Central Bank Policy Impacts on the Distribution of State Prices for Future Interest Rates, 2003–2022

In this article, we extend the 1978 Breeden–Litzenberger method of extracting state prices from option prices, showing how portfolios of butterfly spreads can be combined with right and left tail spreads to nonparametrically extract discrete state prices from option prices. We derive how those state prices should be biased estimates of true, objective probabilities. For interest rate options, we show that the biases can vary predictably over time (sometimes too high, sometimes too low), as the correlation of interest rates with consumption and wealth has changed signs over time. Consumption betas and proper risk premiums on bonds and of their state prices are at times predictably positive and at times predictably negative. We apply our technique to provide a brief 20-year history of central bank intervention impacts in the US, UK, and Eurozone from 2003 to 2022. Movements in state prices are quite large in the Financial Panic of 2008–2009, as well as in the European Sovereign Debt Crisis of 2010–2013, with Brexit and the Trump elections in 2016, and with the coronavirus pandemic in 2020–2021. Tapering in 2013 and 2022 and liftoffs in rates in 2015 and 2022 were shown to strongly shift state price distributions back toward the symmetry of 2003–2007. We show that central banks dramatically impacted entire state price distributions, not just levels of rates.