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We present a thorough empirical study on real interest rates by alsoincluding risk aversion through the introduction of the market price of risk.With the view of complex systems science and its multidisciplinary approach, weuse the theory of bond pricing to study the long term discount rate.Century-long historical records of 3 month bonds, 10 year bonds, and inflationallow us to estimate real interest rates for the UK and the US. Real interestrates are negative about a third of the time and the real yield curves areinverted more than a third of the time, sometimes by substantial amounts. Thisrules out most of the standard bond pricing models, which are designed fornominal rates that are assumed to be positive. We therefore use theOrnstein-Uhlenbeck model which allows negative rates and gives a good match toinversions of the yield curve. We derive the discount function using the methodof Fourier transforms and fit it to the historical data. The estimated longterm discount rate is $1.7$ \% for the UK and $2.2$ \% for the US. The value of$1.4$ \% used by Stern is less than a standard deviation from our estimatedlong run return rate for the UK, and less than two standard deviations of theestimated value for the US. All of this once more reinforces the support forimmediate and substantial spending to combat climate change.

Discounting the distant future: What do historical bond prices imply about the long term discount rate?