Reverse-engineering country risk ratings: a combinatorial non-recursive model

The central objective of this paper is to develop a transparent, consistent, self-contained, and stable country risk rating model, closely approximating the country risk ratings provided by Standard and Poor’s (S&P). The model should be non-recursive, i.e., it should not rely on the previous years’ S&P ratings. The set of variables selected here includes not only economic-financial but also political variables. We propose a new model based on the novel combinatorial-logical technique of Logical Analysis of Data (which derives a new rating system only from the qualitative information representing pairwise comparisons of country riskiness). We also develop a method allowing to derive a rating system that has any desired level of granularity. The accuracy of the proposed model’s predictions, measured by its correlation coefficients with the S&P ratings, and confirmed by k-folding cross-validation, exceeds 95%. The stability of the constructed non-recursive model is shown in three ways: by the correlation of the predictions with those of other agencies (Moody’s and The Institutional Investor), by predicting 1999 ratings using the non-recursive model derived from the 1998 dataset applied to the 1999 data, and by successfully predicting the ratings of several previously non-rated countries. This study provides new insights on the importance of variables by supporting the necessity of including in the analysis, in addition to economic variables, also political variables (in particular “political stability”), and by identifying “financial depth and efficiency” as a new critical factor in assessing country risk.     

The development of a simple and intuitive rating system under Solvency II

Regulatory authorities pay considerable attention to setting minimum capital levels for different kinds of financial institutions. Solvency II, the European Commission’s planned reform of the regulation of insurance companies is well underway. One of its consequences will be a shift in focus to internally based models in determining the regulatory capital needed to cover unexpected losses. This evolution emphasises the importance of credit risk assessment through internal ratings. In light of this new prudential regulation, this paper suggests a Basel II compliant approach to predicting credit ratings for non-rated corporations and evaluates its performance compared to external ratings. The paper provides an interesting modelling of non-financial European companies rated by S&P. In developing the model, broad applicability is set as an important boundary condition. Even though the model developed is fairly simple and maintains a high level of granularity, it gives high rates of accuracy and is very interpretable.     

Normal tempered stable copula

In this paper, we discuss a copula defined by the Gaussian subordination method. The copula can capture the dependence between extreme events, and asymmetric dependence, which are observed in empirical financial return distributions. We further perform an empirical test for this new copula against the standard Gaussian copula using 10 years daily returns of the Standard&Poor’s 500 (S&P500) and the Deutscher Aktien Index (DAX) equity market indices.     

An investigation of model selection criteria for neural network time series forecasting

Artificial neural networks (ANNs) have received more and more attention in time series forecasting in recent years. One major disadvantage of neural networks is that there is no formal systematic model building approach. In this paper, we expose problems of the commonly used information-based in-sample model selection criteria in selecting neural networks for financial time series forecasting. Specifically, Akaike’s information criterion (AIC) and Bayesian information criterion (BIC) as well as several extensions have been examined through three real time series of Standard and Poor’s 500 index (S&P 500 index), exchange rate, and interest rate. In addition, the relationship between in-sample model fitting and out-of-sample forecasting performance with commonly used performance measures is also studied. Results indicate that the in-sample model selection criteria we investigated are not able to provide a reliable guide to out-of-sample performance and there is no apparent connection between in-sample model fit and out-of-sample forecasting performance.     

Self-criticality and stochasticity of an S&P 500 index time series

In this paper, three time series representative of the daily high, low and closing prices of S&P 500 index time series, as from 1 December 1988 to 1 April 1998 are studied. The hypothesis advanced by Osborne that the stock market time series satisfy a log-normal distribution is rejected. The self-critical behavior of these time series is investigated. A fractional Brownian motion model for such time series is supported. Arguments are directed torwards a negation of a chaotic explanation of these time series.     

Data-driven hedging of stock index options via deep learning

We develop deep learning models to learn the hedge ratio for S&P500 index options from options data. We compare different combinations of features and show that with sufficient training data, a feedforward neural network model with time to maturity, the Black-Scholes delta and market sentiment as inputs performs the best in the out-of-sample test under daily hedging. This model significantly outperforms delta hedging and a data-driven hedging model. Our results also demonstrate the importance of market sentiment for hedging.     

