Ph.D. thesis (engl.)

Fields of Interest:

• Causes for stock market crashes 
• Precursors to stock market crashes 
• Predictability of stock market crashes 
• Crashes seen as phase transitions resp. critical phenomena 
• Log-periodic oscillations 
• Discrete scale invariance 
• Historic examples of stock market crashes

Talks:

• Analytic Solutions for Pricing Double Barrier Options in the Presence of Stochastic Volatility
  Summary of my diploma thesis (see below)
  (May 23 2002, Commerzbank) 
• Börsencrashs - existieren Vorboten?
  Introductory talk covering stock market crashes and previous attempts by econophysists to identify precursors.
  (June 05 2007, University of Mannheim) 
• Spekulationsblasen: Modellierung mit Methoden der Hydrodynamik
  Talk focussing on the modelling of stock market crashes as critical phenomena, drawing parallels to hydrodynamic turbulences.
  (May 26 2008, University of Mannheim)

Diploma (M.Sc.) Thesis:

Analytic Methods for Pricing Double Barrier Options in the Presence of Stochastic Volatility University of Kaiserslautern, July 2002, supervised by Prof. Ralf Korn 

Abstract: While there exist closed-form solutions for vanilla options in the presence of stochastic volatility for nearly a decade [Heston, 1993], practitioners still depend on numerical methods - in particular the Finite Difference and Monte Carlo methods - in the case of double barrier options. It was only recently that Lipton [2001] proposed (semi-)analytical solutions for this special class of path-dependent options.
Although he presents two different approaches to derive these solutions, he restricts himself in both cases to a less general model, namely one where the correlation and the interest rate differential are assumed to be zero. Naturally the question arises, if these methods are still applicable for the general stochastic volatility model without these restrictions.
In this paper we show that such a generalization fails for both methods. We will explain why this is the case and discuss the consequences of our results.

Keywords: Stochastic volatility, Heston model, method of images, eigenfunction expansion, double barrier options, digital options, power options, option pricing 

Available files:

• Thesis in PDF format 
• Thesis in PS format 
• Algorithms in Excel 
• Algorithms in Mathematica 
•  Presentation in PDF format

 Ph.D. Thesis:

 In progress

 Miscellaneous:

• Simulating a Ponzi Scheme (Excel-Spreadsheet)