Combinatorics of Option Spreads: The Margining Aspect

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. Only 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. In this paper we present combinatorial models for known and newly discovered option spreads with up to 134 legs. We propose their full characterization in terms of matchings, alternating cycles and chains in graphs with bicolored edges. We show that the combinatorial analysis of option spreads reveals powerful hedging mechanisms in the structure of margin accounts, and that the problem of minimizing the margin requirement for a portfolio of option spreads can be solved in polynomial time using network flow algorithms. We also give recommendations on how to create more efficient margin rules for options

Margining Option Portfolios by Network Flows

As shown in [Rudd and Schroeder, 1982], the problem of margining option portfolios where option spreads with two legs are used for offsetting can be solved in polynomial time by network flow algorithms. However, spreads with only two legs do not provide sufficient accuracy in measuring risk. Therefore, margining practice also employs spreads with three and four legs. A polynomial time solution to the extension of the problem where option spreads with three and four legs are also used for offsetting is not known. In this paper we propose a heuristic network flow algorithm for this extension and present a computational study that proves high efficiency of this algorithm in margining practice

Portfolio Margining: Strategy vs Risk

This paper presents the results of a novel mathematical and experimental analysis of two approaches to margining customer accounts, strategy-based and risk-based. Building combinatorial models of hedging mechanisms of these approaches, we show that the strategy-based approach is, at this point, the most appropriate one for margining security portfolios in customer margin accounts, while the risk-based approach can work efficiently for margining only index portfolios in customer mar-gin accounts and inventory portfolios of brokers. We also show that the application of the risk-based approach to security portfolios in customer margin accounts is very risky and can result in the pyramid of debt in the bullish market and the pyramid of loss in the bearish market. The results of this paper support the thesis that the use of the risk-based approach to margining customer accounts with positions in stocks and stock options since April 2007 influenced and triggered the U.S. stock market crash in October 2008. We also provide recommendations on ways to set appropriate margin requirements to help avoid such failures in the future

On scheduling cycle shops: classification, complexity and approximation

This paper considers problems of finding non‐periodic and periodic schedules in a cycle shop which is a special case of a job shop but an extension of a flow shop. The cycle shop means the machine environment where all jobs have to pass the machines over the same route like in a flow shop but some of the machines in the route can be met more than once. We propose a classification of cycle shops and show that recently studied reentrant flow shops, robotic flow shops, loop reentrant flow shops and V shops are special cases of cycle shops. Problems solvable in polynomial time, pseudopolynomial time, NP‐hard problems and performance guarantee approximations are presented. Related earlier results are surveyed

Affinity sorption analysis of the structure of poly(G)·poly(C) complex obtained by means of template-dependent synthesis

The analysis of the structure of poly(G)·poly (C) complexes obtained by the enzymatic synthesis on poly(C) template was carried out using the method of affinity sorption. This latter was used also for the purification of the synthesized so far complexes from the redundant template as well as for the investigation of the structure of poly(G) ·poly(C) complexes obtained by the «traditional» mixing of complementary homopo-lynucleotides. It was shown that the degree of template transcription depends on the quality of RNA polymerase and the incompleted transcription is connected with the inhibition of the elongation of poly(G) chain.Проведено аналіз структури комплексів полі(Г)·полі(Ц), одержаних ферментативним синтезом на матриці полі (Ц), за допомогою афінної сорбції. Останню застосовано також для очищення препаратів таких комплексів від надміру невикористаної матриці, а також для дослідження структури комплексів полі(Г)·полі(Ц), виділених традиційним методом змішування розчинів комплементарних полінуклеотидів. Показано, що повнота прочитання матриці полі(Ц) залежить від якості РНК-полімерази, а неповне прочитання пов’язане з пригніченням елонгації нитки полі (Г), яка по ній синтезується.Проведен анализ структуры комплексов поли (Г) · поли (Ц), полученных ферментативным синтезом на матрице поли (Ц), с помощью аффинной сорбции. Последняя применена для очистки препаратов таких комплексов от избытка неиспользованной матрицы, а также для исследования структуры комплексов поли (Г) · поли (Ц), выделенных традиционным методом смешивания растворов комплементарных полинуклеотидов. Показано, что полнота прочтения матрицы поли (Ц) зависит от качества РНК-полимеразы, а неполное прочтение связано с угнетением элонгации нити поли (Г), которая по ней синтезируется

Родовище високомінералізованої борної гідрокарбонатної натрієвої мінеральної води Пасіка на Закарпатті та особливості її біологічної дії

Дана характеристика месторождений и биологических свойств борных гидрокарбонатных натриевых вод Закарпатья.It is done the characteristics of layers and biological properties of high mineralized boric hydrocarbonate sodium mineral waters on Zakarpattya

Towards a better solution to the shortest common supersequence problem: the deposition and reduction algorithm

BACKGROUND: The problem of finding a Shortest Common Supersequence (SCS) of a set of sequences is an important problem with applications in many areas. It is a key problem in biological sequences analysis. The SCS problem is well-known to be NP-complete. Many heuristic algorithms have been proposed. Some heuristics work well on a few long sequences (as in sequence comparison applications); others work well on many short sequences (as in oligo-array synthesis). Unfortunately, most do not work well on large SCS instances where there are many, long sequences. RESULTS: In this paper, we present a Deposition and Reduction (DR) algorithm for solving large SCS instances of biological sequences. There are two processes in our DR algorithm: deposition process, and reduction process. The deposition process is responsible for generating a small set of common supersequences; and the reduction process shortens these common supersequences by removing some characters while preserving the common supersequence property. Our evaluation on simulated data and real DNA and protein sequences show that our algorithm consistently produces the best results compared to many well-known heuristic algorithms, and especially on large instances. CONCLUSION: Our DR algorithm provides a partial answer to the open problem of designing efficient heuristic algorithm for SCS problem on many long sequences. Our algorithm has a bounded approximation ratio. The algorithm is efficient, both in running time and space complexity and our evaluation shows that it is practical even for SCS problems on many long sequences

Polynomial-time approximation schemes for scheduling problems with time lags

We identify two classes of machine scheduling problems with time lags that possess Polynomial-Time Approximation Schemes (PTASs). These classes together, one for minimizing makespan and one for minimizing total completion time, include many well-studied time lag scheduling problems. The running times of these approximation schemes are polynomial in the number of jobs, but exponential in the number of machines and the ratio between the largest time lag and the smallest positive operation time. These classes constitute the first PTAS results for scheduling problems with time lags

STRUCTURAL ORGANIZATION LEVELS IN POLYNUCLEOTIDE INDUCTORS OF INTERFERON

The work covers the complexes of the synthetic complementary polyribonucleotides - the interferon inductors. The conception of several levels in the structural organization of the polynucleotide complexes has been firstly proposed in experiment, the conception of their triple structure has been introduced, the connection of the structural ordering, biological activity and physical-chemical characteristics of the solutions in the complexes with quantity of the intramolecular defects has been revealed. A number of the physical methods has been applied for analysis of the defects. The molecular standard of the complex with maximal degree of the structural ordering has been obtained by a matrix synthesis. A principial possibility of directed increasing regularity of the different nucleotide composition complexes has been proved. The poly(G) x poly(Ts) complex has been proposed as an antiviral preparation of the medical purpose, its before-clinic toxic-pharmacological tests have been performed completely, the clinic investigation has been began.Available from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio