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Modelling the number of customers as a birth and death process

Pinto, H. and Howell, S. and Paxson, D. (2009) Modelling the number of customers as a birth and death process. European Journal of Finance, 15 (2). pp. 105-118. ISSN 1351-847X

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Abstract

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.

Item type: Article
ID code: 15121
Keywords: real options, birth and death processes, Frobenius method, Finance, Economics, Econometrics and Finance (miscellaneous)
Subjects: Social Sciences > Finance
Department: Strathclyde Business School > Accounting and Finance
Related URLs:
Depositing user: Miss Donna McDougall
Date Deposited: 03 Feb 2010 18:58
Last modified: 04 Sep 2014 23:36
URI: http://strathprints.strath.ac.uk/id/eprint/15121

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