Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:


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

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:

More articles from Business and Finance:

nachricht Blockchain Set to Transform the Financial Services Market
28.09.2016 | HHL Leipzig Graduate School of Management

nachricht Paper or plastic?
08.07.2016 | University of Toronto

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: Light-driven atomic rotations excite magnetic waves

Terahertz excitation of selected crystal vibrations leads to an effective magnetic field that drives coherent spin motion

Controlling functional properties by light is one of the grand goals in modern condensed matter physics and materials science. A new study now demonstrates how...

Im Focus: New 3-D wiring technique brings scalable quantum computers closer to reality

Researchers from the Institute for Quantum Computing (IQC) at the University of Waterloo led the development of a new extensible wiring technique capable of controlling superconducting quantum bits, representing a significant step towards to the realization of a scalable quantum computer.

"The quantum socket is a wiring method that uses three-dimensional wires based on spring-loaded pins to address individual qubits," said Jeremy Béjanin, a PhD...

Im Focus: Scientists develop a semiconductor nanocomposite material that moves in response to light

In a paper in Scientific Reports, a research team at Worcester Polytechnic Institute describes a novel light-activated phenomenon that could become the basis for applications as diverse as microscopic robotic grippers and more efficient solar cells.

A research team at Worcester Polytechnic Institute (WPI) has developed a revolutionary, light-activated semiconductor nanocomposite material that can be used...

Im Focus: Diamonds aren't forever: Sandia, Harvard team create first quantum computer bridge

By forcefully embedding two silicon atoms in a diamond matrix, Sandia researchers have demonstrated for the first time on a single chip all the components needed to create a quantum bridge to link quantum computers together.

"People have already built small quantum computers," says Sandia researcher Ryan Camacho. "Maybe the first useful one won't be a single giant quantum computer...

Im Focus: New Products - Highlights of COMPAMED 2016

COMPAMED has become the leading international marketplace for suppliers of medical manufacturing. The trade fair, which takes place every November and is co-located to MEDICA in Dusseldorf, has been steadily growing over the past years and shows that medical technology remains a rapidly growing market.

In 2016, the joint pavilion by the IVAM Microtechnology Network, the Product Market “High-tech for Medical Devices”, will be located in Hall 8a again and will...

All Focus news of the innovation-report >>>



Event News

#IC2S2: When Social Science meets Computer Science - GESIS will host the IC2S2 conference 2017

14.10.2016 | Event News

Agricultural Trade Developments and Potentials in Central Asia and the South Caucasus

14.10.2016 | Event News

World Health Summit – Day Three: A Call to Action

12.10.2016 | Event News

Latest News

Oasis of life in the ice-covered central Arctic

24.10.2016 | Earth Sciences

‘Farming’ bacteria to boost growth in the oceans

24.10.2016 | Life Sciences

Light-driven atomic rotations excite magnetic waves

24.10.2016 | Physics and Astronomy

More VideoLinks >>>