Combining multiple probability predictions using a simple logit model

This paper begins by presenting a simple model of the way in which experts estimate probabilities. The model is then used to construct a likelihood-based aggregation formula for combining multiple probability forecasts. The resulting aggregator has a simple analytical form that depends on a single, easily-interpretable parameter. This makes it computationally simple, attractive for further development, and robust against overfitting. Based on a large-scale dataset in which over 1300 experts tried to predict 69 geopolitical events, our aggregator is found to be superior to several widely-used aggregation algorithms.     

Multifactor risk loadings and abnormal returns under uncertainty and learning

We explore the time variation of factor loadings and abnormal returns in the context of a four-factor model. Our methodology, based on an application of the Kalman filter and on endogenous uncertainty, overcomes several limitations of competing approaches used in the literature. Besides taking learning into account, it does not rely on any conditioning information, and it only imposes minimal assumptions on the time variation of the parameters. Our estimates capture both short- and long-term fluctuations of risk loadings and abnormal returns, also showing marked variation across US industry portfolios. The results from mean-variance spanning tests indicate that our baseline model yields accurate predictions and can therefore improve pricing and performance measurement.     

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.     

Geometric Asian option pricing in general affine stochastic volatility models with jumps

In this paper, we present some results on Geometric Asian option valuation for affine stochastic volatility models with jumps. We shall provide a general framework into which several different valuation problems based on some average process can be cast, and we shall obtain closed form solutions for some relevant affine model classes.     

Modeling regional economic dynamics: Spatial dependence,spatial heterogeneity and nonlinearities

Spatial modeling of economic phenomena requires the adoption of complex econometric tools, which allow us to deal with important methodological issues, such as spatial dependence, spatial unobserved heterogeneity and nonlinearities. In this paper we describe some recently developed econometric approaches (i.e. Spatial Autoregressive Semiparametric Geoadditive Models), which address the three issues simultaneously. We also illustrate the relative performance of these methods with an application to the case of house prices in the Lucas County.     

道德哲学视域下的关公崇拜

在中国传统民间信仰之中,关公崇拜是俗文化兴起的产物,是社会道德情感社会潜意识孕育产生的一个道德模范,经典的三国演义为关公崇拜提供了有力的文本支撑,历代统治者的推波助澜也为这种崇拜发展起了重要作用。同时,关公崇拜背后有着深厚的道德内涵和社会价值,它所推崇的"义"是一种超越传统血亲关系的品德。这种品德即使在今天的商业社会也有着其存在发展的土壤,这也是关公崇拜得以延续至今的重要原因。     

Steady state adjusting trends using a data-driven local polynomial regression

Economic variables usually follow a dynamic trend pattern. However, it is difficult to estimate this trend precisely as numerous economically- and statistically-based estimation methods exist. This contribution proposes a data-driven nonparametric trend that is local polynomial, to improve arbitrary trend estimations of commonly used methods concerning the selection of the smoothing parameter and the dependence structure. An iterative plug-in (IPI) algorithm determines the bandwidth endogenously and allows a theory-based interpretation of the length of growth processes. This length of the bandwidth reflects the lengths of the steady state periods. Consequently, the bandwidth identifies the time period of stable economic conditions and can detect economic changes. To demonstrate the power of this estimation approach, an extensive simulation study is performed. Furthermore, examples using US and UK GDP data along with a guide for the optimal choice of algorithms for empirical applications are provided. This proposed method yields new insights for growth dynamics, cyclical movements and their dependence.     

Pricing executive stock options with averaging features under the Heston–Nandi GARCH model

In this paper, we focus on the pricing issue of four types of executive stock options (ESOs) in the Heston–Nandi generalized autoregressive conditional heteroskedasticity option pricing model. Based on the derived benchmark strike prices in the proposed framework, we obtain the closed-form pricing formulae for four types of ESOs. In the numerical part, we investigate the sensitivity and cost efficiency of ESOs and suggest that systematic risk (stock β) and the fraction of wealth invested in restricted stock could impede the cost efficiency of ESOs.