Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

What does a basket of shares cost? Researcher works it out.

05.06.2008
Dutch researcher Coen Leentvaar has been studying the problem that arises if options have to be priced on a number of shares.

From an arithmetical standpoint, the question introduces so many unknown variables that even a modern computer cannot handle the calculation. As part of a Technology Foundation STW project, Leentvaar split the problem into a number of less complex partial problems. He also developed an algorithm that, combined with computer technology, can calculate the option price for a basket of shares.

Using a computer, it is hard to determine the option price for a variety of shares. The multitude of possibilities mean the number of unknowns to be resolved grows exponentially. For example, an option on a basket of five shares involves 32 million unknowns, given a 32-point grid. This is beyond the capabilities of today’s computer systems. Leentvaar used the so-called thin-grid method to split the problem into a number of less complex partial problems that could be handled by a modern computer system. The option price can be estimated accurately by combining the solutions of all the partial problems in the correct manner.

However, the option contract has one annoying feature if the thin-grid method is used, namely it is not always advantageous to exercise an option (i.e. to exercise the right to buy or sell at a particular time). Mathematically, this leads to a ‘kink’ in the final solution to the problem. Leentvaar used variable transforms to minimise this ‘kink’, so that it is dependent on only one variable: the value of the basket itself. The thin-grid method can be used with reasonable accuracy by calculating this particular variable more precisely and the other variables more coarsely.

This leaves the options based on the worst- or best-performing share. These options do not lend themselves to solution using differential equations because the preconditions are missing. Leentvaar used advanced parallelisation methods (Fourier transforms) for this purpose. By cleverly splitting up the problem, these methods are able to solve each part independently of the rest. In this way, the researcher managed to combine the power of the thin-grid method with the parallelisation of the Fourier transforms into a computer model that divides a large problem into many small parts and then solves these.

Trade in underlying futures, or hedging, is based on derivatives of the option prices. This either cannot be done accurately enough using current methods or there is no reference. Leentvaar’s method is one where the derivatives, or Greeks, can easily be determined on the basis of the calculated prices. This offers the prospect of further research into making pricing methods more efficient. Participating organisations are ABN-AMRO, Rabobank, Binck (formerly AOT) and Tilburg University.

David Redeker | alfa
Further information:
http://www.nwo.nl/nwohome.nsf/pages/NWOA_7F2GP6_Eng

More articles from Business and Finance:

nachricht Preferential trade agreements enhance global trade at the expense of its resilience
17.02.2017 | International Institute for Applied Systems Analysis (IIASA)

nachricht How Strong Brands Translate into Money
15.11.2016 | Kühne Logistics University - Wissenschaftliche Hochschule für Logistik und Unternehmensführung

All articles from Business and Finance >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Breakthrough with a chain of gold atoms

In the field of nanoscience, an international team of physicists with participants from Konstanz has achieved a breakthrough in understanding heat transport

In the field of nanoscience, an international team of physicists with participants from Konstanz has achieved a breakthrough in understanding heat transport

Im Focus: DNA repair: a new letter in the cell alphabet

Results reveal how discoveries may be hidden in scientific “blind spots”

Cells need to repair damaged DNA in our genes to prevent the development of cancer and other diseases. Our cells therefore activate and send “repair-proteins”...

Im Focus: Dresdner scientists print tomorrow’s world

The Fraunhofer IWS Dresden and Technische Universität Dresden inaugurated their jointly operated Center for Additive Manufacturing Dresden (AMCD) with a festive ceremony on February 7, 2017. Scientists from various disciplines perform research on materials, additive manufacturing processes and innovative technologies, which build up components in a layer by layer process. This technology opens up new horizons for component design and combinations of functions. For example during fabrication, electrical conductors and sensors are already able to be additively manufactured into components. They provide information about stress conditions of a product during operation.

The 3D-printing technology, or additive manufacturing as it is often called, has long made the step out of scientific research laboratories into industrial...

Im Focus: Mimicking nature's cellular architectures via 3-D printing

Research offers new level of control over the structure of 3-D printed materials

Nature does amazing things with limited design materials. Grass, for example, can support its own weight, resist strong wind loads, and recover after being...

Im Focus: Three Magnetic States for Each Hole

Nanometer-scale magnetic perforated grids could create new possibilities for computing. Together with international colleagues, scientists from the Helmholtz Zentrum Dresden-Rossendorf (HZDR) have shown how a cobalt grid can be reliably programmed at room temperature. In addition they discovered that for every hole ("antidot") three magnetic states can be configured. The results have been published in the journal "Scientific Reports".

Physicist Dr. Rantej Bali from the HZDR, together with scientists from Singapore and Australia, designed a special grid structure in a thin layer of cobalt in...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

Booth and panel discussion – The Lindau Nobel Laureate Meetings at the AAAS 2017 Annual Meeting

13.02.2017 | Event News

Complex Loading versus Hidden Reserves

10.02.2017 | Event News

International Conference on Crystal Growth in Freiburg

09.02.2017 | Event News

 
Latest News

Stingless bees have their nests protected by soldiers

24.02.2017 | Life Sciences

New risk factors for anxiety disorders

24.02.2017 | Life Sciences

MWC 2017: 5G Capital Berlin

24.02.2017 | Trade Fair News

VideoLinks
B2B-VideoLinks
More VideoLinks >>>