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 Mathematical confirmation: Rewiring financial networks reduces systemic risk
22.06.2017 | International Institute for Applied Systems Analysis (IIASA)

nachricht Frugal Innovations: when less is more
19.04.2017 | Fraunhofer-Institut für Arbeitswirtschaft und Organisation IAO

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: Fizzy soda water could be key to clean manufacture of flat wonder material: Graphene

Whether you call it effervescent, fizzy, or sparkling, carbonated water is making a comeback as a beverage. Aside from quenching thirst, researchers at the University of Illinois at Urbana-Champaign have discovered a new use for these "bubbly" concoctions that will have major impact on the manufacturer of the world's thinnest, flattest, and one most useful materials -- graphene.

As graphene's popularity grows as an advanced "wonder" material, the speed and quality at which it can be manufactured will be paramount. With that in mind,...

Im Focus: Exotic quantum states made from light: Physicists create optical “wells” for a super-photon

Physicists at the University of Bonn have managed to create optical hollows and more complex patterns into which the light of a Bose-Einstein condensate flows. The creation of such highly low-loss structures for light is a prerequisite for complex light circuits, such as for quantum information processing for a new generation of computers. The researchers are now presenting their results in the journal Nature Photonics.

Light particles (photons) occur as tiny, indivisible portions. Many thousands of these light portions can be merged to form a single super-photon if they are...

Im Focus: Circular RNA linked to brain function

For the first time, scientists have shown that circular RNA is linked to brain function. When a RNA molecule called Cdr1as was deleted from the genome of mice, the animals had problems filtering out unnecessary information – like patients suffering from neuropsychiatric disorders.

While hundreds of circular RNAs (circRNAs) are abundant in mammalian brains, one big question has remained unanswered: What are they actually good for? In the...

Im Focus: RAVAN CubeSat measures Earth's outgoing energy

An experimental small satellite has successfully collected and delivered data on a key measurement for predicting changes in Earth's climate.

The Radiometer Assessment using Vertically Aligned Nanotubes (RAVAN) CubeSat was launched into low-Earth orbit on Nov. 11, 2016, in order to test new...

Im Focus: Scientists shine new light on the “other high temperature superconductor”

A study led by scientists of the Max Planck Institute for the Structure and Dynamics of Matter (MPSD) at the Center for Free-Electron Laser Science in Hamburg presents evidence of the coexistence of superconductivity and “charge-density-waves” in compounds of the poorly-studied family of bismuthates. This observation opens up new perspectives for a deeper understanding of the phenomenon of high-temperature superconductivity, a topic which is at the core of condensed matter research since more than 30 years. The paper by Nicoletti et al has been published in the PNAS.

Since the beginning of the 20th century, superconductivity had been observed in some metals at temperatures only a few degrees above the absolute zero (minus...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

Call for Papers – ICNFT 2018, 5th International Conference on New Forming Technology

16.08.2017 | Event News

Sustainability is the business model of tomorrow

04.08.2017 | Event News

Clash of Realities 2017: Registration now open. International Conference at TH Köln

26.07.2017 | Event News

 
Latest News

A Map of the Cell’s Power Station

18.08.2017 | Life Sciences

Engineering team images tiny quasicrystals as they form

18.08.2017 | Physics and Astronomy

Researchers printed graphene-like materials with inkjet

18.08.2017 | Materials Sciences

VideoLinks
B2B-VideoLinks
More VideoLinks >>>