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Article
Author(s)
Valery V. Shemetov
Full-Text PDF XML 1217 Views
DOI:10.17265/2328-2185/2020.03.002
Affiliation(s)
ABSTRACT
Extensions of Merton’s model
(EMM) considering the firm’s payments and generating new types of firm value distribution
are suggested. In the open log-value/time space, these distributions evolve from
initially normal to negatively skewed ones, and their means are concave-down functions
of time. When payments are set to zero or proportional to the firm value, EMM turns
into the Geometric Brownian model (GBM). We show that risk-neutral probabilities
(RNPs) and the no-arbitraging principle (NAP) follow from GBM. When firm’s payments
are considered, RNPs and NAP hold for the entire market for short times only, but
for long-term investments, RNPs and NAP just temporarily hold for individual stocks
as far as mean year returns of the firms issuing those stocks remain constant, and
fail when the mean year returns decline. The developed method is applied to firm
valuation to derive continuous-time equations for the firm present value and project
NPV.
KEYWORDS
firm present value, geometric Brownian (Structural) model, risk neutral probabilities, no-arbitrage pricing principle
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