Sökning: "fraktionell Brownsk rörelse"

Hittade 2 uppsatser innehållade orden fraktionell Brownsk rörelse.

1. 1. Financial Modelling Using Fractional Processes And The Wiener Chaos Expansion

   Master-uppsats, KTH/Matematik (Avd.)

   Författare :Olof Hummelgren; [2022]
   Nyckelord :fractional Brownian motion; fBM; applied mathematics; Wiener chaos expansion; Wick product; Hurst parameter; fraktionell Brownsk rörelse; tillämpad matematik; Wiener kaosexpansion; Wickprodukt; Hurstparameter;

   Sammanfattning : The aim of this thesis is to simulate stochastic models that are driven by a fractional Brownian motion process and to apply these methods to financial applications related to yield rate and asset price modelling. Several rough volatility processes are used to model the asset price and yield dynamics. LÄS MER

3. 2. Pricing in the Heston Model and Its Rough Variation

   Master-uppsats, KTH/Matematik (Avd.)

   Författare :Otto Sellerstam; [2021]
   Nyckelord :;

   Sammanfattning : This thesis presents the theoretical material needed to price European call options in the classical and rough version of the Heston model, as well as how to do this in practice from a computational perspective. The theoretical material includes an introduction to measure theory, which is then used to build the foundations of probability theory and stochastic calculus, together with more novel topics such as fractional calculus and a short exposition of the fractional Brownian motion. LÄS MER