Using the finite volume method in computing the propagation of the financial crisis in the real economy.

Vilag, Ruxandra ; Vilag, Valeriu ; Trica, Smaranda 等

1. INTRODUCTION

Taking into consideration the present phenomena of economic globalization and its impact over the cross-country co-movement (Tavares, 2009) the economists are trying to show which are the linkages between different countries' or region's economies. As shown by the present financial crisis, these interdependences will make a country to react in the same manner as the one hit by a crisis.

The financial contagion is defined as a cross-country transmission of shocks or the general cross-country spill over effects. If we take the definition gave by the Merriam Webster's Dictionary of contagion in psychology then contagion is the spread of behaviour pattern, attitude, or emotion from person to person or group to group through suggestion, propaganda, rumour or imitation.

To translate into financial terms it seems that a country might be contaminate by another through different channels, such as:

1) Financial links when two economies are connected through international financial system

2) Real links usually associated with international trade

3) Political links shown by the appurtenance to an international structure like European Union.

2. STARTING

2.1 Financial

The researchers tried and sometimes succeed to compute the strength of the interdependence between two countries. The easiest way to do that is through the correlation between the indexes of the countries' capital markets. There are just two things to comment first the computed correlation doesn't show when the crisis will arrive in the real economy and second in times of crisis the correlation increases because the volatility increases (Horobet & Dumitrescu, 2009).

2.2 Computational fluid dynamics and applied numerical methods

The lasts decades have seen an accelerate growth in the use of Computational Fluid Dynamics (CFD) to predict flows. The basic numerical techniques have been developed around a series of worked examples, which can be easily programmed on a PC. CFD codes are structured around the numerical algorithms that can tackle fluid flow problems. All PC interfaces dealing with this problem include a pre-processor (input information), a solver (numerical solution technique) and a post-processor (solution).

The control volume integration distinguishes the finite volume method from all other CFD techniques. The resulting statements express the exact conservation of relevant properties for each finite size cell, so will have (Versteeg & Malasekera, 1995):

Rate of change of qp in the control volume with respect to time

=

Net flux of [??] due to convection into the control volume

+

Net flux of [??] due to diffusion into the control volume

+

Net rate of creation of [??] inside the control volume (1)

, where [??] is a property of the flow like heat.

2.3 Translation

If we consider the common assertion that "money makes the world go around" we can make the assumption that by their moving money is the element that sustains the economies. This is because in our days every transaction is closed within a monetary equivalent. So the "flow" that moves the economies is the financial flow. If we can consider this flow to have some basic properties like velocity or strength and the beneficiary of this flow all the countries than we can make the following interpretation of the CFD techniques in the propagation of financial crisis:

* The financial flow is the one that propagates.

* The volumes (cells) are the countries that each has specific properties and interaction with other countries.

3. IMPLEMENTATION

In light of the above statement will have the following financial equation:

Rate of change in the economy of the analyzed country in time

=

The changes due to correlation between the country of exit and the analyzed one

+

The changes due to national economic conditions

+

The changes due to measures taken by the policy makers (2)

In order to use a PC interface we have to be in possession of the input information such as: the correlation between two countries that is easy to compute in normal times by using the indexes of the capital market (the correlation coefficient will act like a permeable wall), the evolution of main indicators like Gross Domestic Product (GDP), inflation, rate of unemployment, exchange rate etc (this elements are showing the correlation between the capital market and the real economy) and the measures that will be tacked to prevent the crisis to enter the country (we can guess that are some types of preferred measures based on past reaction or the power of the executive).

If we take Romania as an example then we have some characteristics of the capital market and of the Romanian economy in general (Predescu, 2008). The Romanian capital market, being an open market, can be influenced by external events, meaning that by definition could be the "beneficiary" of the contagion effect. However, to measure the contagion influences in Romania during the current financial crisis we also have to take into account the links with other countries such as trade links, macroeconomic links and policy links. The influence over the Romanian financial market is immediately seen as shown in figure number 1, but as the macroeconomic indicators shown the real economy has a different way to respond to this crisis.

