The Numerics of Premium Bonds

Journal of Gambling Business and Economics 9(3), 14-33, 2015

15 Pages Posted: 10 Feb 2015 Last revised: 7 Jan 2016

See all articles by Dirk Tasche

Dirk Tasche

Swiss Financial Market Supervisory Authority (FINMA)

Date Written: February 2, 2015

Abstract

Premium Bonds sold by the UK National Savings and Investments (NS&I) agency are the possibly most popular example of lottery bonds. Premium Bonds holders renounce interest payments but instead participate in a lottery which distributes the equivalent of aggregate interest payments among them. While the random mechanism used in the lottery is well-documented the details of how to determine the probability distribution of a single bond holder's lottery prizes seem to be less well-known. We observe that the lottery prizes distribution is a multivariate hypergeometric distribution and discuss how to exactly calculate its probability masses as well as how to approximate the distribution by means of the Panjer recursion and Fourier transforms. We find that there are good reasons to prefer the approximations based on Panjer recursion or Fourier transforms to exact calculation of the lottery prize value distribution.

Keywords: Multivariate hypergeometric distribution, number of partitions, Poisson approximation, Panjer recursion, lottery bonds

JEL Classification: C63, G12

Suggested Citation

Tasche, Dirk, The Numerics of Premium Bonds (February 2, 2015). Journal of Gambling Business and Economics 9(3), 14-33, 2015. Available at SSRN: https://ssrn.com/abstract=2562227 or http://dx.doi.org/10.2139/ssrn.2562227

Dirk Tasche (Contact Author)

Swiss Financial Market Supervisory Authority (FINMA) ( email )

Einsteinstrasse 2
Bern, 3003
Switzerland

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