# Johannes Kepler Symposium für Mathematik

Im Rahmen des Johannes-Kepler-Symposiums für Mathematik wird Dr. Gunther Leobacher, Institut für Finanzmathematik, JKU Linz, am Wed, March 21, 2012 um 17:15 Uhr im HS 13 einen öffentlichen Vortrag (mit anschließender Diskussion) zum Thema "Path Construction, Monte Carlo Pricing and Calibration, Utility Indifference Pricing" halten, zu dem die Veranstalter des Symposiums,

O.Univ.-Prof. Dr. Ulrich Langer,
Univ.-Prof. Dr. Gerhard Larcher
A.Univ.-Prof. Dr. Jürgen Maaß, und
die ÖMG (Österreichische Mathematische Gesellschaft)

Series B - Mathematical Colloquium:

The intention is to present new mathematical results for an audience interested in general mathematics.

### Path Construction, Monte Carlo Pricing and Calibration, Utility Indifference Pricing

I will present a selection of topics in the field of computational finance.
First we will concern ourselves with the (fast) generation of discrete Brownian
paths, by which we mean generation methods which need at most O(n log(n))
floating point operations for a discrete path with n nodes.
I will present some classical and some new constructions, highlight some of
their relations and show how they can be used in fast generations of
discrete Levy paths. We discuss how our method can be applied to more
general simulation problems.

Next we consider the problem of (quasi-)Monte Carlo valuation and
(quasi-)Monte Carlo calibration of credit risk models. We will see
theoretical reasons why quasi-Monte Carlo simulation is more suited to
the calibration problem than Monte Carlo. This is also discussed for
a stochastic volatility model.

In the final part of the talk we will see applications of the so-called
utility indifference pricing method for rainfall derivatives and
catastrophe bonds. One intriguing aspect of the first problem is that
a large portion of the simulation part disappears, thus rendering it more
tractable. In the second problem it emerges that the problem has a semi-exact
solution, i.e. the price of the derivative can be written as a solution to an
integro partial differential equation.