Using a utility function to adjust the risk-neutral PDF embedded in cross sections of options, we obtain measures of the risk aversion implied in option prices. Using FTSE 100 and S&P 500 options, and both power and exponential-utility functions, we estimate the representative agent's relative risk aversion (RRA) at different horizons. The estimated coefficients of RRA are all reasonable. The RRA estimates are remarkably consistent across utility functions and across markets for given horizons. The degree of RRA declines broadly with the forecast horizon and is lower during periods of high market volatility.ESTIMATING THE REPRESENTATIVE AGENT'S or the market's degree of risk aversion from securities prices has a long history. However, it is only recently that scholars have begun using options data to do so. Options provide a particularly promising context for studying risk preferences. Stocks are infinitely lived and so inferences must be drawn from the discounted stream of cash f lows over an indefinite horizon. Usually this involves additional assumptions as to how those cash f lows evolve (e.g., constant growth of dividends). Since only one value, the discounted present value of all cash f lows, is known, no inferences are possible about variations in preferences over different horizons. Options on the other hand have a fixed expiry date at which payoffs are realized. 1 Furthermore, options contracts exist for different investment horizons. Options thus permit studying preferences over specific horizons and simultaneously over multiple horizons. Futures contracts also share this fixed-horizon characteristic. Options * Bliss is with the Federal Reserve Bank of Chicago and Panigirtzoglou is with the Bank of England. We are particularly grateful for helpful discussions with Lars Hansen; for comments for the guidance and suggestions of the editor Richard Green; and the referee. We thank Darrin Halcomb for his excellent research assistance. The views expressed herein are those of the authors and do not necessarily ref lect those of the Federal Reserve Bank of Chicago or the Bank of England. This paper was previously titled "Recovering Risk Aversion from Options." Any remaining errors are our own. 1 American options present a somewhat more complicated investment horizon, but only to the extent that early exercise is optional. Still, even in that case, American options allow a greater specificity of investment horizon than stocks do. furthermore, several central banks track monthly changes in implied PDFs to infer changes in market sentiment. Though to be absolutely fair, this evidence is indirect and not necessarily conclusive. We know of no study that has directly tested whether it is possible to reject the stationarity of implied risk-neutral PDFs over various time intervals. 10 Of course, "failure to reject" does not mean we should "accept." Our use of the term a "good forecast" is merely an expositional convenience and should be understood as such.11 Short Sterling options were also examined but failed to produc...

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The paper considers two small analytical models, one Old‐Keynesian, the other New‐Keynesian, possessing equilibria where nominal interest rates at all maturities can be stuck at their zero lower bound. When the authorities remove the zero nominal interest rate floor by adopting an augmented monetary rule that systematically keeps the nominal interest rate on base money at or below the nominal interest rate on non‐monetary instruments, the lower bound equilibria are eliminated, thus allowing an economic system to avoid or escape from the trap. This involves paying negative interest on currency, ie, imposing a ‘carry tax’ on currency, an idea first promoted by Gesell.

The paper considers ways of avoiding a liquidity trap and ways of getting out of one. Unless lower short nominal interest rates are associated with significantly lower interest volatility, a lower average rate of inflation, which will be associated with lower expected nominal interest rates, increases the odds that the zero nominal interest rate floor will become a binding constraint. The empirical evidence on this issue is mixed. Once in a liquidity trap, there are two means of escape. The first is to use expansionary fiscal policy. The second is to lower the zero nominal interest rate floor. This second option involves paying negative interest on government 'bearer bonds'-coin and currency, that is 'taxing money', as advocated by Gesell. This would also reduce the likelihood of ending up in a liquidity trap. Taxing currency amounts to having periodic 'currency reforms', that is, compulsory conversions of 'old' currency into 'new' currency, say by stamping currency. The terms of the conversion can be set to achieve any positive or negative interest rate on currency. There are likely to be significant shoe leather costs associated with such schemes. The policy question then becomes how much shoe leather it takes to fill an output gap? Finally the paper develops a simple analytical model showing how the economy can get into a liquidity trap and how Gesell money is one way of avoiding it or escaping from it.