Abstract
We present a model for stock price and volume behaviour during market crashes. The model incorporates amarket mechanism for the share exchange between buyers and sellers while taking into account their cashbalances. Using an analytical approach and the Monte-Carlo technique for the simulation of the trading volume,we analyzed the dynamics of the stock price and trading volume during market crashes. The trading volume wassimulated through the trading exchange process using Monte-Carlo technique. We found that trading volume isinversely proportional to the square of the stock price in the case of the sharp price declines. This result isempirically supported in price and volume data for major recent US stock bankruptcies and market crashes,including Lehman Brothers Inc, Enron, Wachovia, Washington Mutual, Citigroup, Merrill Lynch, and MFGlobal. The results of the analytical approach may be used for marketing analysis of the sales in the case of theshocking market conditions.
Highlights
Stock price modeling has an extensive empirical and theoretical research history
Using an analytical approach and the Monte-Carlo technique for the simulation of the trading volume, we analyzed the dynamics of the stock price and trading volume during market crashes
We found that trading volume is inversely proportional to the square of the stock price in the case of the sharp price declines
Summary
Stock price modeling has an extensive empirical and theoretical research history. Existing mathematical models have mainly focused on the empirical investigation of the time-series of price returns and volatility. The assumption of the random walk of the return movement was suggested by Bachelier in 1900. The Efficient Markets Hypothesis (EMH) plays a key role in the assumption of the random walk, which allows to widely use the Black-Scholes paradigm for the valuation of the derivative instruments (Black & Scholes, 1973). Numerous empirical studies have shown that the stock market does not follow a random walk. Mandelbrot suggested that the exchange of money as an economic interaction can be considered by analogy as the exchange of energy between gas-phase molecules. There are similarities between the collision theory of the ideal gas and the Random Walk price dynamics of the trading market, the interaction between agents in the trading market can deviate from the collision theory because of the properties of the self-organized market and uncertain human behaviour
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