Nonlinearity is an important consideration in many problems of finance and economics, such as pricing securities and solving equilibrium models. This article provides analytical treatment of a general class of nonlinear transforms for processes with tractable conditional characteristic functions. We extend existing results on characteristic function-based transforms to a substantially wider class of nonlinear functions while maintaining low dimensionality by avoiding the need to compute the density function. We illustrate the applications of the generalized transform in pricing defaultable bonds with stochastic recovery. We also use the method to analytically solve a class of general equilibrium models with multiple goods and apply this model to study the effects of time-varying labor income risk on the equity premium.

We study the implications of inflation heterogeneity for individuals and firms through the lens of accounting research, applying measurement frameworks to the national accounting measurement of inflation. We first examine the systematic exposure of individuals in low‐income households to higher inflation relative to those in high‐income households. We show that this “inflation gap” is linked with future rising inequality in the form of widening gaps in healthcare insurance, education, homeownership, and credit card debt, as well as in a higher frequency of property crimes. We also provide an economic mechanism connecting the inflation gap with rising inequality, empirically demonstrating the role of basic goods in reducing the ability of individuals in the low‐income group to attain the social and economic implications that we study. In addition, we show a channel that connects the inflation gap to firms' profitability. Indeed, consistent with the inflation gap disadvantaging low‐income households mainly through basic goods, the inflation gap fluctuations are especially strongly connected to the profitability of firms operating in the energy and consumer staples sectors. Finally, we find that market power plays a role in this connection, where this link is even stronger for firms with high market power. Taking its findings together, the paper shows that differential inflation pressures have major implications for household well‐being and corporate profitability.

We propose a new measure of financial intermediary constraints based on how intermediaries manage their tail risk exposures. Using data for the trading activities in the market of deep out-of-the-money index put options, we identify periods when the variations in the net amount of trading between financial intermediaries and public investors are likely to be mainly driven by shocks to intermediary constraints. We then infer tightness of intermediary constraints from the quantities of option trading. A tightening of intermediary constraints according to our measure is associated with increasing option expensiveness, higher risk premia, deteriorating funding liquidity, and broker-dealer deleveraging. Received December 1, 2014; editorial decision May 19, 2017 by Editor Geert Bekaert.

Although the threat of rare economic disasters can have large effect on asset prices, difficulty in inference regarding both their likelihood and severity provides the potential for disagreements among investors. Such disagreements lead investors to insure each other against the types of disasters each one fears the most. Due to the highly nonlinear relationship between consumption losses in a disaster and the risk premium, a small amount of risk sharing can significantly attenuate the effect that disaster risk has on the equity premium. We characterize the sensitivity of risk premium to wealth distribution analytically. Our model shows that time variation in the wealth distribution and the amount of disagreement across agents can both lead to significant variation in disaster risk premium. It also highlights the conditions under which disaster risk premium will be large, namely when disagreement across agents is small or when the wealth distribution is highly concentrated in agents fearful of disasters. Finally, the model predicts an inverse U-shaped relationship between the equity premium and the size of the disaster insurance market.

Models of heterogeneous beliefs can generate rich implications for trading and asset pricing (see Suleyman Basak 2005 for a recent survey). When studying such models, aggregation often leads to difficulty in computing equilibrium outcomes. In this paper, we introduce a flexible framework to model heterogeneous beliefs in the economy, which we refer to as “affine’’ disagreement about fundamentals. Affine processes (see Darrel Duffie, Jun Pan, and Kenneth Singleton 2000) are appealing as they provide a large degree of flexibility in modeling the conditional means, volatilities, and jumps for various quantities of interest while remaining analytically tractable. Our affine heterogeneous beliefs framework allows further for stochastic disagreement among agents about growth rates, volatility dynamics, as well as the likelihood of jumps and the distribution of jump sizes.