The numerics of Premium Bonds


  • Dirk Tasche Prudential Regulation Authority



Lottery bonds, multivariate hypergeometric distribution, number of partitions, multinomial distribution, Poisson approximation, Panjer recursion


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 recursionor Fourier transforms to exact calculation of the lottery prize value distribution.

Author Biography

Dirk Tasche, Prudential Regulation Authority

Technical specialist in Supervisory Risk Specialists division


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