Short-time at-the-money skew and rough fractional volatility

The Black–Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time to maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power law. The volatility process of the model is driven by a fractional Brownian motion with Hurst parameter less than half. The fractional Brownian motion is correlated with a Brownian motion which drives the asset price process. We derive an asymptotic expansion of the implied volatility as the time to maturity tends to zero. For this purpose, we introduce a new approach to validate such an expansion, which enables us to treat more general models than in the literature. The local-stochastic volatility model is treated as well under an essentially minimal regularity condition in order to show such a standard model cannot be dynamically consistent to the power law.     

Can negative interest rates really affect option pricing? Empirical evidence from an explicitly solvable stochastic volatility model

The profound financial crisis generated by the collapse of Lehman Brothers and the European sovereign debt crisis in 2011 have caused negative values of government bond yields both in the USA and in the EURO area. This paper investigates whether the use of models which allow for negative interest rates can improve option pricing and implied volatility forecasting. This is done with special attention to foreign exchange and index options. To this end, we carried out an empirical analysis on the prices of call and put options on the US S&P 500 index and Eurodollar futures using a generalization of the Heston model in the stochastic interest rate framework. Specifically, the dynamics of the option’s underlying asset is described by two factors: a stochastic variance and a stochastic interest rate. The volatility is not allowed to be negative, but the interest rate is. Explicit formulas for the transition probability density function and moments are derived. These formulas are used to estimate the model parameters efficiently. Three empirical analyses are illustrated. The first two show that the use of models which allow for negative interest rates can efficiently reproduce implied volatility and forecast option prices (i.e. S&P index and foreign exchange options). The last studies how the US three-month government bond yield affects the US S&P 500 index.     

How should Engel's law be formulated?

Engel's law expresses a “negative stochastic association” of income and the proportion of income that is spent on food. However, there are many quite different notions of “negative stochastic association” and consequently there are different ways of defining Engel's law. We relate these different concepts to Engel's original statistical analysis and show that one must give credit to Engel for the first non-parametric statistical analysis of budget-data.     

Feed use intensification and technical efficiency of dairy farms in New Zealand

In recent years, the traditionally pasture‐based dairy farms in New Zealand have become more intensive by using higher proportions of supplementary feed. This trend has been attributed to a range of factors, such as productivity enhancement, overcoming pasture deficits and the improvement of body condition scores. However, there is a lack of knowledge as to how feed use intensification affects the technical efficiency of dairy farms in New Zealand. This paper addresses the research gap by estimating the impact of feed use intensification on the technical efficiency of New Zealand dairy farms, using a fixed effects stochastic production frontier model and a balanced panel of 257 farms from 2010 to 2013. The empirical results show that technical efficiency on New Zealand dairy farms is positively and significantly influenced by feed use intensification, herd size and milking frequency.     

Bond Pricing with a Time‐Varying Price of Risk in an Estimated Medium‐Scale Bayesian DSGE Model

New Keynesian model in which households have Epstein–Zin preferences with time‐varying risk aversion and the central bank has a time‐varying inflation target can match the dynamics of nominal bond prices in the U.S. economy well. The model generates a large steady‐state term spread and its fitting errors for bond yields are comparable to those obtained from a nonstructural three‐factor model, and one‐third smaller than in models with a constant inflation target or risk aversion. Including data on interest rates has large effects on variance decompositions, making investment technology shocks much less important than found in other recent papers.     

Estimating input-mix efficiency in a parametric framework: application to state-level agricultural data for the United States

ABSTRACT

This paper contributes to the productivity literature by demonstrating novel econometric methods to estimate input-mix efficiency (IME) in a parametric framework. Input-mix efficiency is defined as the potential improvement in productivity with change in input mix. Any change in input-mix (e.g., land to labou r ratio) will result in change in productivity. The advantage of this approach is that it does not require data on input prices to estimate the mix efficiency levels. A nonlinear input-aggregator function (e.g., Constant Elasticity of Substitution) is used to derive an expression for input-mix efficiency. Bayesian stochastic frontier is estimated for obtaining mix efficiency using US state-level agricultural data for the period 1960–2004. Significant variation in input-mix efficiency is noted across the states and regions, attributable to diverse topographic and geographic conditions. Furthermore, comparisons of allocative and mix efficiencies provide insightful policy implications. The production incentives such as taxes and subsidies could help farmers in adjusting their input mix in response to changes in input prices, which can affect the US agricultural productivity significantly. The proposed methodology can be extended by i) using flexible functional forms; ii) introducing various time- and region-varying input aggregators; and iii) defining more sophisticated weights for input aggregators.     

Socio-institutional determinants of educational resource efficiency according to the capability approach: An endogenous stochastic frontier analysis

We investigate the role of private and public resources in educational attainments and the socio-institutional determinants of educational resource efficiency in Italy. Following the Sen's capability approach, we consider social capital and the quality of government part of the social conversion factors through which resources can be converted into human capabilities, such as education. We analyze the case of Italy by constructing a new longitudinal dataset from 1993 to 2012, using repeated cross sections from the main social survey of the Italian Statistical Institute and a panel stochastic frontier model that takes into account endogeneity. The results show the relative importance of private resources (measured by an ad hoc constructed wealth index), the complementarity between private wealth and public expenditures on education, and the positive impact of social capital and the quality of government on educational resource efficiency.     

Inference for large financial systems

We treat the parameter estimation problem for mean‐field models of large interacting financial systems such as the banking system and a pool of assets held by an institution or backing a security. We develop an asymptotic inference approach that addresses the scale and complexity of such systems. Harnessing the weak convergence results developed for mean‐field financial systems in the literature, we construct an approximate likelihood for large systems. The approximate likelihood has a conditionally Gaussian structure, enabling us to design an efficient numerical method for its evaluation. We provide a representation of the corresponding approximate estimator in terms of a weighted least‐squares estimator, and use it to analyze the large‐system and large‐sample behavior of the estimator. Numerical results for a mean‐field model of systemic financial risk highlight the efficiency and accuracy of our estimator.     

Heterogeneity and netting efficiency under central clearing: A stochastic network analysis

This paper examines the effect of heterogeneity in clearing members’ exposure management practices under central clearing. Our network model specifies the dynamics of prenetted interbank exposures to shape interdependent exposure distributions beyond normality. Employing over-the-counter derivatives market data from the U.S. Office of the Comptroller of the Currency, our simulation results indicate that heterogeneity in bank-to-bank exposure dynamics is systemically desirable, while the entire system benefits more from the central clearing in more homogeneous environments. Policymakers should incentivize individual clearing members to enhance resiliency and stability in counterparty exposure management to maximize netting efficiency under central clearing.     

Robust consumption‐investment problem under CRRA and CARA utilities with time‐varying confidence sets

We consider a robust consumption‐investment problem under constant relative risk aversion and constant absolute risk aversion utilities. The time‐varying confidence sets are specified by Θ, a correspondence from [0, T] to the space of the Lévy triplets, and describe a priori drift, volatility, and jump information. For each possible measure, the log‐price processes of stocks are semimartingales, and the triplet of their differential characteristics is almost surely a measurable selector from the correspondence Θ. By proposing and investigating the global kernel, an optimal policy and a worst‐case measure are generated from a saddle point of the global kernel, and they constitute a saddle point of the objective function.