What is it about?
We develop a stochastic continuous-time cash management model that minimises extreme variations in firm cash balances. The model is based on a stochastic differential equation that describes the evolution of cash balances. The specification used includes a linear drift function and a quadratic diffusion function. The quadratic diffusion function is a particular form of a general quadratic diffusion function and admits a hyperbolic transformation to find solutions. Empirical analysis shows that non-Gaussian distributions (more specifically: a Pearson Type IV density) are highly compatible with the quarterly cash flow data of a randomly selected sample of 100 large U.S. corporations.
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Why is it important?
The benchmark model is developed by Miller and Orr (1966) and is based on the assumption that firm cash balances evolve in terms of a pure random walk. In the meantime, the validity of this assumption has been challenged by a number authors. In this paper, we propose and then empirically validate a more general cash management model that includes a linear drift function and a particular form of a quadratic diffusion function.
Perspectives
Stochastic continuous-time cash balance models are a very interesting and rapidly expanding area of research. The theoretical development of sophisticated cash models, and, more importantly, their practical applications, has been hindered by (significant) mathematical and statistical challenges. In our research we are trying to find a balance between complexity and practical use.
Dr John van der Burg
Victoria University of Wellington
Read the Original
This page is a summary of: A hyperbolic model of optimal cash balances, European Journal of Finance, June 2018, Taylor & Francis,
DOI: 10.1080/1351847x.2018.1482834.
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