When: Wednesday, November 24, 2010 @ 5 pm
Where: Room MC310, Mechanical Building

Click here to download the presentation slides

Oleksandr Romanko is currently a research fellow at Algorithmics (Quantitative
Research Group) and a MITACS postdoctoral fellow at McMaster University
(Department of Computing and Software). He holds Ph.D. in Computer Science from McMaster University. Oleksandr's research interests include operational
research, multi-objective and parametric optimization, algorithms, portfolio
optimization, financial and risk modeling. He has published a number of
research papers and won several awards from the Canadian Operational Research Society and MITACS.

This talk is based on the research done at Algorithmics, and illustrates how
operational research and optimization are applied to real-world financial and
risk management problems in the industrial setting. Algorithmics is the world's
leading provider of risk solutions. Financial organizations from around the
world use Algorithmics' software, analytics and advisory services to help them
make risk-aware business decisions.

Abstract
Replicating portfolios are used by insurance companies to measure and
manage risk. A replicating portfolio comprises a set of standard
financial assets whose value closely matches that of a liability
portfolio under current and future market conditions. If the replication
is sufficiently precise and the assets can be priced faster than the
liability then the replicating portfolio is a computationally efficient
proxy for conducting risk analysis of the liability. Replicating
portfolios are typically constructed by minimizing the difference
between the cash flows of the liability and the replicating portfolio in
a set of stochastic scenarios. For practical reasons it is desirable for
the replicating portfolio to be sparse, i.e., to contain a relatively
small number of assets. Sparse replicating portfolios perform better
out-of-sample and can be priced faster.

Regularized optimization, by means of trading penalties or constraints,
is an effective way to obtain sparse replicating portfolios. Previous
studies considered only a simple type of trading constraint when an
identical trading cost is assigned to all instruments. Studies of
similar problems in regression analysis and signal processing indicate
that more sophisticated costing schemes can yield better results. In
this research we evaluate a number of alternative schemes for specifying
trading costs based on their out-of-sample performance under different
optimization models. The performance of trading cost restrictions is
compared to that of cardinality-constraints, i.e., the portfolio is
explicitly limited to contain at most a specified number of instruments.
We find that trading costs based on simple statistics of the instrument
and liability cash flows are an effective choice in practice.

Based on our experience at Algorithmics Inc., we discuss practical
issues relevant to industrial-strength implementation of software for
portfolio replication. Those issues, among others, include overcoming
numerical difficulties occurring due to badly scaled financial data
while solving large-scale portfolio optimization problems. We describe
optimization techniques utilized for fast computing of efficient
portfolio frontiers. Criteria for selecting a final replicating
portfolio on the computed efficient frontier are discussed as well.