Events

Visitors

Opening Event : TBA.

2014

Professor Daniel Dufresne, Centre for Actuarial Studies, Department of Economics, University of Melbourne. April 21-25 and May 2 - 8.

During his visit to the Institute, Prof Dufresne conducted research on computational efficiency for problems in financial mathematics. His lectures provided the basis for a scholarly paper on the simulation of financial options under a change of measure for stochastic volatility models. Students that work within these projects include Elizabeth Pysher (orthogonal polynomials and mathematica code) and Alexey Nikolaev (Filtered Monte Carlo simulation for the estimation of Lyapunov exponents).

April 23 and 25: 2 - 3 pm. "Recursion formulas for Gram Charlier distributions", Room N 1000 C.

May 5 and 6: 2 - 3 pm. "Change of Measure for the Square Root Process", Room N 1000 C.

Professor Daniel Dufresne, Centre for Actuarial Studies, Department of Economics, University of Melbourne.

Originally from Canada, Professor Daniel Dufresne has been in the Dept. of Economics of the University of Melbourne in Australia since 2003. He works on option pricing, probability theory and actuarial science.

Title: Change of Measure for the square-root process

Date: 12 November 2014, 4:30 pm

Room: Hunter North C102

Abstract: The square-root process is used to model interest rates and volatility in financial mathematics. The pricing of derivatives involving that process often requires simulating it, since there are often no explicit formulas for prices. We study how a change of measure (CM) may improve those simulations. We compare with Andersen's quadratic-exponential scheme (QE), which so far appears to be the most efficient technique to simulate the stochastic differential equation satisfied by the square-root process. An integer-dimension squared Bessel process, easy to simulate, is used to generate the law of the square-root process using a change of measure. The new method performs very well, and the two algorithms execute at similar speeds; however, CM is slower than QE if random number generation is taken into account, because CM requires more random numbers. The Radon-Nikodym derivative sometimes has a rather intriguing behavior, which is itself of interest. We propose an explanation.

Title: Gram-Charlier processes and option pricing

Date: 19 November 2014, 4:30 pm

Room: Hunter North C102

Abstract: A Gram-Charlier distribution has a density that is a polynomial times a normal density. Those distributions have been used to model stock returns in option pricing, as an improvement over the normal distribution. Properties of the Gram-Charlier distributions are derived, including moments, tail estimates, moment indeterminacy of the exponential of a Gram-Charlier distributed variable, non-existence of a continuous-time Levy process with Gram-Charlier increments, as well as formulas for option prices and their sensitivities. A procedure for simulating Gram-Charlier distributions is given. Multiperiod Gram-Charlier modelling of asset returns is described, apparently for the first time. Formulas for equity indexed annuities' premium option values are given, and a numerical illustration shows the importance of skewness and kurtosis of the risk neutral density.