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Stummer, Wolfgang
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[Journal:] Journal of Entrepreneurial Finance, JEF [ISSN:] 1551-9570 [Volume:] 7 [Year:] 2002 [Issue:] 3 [Pages:] 39-51
In some modern venture valuation approaches, option pricing theory plays an important role.The aim of this paper is to present some tools and viewpoints which might be helpful for future investigations along this line. We model the value-dynamics Xt of an imbedded underlying X as a non-lognormally-distributed generalization of the geometric Brownian motion. In detail, Xt is supposed to be a solution of a stochastic differential equation of the form dXt = b(Xt ) dt o(t) Xt dWt with non-constant volatility function o(t) and Brownian motion Wt . For this, we discuss a certain decision problem concerning the size of the trend function b . Under some handy-toverify but far-reaching assumptions, we investigate the (average) reduction of decision risk that can be obtained by observing the sample path of X . Furthermore, we also show some connections with the valuation of call options on X .
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