Properties of learning models in collective action: Rationality of backward-looking players

This article intends to clarify properties of learning models in simulation studies and to conduct a comparison of preceding learning models. Learning models are often used in many simulation studies, but there is no uniform rule of learning. We introduce three technical properties (monotonicity, condition of probability, neutrality) and three rational properties (rationality is fixed situations, rationality in first order stochastic domination, rationality with risk preference in stocahstic situations). We examine Michael Macy's model, the Erev & Roth model, and some others. We find that these models have different properties. Though learning is treated as one of the solutions of social dilemma from the results of Macy's model (Kollock, 1998), Macy's model is peculiar learning model. Learning is not always a solution of social dilemma. A comparison of learning models from a uniform point of view clarifies the properties of each model, and helps to probe conformity of a learning model and human behavior.     

On the parity of generalized partition functions II

Let A = {а 1 < a 2 < ...} be a set of positive integers and A(x) its counting function. Let us denote the number of partitions of n with parts in A by p( A , n). Improving on two preceding papers jointly written with I.Z. Ruzsa and A. Sárközy (J. Number Theory, 1998) and with A. Sárközy (Millennial Conference on Number Theory, May 2000, Urbana, Illinois, U.S.A.), it is shown that there exists a set A satisfying A(x) > c xlog log x/ (log x) 1/3 , c<0, such that, for n large enough, p( A ; n) isalways even.     

Skewness Term-Structure Tests

In this paper, we conduct skewness term-structure tests to check whether the temporal structure of risk-neutral skewness is consistent with rational expectations. Because risk-neutral skewness is substantially mean reverting, skewness shocks should decay quickly and risk-neutral skewness of more distant option should display the rationally expected smoothing behaviour. Using an equilibrium asset and option-pricing model in a production economy under jump diffusion with stochastic jump intensity, we derive this elasticity analytically. In an empirical application of the model using more than 20 years of data on S&P500 index options, we find that this elasticity turns out to be different than suggested under rational expectations – smaller on the short end (underreaction) and larger on the long end (overreaction) of the ‘skewness curve’.     

Bayesian Filtering for Jump-Diffusions With Application to Stochastic Volatility

In this article, the problem of sequentially learning parameters governing discretely observed jump-diffusions is explored. The estimation framework involves the introduction of latent points between every pair of observations to allow a sufficiently accurate Euler–Maruyama approximation of the underlying (but unavailable) transition densities. Particle filtering algorithms are then implemented to sample the posterior distribution of the latent data and the model parameters online. The methodology is applied to the estimation of parameters governing a stochastic volatility (SV) model with jumps. As well as using S&P 500 Index data, a simulation study is provided. Supplemental materials for this article are available online.     

Long-Range Dependence in the Risk-Neutral Measure for the Market on Lehman Brothers Collapse

This paper discusses the long-range dependence in the risk-neutral stock return process of the S&P 500 index option market. To observe the long-range dependence together with fat-tails, I define the parametric model of fractional Lévy process. Since the continuous time fractional Lévy process allows arbitrage, I use discrete time option pricing model based on the fractional Lévy process. By model calibration, we can capture the long-range dependence in the S&P 500 index option market. The paper finds that the long range dependence becomes stronger for the volatile market caused by the Lehman Brothers Collapse, comparing with other less volatility markets.     

Ideals of Priestley powers of semilattices

Let X be a poset and Y an ordered space; X ^Y denotes the poset of continuous order-preserving maps from Y to X with the discrete (respectively, Scott, Lawson) topology. If S is a -semilattice, its ideal semilattice, and T a bounded distributive lattice with Priestley dual space P(T), it is shown that the following isomorphisms hold: Moreover, and sufficient conditions and necessary conditions for the isomorphism to hold are obtained (both necessary and sufficient if S is a distributive -semilattice). Received September 27, 1995; accepted in final form April 6, 1998.     

Inducing Stock Screening Rules for Portfolio Construction

This study describes a technique originated from the emerging field of machine learning and demonstrates its effectiveness in stock screening. We have derived screening rules by applying a rule induction method, constructed portfolios using the rules, and evaluated the portfolios' performance using the Sharpe, Treynor and Jensen indexes. Results indicate that regularities among stocks can be identified, and portfolios so constructed outperformed the NYSE Composite index and the S&P 500 over the same period.     

N-tuple S&P patterns across decades, 1950–2011

Numerous studies have analyzed the movements of the S&P 500 index using several methodologies such as technical analysis, econometric modeling, time series techniques and theories from behavioral finance. In this paper we take a novel approach. We use daily closing prices for the S&P 500 index for a very long period from 1/3/1950 to 7/19/2011 for a total of 15,488 daily observations. We then investigate the up and down movements and their combinations for 1–7 days giving us multiple possible patterns for over six decades. Some patterns of each type are more dominant across decades. We split the data into training and validation sets and then select the dominant patterns to build conditional forecasts in several ways, including using a decision tree methodology. The best model is correct 51 % of the time on the validation set when forecasting a down day, and 61 % when forecasting an up day. We show that certain conditional forecasts outperform the unconditional random walk model.     

