Modelling the number of customers as a birth and death process

H. Pinto, S. Howell, D. Paxson

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)105-118
Number of pages14
JournalEuropean Journal of Finance
Volume15
Issue number2
DOIs
Publication statusPublished - Feb 2009

Fingerprint

Modeling
Geometric Brownian motion
Real options
Brownian motion
Monopoly
Option value
Call option

Keywords

  • real options
  • birth and death processes
  • Frobenius method

Cite this

Pinto, H. ; Howell, S. ; Paxson, D. / Modelling the number of customers as a birth and death process. In: European Journal of Finance. 2009 ; Vol. 15, No. 2. pp. 105-118.
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Modelling the number of customers as a birth and death process. / Pinto, H.; Howell, S.; Paxson, D.

In: European Journal of Finance, Vol. 15, No. 2, 02.2009, p. 105-118.

Research output: Contribution to journalArticle

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