Mathematics (English Text)

Monte-Carlo Methods on GPGPU with Applications to Mathematical Finance

There will be a workshop on
Monte-Carlo Methods on GPGPU with Applications to Mathematical Finance
at the LMU quantLab. For details see

LIBOR Market Model: Spreadsheet and Source Code

Spreadsheet and code for the LIBOR market model added to Java source code availabe from the finmath lib subversion repository.


Curve Calibration: Spreadsheet and Source Code

Demo spreadsheet for the calibration of curves (discount curves, forward curves) to interest rate swaps added to the spreadsheets section of Java source code availabe from the finmath lib subversion repository.


Computational Finance: Job Offer at LMU Department of Mathematics

The Ludwig-Maximilian-University Munich, Department of Mathematics, is advertising a

Post Doctoral or Doctoral position

in the field of financial and insurance mathematics with special IT duties. The position is commencing at the earliest convenience for a term of 2 years with possible extension.
For details see

Conditional Analytic Monte-Carlo Pricing Scheme for Auto-Callables

We renamed the paper cited in the Journal of Computational Finance 11(3) as "A semi-analytic Monte Carlo pricing scheme for auto-callable products". Its new title is "Conditional Analytic Monte Carlo Pricing Scheme for Auto-Callable Products".

Book: Mathematical Finance: Second Printing

Wiley released a second printing of my book. The second printing is based on Version 1.6.11 of the PDF file. It thus contains many of the error corrections listed on the errata page. In addition, I rewrote a few sections (25 pages changed), but the difference to the old version is still minor. Major improvements, like new sections will be posted to the book's update page. (The version number is printed on page v).

PS: I will donate a larger part of my 2007 net revenue to charity organizations (like the Fördergemeinschaft Deutsche Kinderherzzentren and Deutsche Krebshilfe (German Cancer Aid)). However: my net revenue is comparably small. From Wiley I get approximately $3 per book. BTW: Sorry for the price tag. I wasn't aware that the author does not have any influence on the pricing of his book.

Sample Chapters

Sample chapters for "Mathematical Finance" are available as a free download from the book's homepage.

Joshi on LMM

Mark Joshi is giving a seminar on "Implementing the LIBOR Market Model". The seminar will take place in London, 24th-25th January 2008. For more information see the flyer. Literature: Mark's books at,,

Mathematical Finance: Picture Book

The "Mathematical Finance Picture Book" presents some aspects of mathematical finance in pictures. It is a companion to "Mathematical Finance: Theory, Modeling, Implementation" (which contains these figures in grayscale only).

The "Mathematical Finance Picture Book" is available as PDF.

Book: Mathematical Finance: Theory, Modeling, Implementation: Errata

Version 1.5 of "Mathematical Finance" is published by Wiley on August 24th. I will maintain an errata online at

Book: Mathematical Finance: Theory, Modeling, Implementation

Version 1.5 of my book may be pre-ordered at Amazon™:

Mathematical Finance Lecture Notes

The translation of my lecture notes on "mathematical finance" has been completed. The manuscript still needs some proofreading and polishing. If you would like to do a payed proofreading job on the manuscript please contract me via email (a native english speaker with good knowledge of german and some knowledge of math would be an ideal candidate).

I have released version 1.4 of the manuscript (in both german and english).

For a detailed table of contents see

Talk on Proxy Simulation Scheme Method

I gave a talk at the WBS 3rd Fixed Income Conference, Amsterdam, 21-22 September 2006 presenting the proxy simulation scheme method. The talk covered the "full proxy" and the "partial proxy" simulation scheme method. The first part (full proxy) had been presented at the Quantitative Methods in Finance Conference, Sydney, 2005. I have posted an updated version of the slides at

In addition I gave a 10 min talk at the "interest rate plenary panel". If you are interest in the "foresight bias correction" mentioned there, see

Partial Proxy Simulation Schemes for Robust Monte-Carlo Sensitivities

We consider a generic framework which allows to calculate robust Monte-Carlo sensitivities seamlessly through simple finite difference approximation. The method proposed is a generalization and improvement of the proxy simulation scheme method (Fries and Kampen, 2005).

As a benchmark we apply the method to the pricing of digital caplets and target redemption notes using LIBOR and CMS indices under a LIBOR Market Model. We calculate stable deltas, gammas and vegas by applying direct finite difference to the proxy simulation scheme pricing.

The framework is generic in the sense that it is model and almost product independent. The only product dependent part is the specification of the proxy constraint. This allows for an elegant implementation, where new products may be included at small additional costs.

For more information see

Mathematical Finance Lecture Notes

Version 1.3.x of the lecture notes on "mathematical finance" now contains the missing chapter on Monte-Carlo sensitivities. The calculation of Monte-Carlo sensitivities (a.k.a. Greeks) was discussed in the last two sessions of the 2005/2006 lecture. Apart from two new chapters this version contains over 100 corrections.

For a detailed table of contents see

Cross-Currency Markov Functional Model with FX Smile

We have a paper on the cross-currency Markov functional model where the FX functional allow a calibration to a given market implied volatility smile. Calibration works for twenty years and beyond. More details may be found in the Diploma thesis of Fabian Eckstädt.

One Day Lecture at s:f:i

I will give a one day lecture as part of the Certificate FAME Program 2006 at the swiss finance institute.

The lecture will take place August 2
nd at University of Lausanne. See the program of this event for details. As precourse reading you should consider Chapter 8, 9 and 10 (interest rate basics), Chapter 12 (exotic derivatives) and Chapter 15 (libor market model) of my lecture notes. These chapters are available in english and german.

Foresight Bias

I participated in the ECMI 2006 Mini-Symposium "Optimal stopping and optimal control problems in finance", Madrid, and the Risk Quant Congress USA 2006, New York. The updated presentation of my talk "Monte-Carlo Pricing of Bermudan Options: Removal of Super-Optimal and Sub-Optimal Exercise" may be download as a PDF file.

Mathematical Finance Lecture Notes

A first draft of the english version of "Mathematical Finance" is available on my home page. Chapters which are not yet translated will be given in German. I will add more translations depending on my spare time.

The book arose from my lecture notes for the lectures on mathematical finance held at University of Mainz and University of Frankfurt. It tries to give a balanced representation of the theoretic foundations, state of the art models, which are actually used in practice and their implementation.

For more information see

Equity Markov Functional Model

I wrote a small note on how to do Markov Functional Modeling for a single asset (like equity). The "trick" only works if you use the asset itself as Numéraire. However, on the other hand, this is exactly what you do in Markov Functional Modeling of interest rates, where the Numéraire is an interest rate product. The approach in this note is very similar to the Markov Functional Model in spot LIBOR measure (the original Makov Functional Model was specified in terminal measure).
Version 0.4 of the paper is still lacking an introduction.

(Edit 14.04.06): In Version 0.8 I have added a nice discussion on model dynamics, using Black-Scholes like functionals as a starting point for my examples. The discussion shows how to calibrate the joint asset-interest rate dynamics (ie. r(S)) and forward volatility (all this in addition to the calibration to a full two dimensional smile surface.

Smile Modeling in the LIBOR Market Model

I have put online the Diploma thesis of Markus Meister "Smile Modeling in the LIBOR Market Model". See