Constructing Historical Yield Curves from Very Sparse Spot Rates: A Methodology and Examples from the 1920s Canadian Market

Legal disputes over compensation paid almost a century ago in lieu of a cash flow stream spanning a few decades present a number of challenges. These difficulties involve interrelated conceptual issues as well as technical obstacles. The re-evaluation of the compensation, in terms of dollars of the compensation time, requires knowledge of the yield curve at that time. However, the kept records of historical yield, is of only one rate: the long term spot rate. The rate was recorded and kept for the first business day of each month. Furthermore, the evaluation in today's dollars requires present/future value calculations spanning over thirty years while yields for such a long duration are not observable. The paper offers a conceptual overview, proposes a methodology to overcome the technical difficulties, and exemplifies the implementation process.