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Centre for Discrete and Applicable Mathematics |
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CDAM Research Report, LSE-CDAM-2004-13
July 2004 |
`Equity smirks' and embedded options: the shape of a
firm's value function
Adam Ostaszewski
Abstract
This paper examines the methodology and assumptions of Ashton, D.,
Cooke, T.,Tippett, M., Wang, P. (2004) employing recursion value
&eta as an explanatory single-variable in a model of the firm,
first introduced by Ashton, D.,Cooke,T.,Tippett in (2003). A
qualitative analysis of all of their numerical findings is given
together with an indication of how more useful is the tool of
special function theory, here requiring confluent
hypergeometric functions associated with the Merton-style valuation equation
A justification and a wider interpretation of their model
and findings is offered: these come from inclusion of strictly
convex dissipating frictions arising either as insurance costs,
replacement costs of funds paid out, or of debt service, and from
the inclusion of alternative adaptation options embedded in the
equity value of a firm; these predict not only a J-shaped equity
curve, but also, under the richer modelling assumption, a
snake-like curve that may result from financial frictions like
insurance. These `smirks' in the equity curve may be empirically
tested. It is shown that the inclusion of frictions in dividend
selection (e.g. the signalling costs of Bhattacharya) leads to an
optimal dividend payout of &alpha &eta that is a constant
coupon for an interval of &eta values preceded by an interval
in which &alpha=r; this is at variance with the ACTW model
where the exogeneous assumption of a constant &alpha is made.
This is the full, detailed, version of a discussion paper
presented at State of the Art International Advances in Accounting
Based Valuation at the Cass Business School, a conference held in
association with the journal, Accounting & Business Research,
London, December 12th and 13th 2003. I am indebted to Ken Peasnell
for suggesting the word `smirk'. I am grateful to Jim Ohlson, Mark
Tippett, Miles Gietzmann, to colleagues at LSE, and to colleagues
at University College London Mathematics Department, particularly
Susan Brown and S.N. Timoshin for very helpful discussions.
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Last changed: Wed 9 Feb 2005
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