In my opinion it is not possible because contagion has been defined in the literature as any transmission of shocks across countries. It means that you should have at least one other market with high-volatility. Contagion is a significant increase in cross-market linkages after a shock to one country (or group of countries). Another important problem is that contagion can be confused with the integration effect since both have a tendency to increase correlations among markets.
ISSUE: Is it possible to test financial contagion in a single stock market?
ANSWER: Yes.
CONTAGION: By definition contagion means a phenomenon started with a small shock that sends ripples through the system. The initial systemic shock affects the domestic market or financial institutions within a “single” market. Due to economic interdependence---and degree of such interdependence---the ripple transcends the domestic market to other trading partners. For instance, the subprime mortgage problem of the US was a domestic issue. When the shock hits the system, the ripple rips through the US financial markets then sends the shock waves to other economies that has significant ties to the US economy.
The second evidence of an intra-market contagion effect is the Lehman brother debacle (also related to subprime) was another shock wave sent through the US stock market (2008). From that shock, the effect also became transnational in economies that have ties with the US. The third evidence in recent history that shook the system was Enron-Arthur Anderson case (2001-2002).
The basis of the test should be that if there is an event started at one firm, does it send a shock wave through the system (stock market)? This is a clear case of event study. Alternatively, if the shock is a bubble-type, then look at it as a bubble-burst effect in a particular sector of the economy, does it have a contagion effect throughout the system within the market?
MODELING FOR TEST: Let the following terms have the following meanings:
T = time
Xc = returns (%) for industry or market in crisis
XJ = returns (%) of industry or market where c is traded
XT = transposed vector of returns of both companies
D(L) and d(L) = vectors of lags
Ic = short-term returns of company in crisis
IJ = short-term returns in the market
Et = vector of noise
Then the model may be proposed thus:
XT = D(L)XT + d(L)It + e
There are plenty of data sources to test this model: Lehman brother crisis, or subprime crisis that hit the US economy following the Lehman crisis.
REFERENCES:
(1) Auletta, Ken. Greed and Glory on Wall Street: The Fall of the House of Lehman. Random House, 1985
(2) Kristin J. Forbes and Roberto Rigobon, 2002, No Contagion, Only Interdependence: Measuring Stock Market Comovements, The Journal of Finance, Vol. 57, No. 5, pp 2223-2261.
Financial contagion tests can be done. However, we know very little about what exactly it is transmitted. There is no clear taxonomy of abnormalities plaguing the companies or the financial markets. So, what it is you want to test for?
Actually the whole theory about contagion is lacking key concepts. Nevertheless it is a hugely promising research area.
There are way more types of contagion than people assume now. Some are severe, like the ones detected using the nice model presented by Paul Louangrath, others are more subtle and less obvious, nevertheless damaging.
Contagion is the spread of an economic crisis from one market or region to another and can occur at both a domestic or international level. Because markets are interdependent, events in one market can impact other markets.