Statistical analysis and stochastic interest rate modeling for valuing the future with implications in climate change mitigation
Abstract
High future discounting rates favor inaction on present expending while lower rates advise for a more immediate political action. A possible approach to this key issue in global economy is to take historical time series for nominal interest rates and inflation, and to construct then real interest rates and finally obtaining the resulting discount rate according to a specific stochastic model. Extended periods of negative real interest rates, in which inflation dominates over nominal rates, are commonly observed, occurring in many epochs and in all countries. This feature leads us to choose a wellknown model in statistical physics, the OrnsteinUhlenbeck model, as a basic dynamical tool in which real interest rates randomly fluctuate and can become negative, even if they tend to revert to a positive mean value. By covering 14 countries over hundreds of years we suggest different scenarios and include an error analysis in order to consider the impact of statistical uncertainty in our results. We find that only 4 of the countries have positive longrun discount rates while the other ten countries have negative rates. Even if one rejects the countries where hyperinflation has occurred, our results support the need to consider low discounting rates. The results provided by these fourteen countries significantly increase the priority of confronting global actions such as climate change mitigation. We finally extend the analysis by first allowing for fluctuations of the mean level in the OrnsteinUhlenbeck model and secondly by considering modified versions of the Feller and lognormal models. In both cases, results remain basically unchanged thus demonstrating the robustness of the results presented.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 April 2020
 DOI:
 10.1088/17425468/ab7a1e
 arXiv:
 arXiv:1910.01928
 Bibcode:
 2020JSMTE..04.3210P
 Keywords:

 stochastic processes;
 models of financial markets;
 risk measure and management;
 quantitative finance;
 Quantitative Finance  Mathematical Finance;
 Condensed Matter  Statistical Mechanics;
 Physics  Physics and Society
 EPrint:
 29 pages, 5 figures, 5 tables. arXiv admin note: text overlap with arXiv:1311.4068