Abstract

This paper deals with the question, whether subjective probabilities of takeover completion, estimated from current observable spot-prices of target stock, from expected bid price and from current forecasted stand-alone price of target stock, enhance classical subjective probability forecasts, such as Black-Scholes model. Under Black-Scholes assumptions the future log stock price is normally distributed and one is able to forecast it knowing the current stock price and the mean and variation of the stock returns. However, if one pre-estimates the probability of takeover completion and current (also non observable) stand alone price of target stock, one can derive a mixed distribution for the target stock price at the expected completion date: It is then a mixture of a point probability at the expected takeover price and of a continuous stand alone distribution on the rest of the space. The problem is, that the reliability of such estimation can be hardly assessed based only on this data: probabilities are unique at any time point and there are no reasonable arguments why they should follow some parametric stochastic process, thus making filtering techniques useless. But the recent research in pricing derivatives (Ait-Sahalia and Lo 1998, Jackwerth and Rubinstein 1996) enables to recover subjective (risk-neutral) probabilities of certain future states of nature from derivative prices. The case of an expected M&A deal is exactly a situation where we expect a well-specified event to occur at rather certain time point in nearest future. Therefore, using nonparametric tests it can be shown, that the spot price model is more adequate to describe the option price distribution and hence subjective probability function of target stock price at the expected completion date.

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