虽有研究对兼并标的资产价值服从连续随机分布情形下交易价格确定问题进行了讨论,但对离散随机分布情形下交易价格确定问题的讨论不够深入,这就不仅仅使得研究与实践相互脱节,更降低了研究对现实的解释力。现在对一类标的资产价值服从二叉树离散分布情形下交易价格问题进行研究,运用实物期权理论和博弈论的研究方法对标的价值评估与交易价格确定分别进行了讨论。研究运用中心极限定理分析了标的资产价值呈现二叉树特征,并且存在无限次上涨与下降状态情形下实物期权的极限分布。然后在对著名的Rubinstein讨价还价定理进行改进的基础上,给出了离散二叉树分布情形下的标的资产交易价格确定的解析表达式。最后,通过数值仿真揭示不同参数变化所引起的交易价格变化趋势,从而进一步说明模型的合理性和对现实的解释力。
In the process of M&A,the key problem is how to decide the transaction price, which can be divided into two steps including the evaluation of transaction asset and the process of pricing the target asset. The former must be processed to disclose the volume of real option hidden in uncertain attained profit and cost spending, while the latter can be processed based on the game analyses of bilateral transaction sides of M&A.Up to now, the measurement of real options under continuous stochastic surroundings has been studied by many scholars all over the world, whilst the measurement of real options under discrete stochastic surroundings has also been studied by way of using binary tree and trigeminal tree methods on the condition of limited transformation times of target asset.
In this paper, the measurement of real options under unlimited times of asset transformation is studied by way of using binary tree method in reference to some existing related studies.Firstly, the distribution of real option of binary tree with unlimited transformation times of asset can be deduced to be normal function by way of applying the central limited theorem.Secondly, the detailed analyses of famous Rubinstein bargaining theorem is conducted to disclose an important fact that the transaction asset is assumed to be distributed as uniform distribution, thus how to price the normal distributed target asset is studied to attain the equilibrium price.Finally, the analytical expression of equilibrium transaction price can be deduced to measure the real option value of target asset which is assumed to be distributed as discrete binary tree, the corresponding numerical simulation is given to illustrate its rationality and the explaining power to reality.
In summary, a new idea of price the real option is proposed on the condition that the transformation status of asset is assumed to be binary tree, and then the problem solving approach can be referenced to other similar problems, especially to the discrete distributions including trigeminal tree.
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