Option pricing with random risk aversion

Based on a standard general equilibrium economy, we develop a framework for pricing European options where the risk aversion parameter is state dependent, and aggregate wealth and the underlying asset have a bivariate transformed-normal distribution. Our results show that the volatility and the skewness of the risk aversion parameter change the slope of the pricing kernel, and that, as the volatility of the risk aversion parameter increases, the (Black and Scholes) implied volatility shifts upwards but its shape remains the same, which implies that the volatility of the risk aversion parameter does not change the shape of the risk neutral distribution. Also, we demonstrate that the pricing kernel may become non-monotonic for high levels of volatility and low levels of skewness of the risk aversion parameter. An empirical example shows that the estimated volatility of the risk aversion parameter tends to be low in periods of high market volatility and vice-versa.

Consumption, aggregate wealth and expected stock returns: a quantile cointegration approach

This paper empirically examines the long-run relationship between consumption, asset wealth and labor income (i.e., cay) in the United States through the lens of a quantile cointegration approach. The advantage of using this approach is that it allows for a nonlinear relationship between these variables depending on the level of consumption. We estimate the coefficients using a Phillips–Hansen type fully modified quantile estimator to correct for the presence of endogeneity in the cointegrating relationship. To test for the null of cointegration at each quantile, we apply a quantile CUSUM test. Results show that: (i) consumption is more sensitive to changes in labor income than to changes in asset wealth for the entire distribution of consumption, (ii) the elasticity of consumption with respect to labor income (asset wealth) is larger at the right (left) tail of the consumption distribution than at the left (right) tail, (iii) the series are cointegrated around the median, but not in the tails of the distribution of consumption, (iv) using the estimated cay obtained for the right (left) tail of the distribution of consumption improves the long-run (short-run) forecast ability on real excess stock returns over a risk-free rate.

Where Is the Middle Class? Evidence from 60 Million English Death and Probate Records, 1892–1992

This article analyzes a newly constructed individual level dataset of every English death and probate from 1892–1992. This analysis shows that the twentieth century’s “Great Equalization” of wealth stalled in mid-century. The probate rate, which captures the proportion of English holding any significant wealth at death rose from 10 percent in the 1890s to 40 percent by 1950 and has stagnated to 1992. Despite the large declines in the wealth share of the top 1 percent, from 73 to 20 percent, the median English individual died with almost nothing throughout. All changes in inequality after 1950 involve a reshuffling of wealth within the top 30 percent. I translate the individual level data to synthetic households; the majority have at least one member probated. Yet the bottom 60 percent of households hold only 12 percent of all wealth, at their peak wealth-holding level, in the early 1990s. I also compare the new wealth data with existing estimates of top wealth shares, home-ownership trends, wealth survey distributions, aggregate wealth, and the wealth Gini coefficient.

Consumption, Aggregate Wealth and Expected Stock Returns: An FCVAR Approach

In their seminal work, Lettau, M., and S. Ludvigson, 2001, “Consumption, Aggregate Wealth, and Expected Stock Returns.” The Journal of Finance 56 (3): 815–49. https://doi.org/10.1111/0022-1082.00347, demonstrated that there exists a long-run relationship between consumption, asset holdings, and labor income. They denoted this relationship as cay and showed it to be quite successful in predicting the behavior of real stock returns. Their estimation procedure assumes that consumption, asset wealth, and labor income are first-order integrated (I(1), nonstationary) and that their linear combination forms a zero-order integrated (I(0), stationary) series. This paper proposes a more general framework in the estimation of the cay model by allowing both the series and the long-run equilibrium to be fractionally integrated. We use the recently developed Fractionally Cointegrated VAR (FCVAR) approach to estimate the cay model. Results show that: (i) the series are nonstationary but mean-reverting processes, (ii) there exists a long-run equilibrium between consumption, asset wealth, and labor income, (iii) this long-run relationship is a stationary fractionally integrated process, and (iv) the estimated cay using the FCVAR approach shows the same desirable forecasting properties as its predecessor.

On households and unemployment insurance

We study unemployment insurance in a framework where the main source of heterogeneity among agents is the type of household they live in: some agents live alone while others live with their spouses as a family. Our exercise is motivated by the fact that married individuals can rely on spousal income to smooth labor market shocks, while singles cannot. We extend a version of the standard incomplete‐markets model to include two‐agent households and calibrate it to the US economy with special emphasis on matching differences in labor market transitions across gender and marital status as well as aggregate wealth moments. Our central finding is that changes to the current unemployment insurance program are valued differently by married and single households. In particular, a more generous unemployment insurance reduces the welfare of married households significantly more than that of singles and vice versa. We show that this result is driven by the amount of self‐insurance existing in married households, and thus, we highlight the interplay between self‐ and government‐provided insurance and its implication for policy.