values cannot be calculated explicitly and numerical methods need to be applied to approximate the desired quantity. Monte Carlo simulations, numerical methods for PDEs and the lattice approach are the methods typically employed. In this thesis we consider the latter approach, with the main focus on binomial trees. The binomial method is based on the concept of weak convergence. The discrete-time model is constructed so as to ensure convergence in distribution to the continuous process. This means that the expectations calculated in the binomial tree can be used as approximations of the option prices in the continuous model. The binomial method is easy to implement and can be adapted to options with different types of payout structures, including American options. This makes the approach very appealing. However, the problem is that in many cases, the convergence of the method is slow and highly irregular, and even a fine discretization does not guarantee accurate price approximations. Therefore, ways of improving the convergence properties are required. We apply Edgeworth expansions to study the convergence behavior of the lattice approach. We propose a general framework, that allows to obtain asymptotic expansion for both multinomial and multidimensional trees. This information is then used to construct advanced models with superior convergence properties. In binomial models we usually deal with triangular arrays of lattice random vectors. In this case the available results on Edgeworth expansions for lattices are not directly applicable. Therefore, we first present Edgeworth expansions, which are also valid for the binomial tree setting. We then apply these result to the one-dimensional and multidimensional Black-Scholes models. We obtain third order expansions for general binomial and trinomial trees in the 1D setting, and construct advanced models for digital, vanilla and barrier options. Second order expansion are provided for the standard 2D binomial trees and advanced models are constructed for the two-asset digital and the two-asset correlation options. We also present advanced binomial models for a multidimensional setting.

Volltext Dateien herunterladen

Metadaten exportieren

Verfasserangaben:Alona Bock
URN (Permalink):urn:nbn:de:hbz:386-kluedo-38616
Betreuer:Ralf Korn
Sprache der Veröffentlichung:Englisch
Veröffentlichungsdatum (online):31.08.2014
Jahr der Veröffentlichung:2014
Veröffentlichende Institution:Technische Universität Kaiserslautern
Titel verleihende Institution:Technische Universität Kaiserslautern
Datum der Annahme der Abschlussarbeit:22.08.2014
Datum der Publikation (Server):02.09.2014
Seitenzahl:II, 128
Fachbereiche / Organisatorische Einheiten:Fachbereich Mathematik
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 510 Mathematik
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vom 10.09.2012