Modelling the number of customers as a birth and death process

Autor:	Sydney Howell, Helena Pinto, Dean Paxson
Rok vydání:	2009
Předmět:	Geometric Brownian motion Frobenius method Economics Econometrics and Finance (miscellaneous) Quantitative Biology::Populations and Evolution Call option Singular point of a curve Monopoly Mathematical economics Value (mathematics) Birth–death process Brownian motion Mathematics
Zdroj:	The European Journal of Finance. 15:105-118
ISSN:	1466-4364 1351-847X
DOI:	10.1080/13518470802042021
Popis:	Birth and death may be a better model than Brownian motion for many physical processes, which real options models will increasingly need to deal with. In this paper, we value a perpetual American call option, which gives the monopoly right to invest in a market in which the number of active customers (and hence the sales rate) follows a birth and death process. The problem contains a singular point, and we develop a mixed analytic/numeric method for handling this singular point, based on the method of Frobenius. The method may be useful for other cases of singular points. The birth and death model gives lower option values than the geometric Brownian motion model, except at very low volatilities, so that if a firm incorrectly assumes a geometric Brownian motion process in place of a birth and death process, it will invest too seldom and too late.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c349cc74ee5fd755afa88e7c47372239 https://doi.org/10.1080/13518470802042021 Zobrazit plný text záznamu