Yesterday, my teenage daughter asked me to write about Everything Worth Knowing in Finance. Coincidentally, and, propitiously yesterday, one of my former students, Dr. Dmytro Matsypura of the University of Sydney, gave a talk in our Speaker Series on Combinatorial Analysis of Option Spreads. He spoke on margining accounts, i.e., the calculation of minimum regulatory margin requirements for margin accounts, which is a critical intra-day and end-of-day risk management operation in the list of mandatory activities of any prime brokerage firm. Margining an account without positions in options or other derivatives is simply the calculation of the total margin requirement for all positions in the account. Options, however, he noted, bring a nontrivial combinatorial component to the calculation because margin regulations for positions in options permit the use of different hedging strategies for margin reductions. Hedging strategies usually imitate trading strategies designed for margin trading. Hedging strategies involving only options are called option spreads.In December 2005, the U.S. Securities and Exchange Commission approved margin rules for complex option spreads with 5, 6, 7, 8, 9, 10 and 12 legs (positions in options). Only basic option spreads with 2, 3 or 4 legs were recognized before. Taking advantage of option spreads with a large number of legs substantially reduces margin requirements and, at the same time, adequately estimates risk for margin accounts with positions in options. Dr. Matsypura presented combinatorial models for option spreads with any number of legs and proposed their full characterization in terms of matchings, alternating cycles and chains in colored graphs. With co-authors, he showed that the combinatorial analysis of option spreads reveals powerful hedging mechanisms in the structure of margin accounts. He also provided recommendations on how to create more efficient margin rules for options.
My favorite part of his presentation came at the very end, when he showed that what was considered to originally be an NP hard problem could be transformed into a maximum flow network problem! This was a really exciting result! Having co-authored with Dr. Stavros Siokos, the book, Financial Networks: Statics and Dynamics, I love to see additional network structures identified in financial problems!
The photos above were taken at Dr. Matsypura's talk and the lunch that followed.
Plus, yesterday, I received a new book in the mail, co- authored by two of my colleagues in my department, Professors Thomas Schneeweis and Hossein Kazemi, and Garry B. Crowder, a lawyer and financier. Their book, published by Wiley, is called, The New Science of Asset Allocation: Risk Management in a Multi-Asset World. This will be good reading during my air travels.
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