外资评级机构进入中国能否发挥“鲶鱼效应”?

近年来,中国信用评级行业逐步对外开放。我国监管部门相继批准标普、惠誉等具有国际影响力的外资评级机构进入我国市场。在此背景下,本文采用博弈模型分析了外资评级机构进入中国市场对本土评级机构评级质量的影响。研究发现,高声誉外资评级机构进入中国市场能够起到激励本土评级机构公正评级并促进评级行业形成良性循环的作用。本文研究结论为我国信用评级行业对外开放以及引入更多具有国际影响力的外资评级机构提供了理论支撑。     

A DEA study of gender equity in executive compensation

This study assesses whether annual and long-term compensation for senior executive women is equal to annual and long-term compensation for senior executive men. The group of executive women includes those women reported in the compensation tables of proxy statements for the companies in the Standard and Poors (S&P) 500 for 1997. Their compensation was compared to the compensation for two samples of executive men from S&P 500 firms using data envelopment analysis. The results indicate that the compensation paid to executive women is equitable to the compensation paid to executive men.     

Optimization of covered call strategies

We present a risk-return optimization framework to select strike prices and quantities of call options to sell in a covered call strategy. Covered calls of a general form are considered where call options with different strike prices can be sold simultaneously. Tractable formulations are developed using variance, semivariance, VaR, and CVaR as risk measures. Sample expected return and sample risk are formulated by simulating the price of the underlying asset. We use option market price data to perform the optimization and analyze the structure of optimal covered call portfolios using the S&P 500 as the underlying. The optimal solution is shown to be directly linked to the options’ call risk premiums. We find that from a risk-return perspective it is often optimal to simultaneously sell call options of different strike prices for all risk measures considered.     

Analysis of VIX Markets with a Time-Spread Portfolio

This paper explores the relationship between option markets for the S&P500 (SPX) and Chicago Board Options Exchange’s CBOE’s Volatility Index (VIX). Results are obtained by using the so-called time-spread portfolio to replicate a future contract on the squared VIX. The time-spread portfolio is interesting because it provides a model-free link between derivative prices for SPX and VIX. Time spreads can be computed from SPX put options with different maturities, which results in a term structure for squared volatility. This term structure can be compared to the VIX-squared term structure that is backed-out from VIX call options. The time-spread portfolio is also used to measure volatility-of-volatility (vol-of-vol) and the volatility leverage effect. There may emerge small differences in these measurements, depending on whether time spreads are computed with options on SPX or options on VIX. A study of 2012 daily options data shows that vol-of-vol estimates utilizing SPX data will reflect the volatility leverage effect, whereas estimates that exclusively utilize VIX options will predominantly reflect the premia in the VIX-future term structure.     

Stable local volatility function calibration using spline kernel

We propose an optimization formulation using the l ₁ norm to ensure accuracy and stability in calibrating a local volatility function for option pricing. Using a regularization parameter, the proposed objective function balances calibration accuracy with model complexity. Motivated by the support vector machine learning, the unknown local volatility function is represented by a spline kernel function and the model complexity is controlled by minimizing the 1-norm of the kernel coefficient vector. In the context of support vector regression for function estimation based on a finite set of observations, this corresponds to minimizing the number of support vectors for predictability. We illustrate the ability of the proposed approach to reconstruct the local volatility function in a synthetic market. In addition, based on S&P 500 market index option data, we demonstrate that the calibrated local volatility surface is simple and resembles the observed implied volatility surface in shape. Stability is illustrated by calibrating local volatility functions using market option data from different dates.     

Image denoising via solution paths

In this paper, we propose a two-step kernel learning method based on the support vector regression (SVR) for financial time series forecasting. Given a number of candidate kernels, our method learns a sparse linear combination of these kernels so that the resulting kernel can be used to predict well on future data. The L ₁-norm regularization approach is used to achieve kernel learning. Since the regularization parameter must be carefully selected, to facilitate parameter tuning, we develop an efficient solution path algorithm that solves the optimal solutions for all possible values of the regularization parameter. Our kernel learning method has been applied to forecast the S&P500 and the NASDAQ market indices and showed promising results.