# Some Applications of Sequential Analysis in Quantitative Finance

*Stochastic Processes Seminar*

Joint seminar Series on Stochastic Processes and Financial Mathematics

*by William P. Malcolm*

*Institution:*Statistical Machine Learning Program National ICT Australia (NICTA), Canberra

*Date: Fri 25th May 2007*

*Time: 1:15 PM*

*Location: Russell Love Theatre, Richard Berry Building, The University of Melbourne*

*Abstract*: In modern Electrical Engineering, the term $M$-ary detection generally refers to what is known as sequential hypothesis testing, or sequential analysis within the statistics community. Here, $M$ is any natural number

greater than or equal to the number 2.

Some common applications of $M$-ary detection in Electrical Engineering

are determining which from a collection of candidate dynamical systems might best explain an observed process. In this context the term {\em

best} refers to the technique of maximum likelihood.

In this seminar we consider the application of sequential analysis techniques to mainstream problems in quantitative finance. In the first part of our seminar, we investigate model calibration for the log normal asset dynamics. It is common practice to approach this problem with Expectation Maximization (EM) algorithm techniques, however, computation time is critical in quantitative finance and the EM algorithm is often

slow to converge. We revisit the above model calibration problem recast as a sequential analysis problem. Sequential analysis algorithms to determine the mean-annual return and the volatility are given. It is interesting to

note that classical estimation of the mean-annual return can take the order of 100 years of data, however, a sequential analysis algorithm can

reduce this computation time substantially, as will be shown with simulation studies.

*For More Information:* Daniel Dufresne dufresne@unimelb.edu.au or Aihua Xia: xia@ms.unimelb.edu.au