To measure Romania's commercial linkages with another country we calculated the share of foreign trade with this country from total foreign trade of Romania. Romania has the strongest trade links with Italy (22.06% of total) and Germany (15.38% of total). We computed that the foreign trade with the European Union member states holds over 70% of total foreign trade of our country. Futher more, starting with 2007 Romania is an European Union member state, so we could draw the conclusion that trade links, political links and even those made on macroeconomic bases (since the entry into the EU implies the integration into a common market with the same operating rules and later, entering into the euro area) between Romania and the European Union are strong enough that our capital market can be influenced by the development of the European Union capital markets. As we have brought into question in the beginning of the paper, a financial market crisis is transmitted primarily through the classical channels, showing that the evolution of the Romanian capital market will be influenced by the evolution of capital markets in European Union in a very large proportion.

If we look at the evolution of BET index (shows the evolution of the market, its capitalization) in the two year period that we analyzed we see that the Romanian capital market is "contaminated" immediately after a major event occurs on the international capital market. So we see that even the real economy has no direct links (or too few) to the United States, our market start to fall after the first outburst of the financial crisis (23.07.2007). The last visible fall is in October 2008 immediately after the entire financial world entered in collapse.

Given the above assertions we might easily draw the conclusion that the Romania economy started to fall in September 2007. But this conclusion is not true. The financial crisis has its first repercussion in Romania in the winter 2008-2009, a year later than the beginning of the crisis.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

So the question is: what had happened all this time?

We can guess that the real economy is a slow running mechanism. The effects of one country crisis in another country appear to have their own way of transmitting. They only hit the second country when the financial flow that accompanies commercial trades enters the country.

4. CONCLUSIONS

The usefulness of using the finite volume method is given by the computation of the entire entering "flow" and the necessary time to get there. As seen in figure number 2 we can consider each country a separate cellule with its own characteristic. If we take into account the links between countries we would obtain a cluster of cells which are influenced by the financial flow running from a cell to another on determined basis (linkages computed using commercial and financial trade, political and macroeconomic integration) (Voicu & Ionescu, 2009). The only problem of this solution is that we have to calibrate again the software inputs (e.g. we have to compute again the relation between countries after a period of 3 to 5 years).

If we gather sufficient information about the world economy and about each country that is part of it, we can implement the CFD in economics. The results will be to know the exact time when a crisis will enter a specific country and by knowing that we than try to stop it by implementing specific measures and by doing that we can manage to limit the propagation of financial or economic crisis in other countries. So our next step will be to make a small model for the European Union area which will demonstrate our assertions.

5. REFERENCES

Horobet, A. & Dumitrescu, S. (2009). Correlation and volatility in Central and Eastern European stock markets, Proceedings of the 16th International Economic Conference--IECS Industrial revolution, from globalization and post globalization perspective, ISBN 978-973-739-775-1, Lucian Blaga University, Sibiu

Predescu, I. (2008). The influence of the financial factors on cash flow, as determining factor of firm's investment decisions, International Scientific Conference "European Integration-New Challenges for the Romanian Economy", Faculty of Economics, University of Oradea, Tom XVII" ISSN-1582-5450, pp.499-504

Tavares, J (2009). Economic integration and the comovement of stock returns, Available from: 10.1016/j-econlet.2009.01.016

Versteeg, H.K. & Malalasekera, W. (1995). An introduction to Computational Fluid Dynamics. The Finite Volume Method, Addison Wesley Longman Limited, ISBN 0-582-21884-5, Edinburg Gate

Voicu, A.R. & Ionescu, A. (2009). Monetary Mechanism to Propagate Macroeconomics Policies, Proceedings of the 10th WSEAS International Conferences on Mathematical and Computational methods in science and engineering, Cambridge, ID: 699-153.pdf