Modelling the number of customers as a birth and death process

Helena Pinto, Sydney Howell, Dean Paxson

Research output: Contribution to journalArticlepeer-review


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 pages13
JournalEuropean Journal of Finance
Issue number2
Publication statusPublished - Feb 2009


  • Birth and death processes and Frobenius method
  • Real options


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