Electronic Thesis and Dissertation Repository


Master of Science


Applied Mathematics


Mark Reesor


The Peterborough Prison Bond is a social impact bond (SIB) that was issued by the UK government to reduce recidivism rate in the Peterborough prison. Most of the literature on the SIB so far has been focused on the opportunities, challenges, and the related policy issues (see (Fox), (Strickland), and (Disley)), and little effort has been made to provide a mathematical framework to determine a fair price for such instruments. Here, we aim to provide a pricing framework for the bond. We price the bond both from the issuer's and the buyer's perspective, by adjusting for the bond's risk, ambiguity, and social impact. Results suggest that the issuer could maximize its financial profit by targeting investors with a lower aversion to charity, and it could maximize the bond’s social impact by targeting the investors with lower aversion to risk.