Can Markov switching models replicate chartist profits in the foreign exchange market?

In this paper we show that the Markov switching model is a relevant statistical alternative to the classical martingale model for exchange rates. By extending the standard Markov switching model we decisively reject the martingale model. Moreover, the model generates autocorrelations and linear structures in line with what is observed in reality. Subsequently, we test whether this model can explain chartist profits. We find that the extended Markov switching model is able to explain the profitability of a simple MA-30 rule. Finally, we decompose the profitability of the MA-30 rule into a linear and nonlinear part. We find that, although the implied linear structure of the Markov model explains a substantial part of the profitability, part of the profits of the MA-30 rule can be attributed to the specific nonlinearities implicit in the Markov model.     

Stock returns,dividend yield,and book-to-market ratio

A dividend yield model has been widely used in previous research that relates stock market valuations to cash flow fundamentals. Given controversies about using dividends as a proxy for cash flows, a loglinear book-to-market model has recently been proposed. However, these models rely on the assumption that dividend yield and book-to-market ratio are both stationary, and empirical evidence for this is, at best, mixed. We develop a new model, the loglinear cointegration model, that explains future profitability and excess stock returns in terms of a linear combination of log book-to-market ratio and log dividend yield. The loglinear cointegration model performs better than the log dividend yield model and the log book-to-market model in terms of cross-equation restriction tests and forecasting performance comparisons. The superior performance of the loglinear cointegration model suggests that the linear combination may be a better indicator of intrinsic fundamentals than the dividend yield or the book-to-market ratio separately.     

It takes a model to beat a model: Volatility bounds

Models like the CAPM and Fama–French three-factor models are commonly used as benchmarks for calculating cost of capital and evaluating portfolio performance, despite the empirical evidence to reject them. For many practical purposes, “it takes a model to beat a model.” In this paper we derive restrictions on models that could “beat” a bench-mark model but might still be misspecified. In these “takes-a-model-to-beat-a-model” (TMBM) bounds, model A beats model B if model A's quadratic form of pricing errors is smaller. The bounds generalize the Hansen–Jagannathan bound and distance measure. We use the TMBM bounds to evaluate various linear factor models and consumption-based models. The failure of the power utility model is much less extreme when it is compared with the CAPM and Fama–French model. For reasonable utility curvature, the Ferson–Constantinides model and Epstein–Zin model perform best among the consumption-based models, beating the model of Campbell and Cochrane, in which model the value of the persistence parameter that matches the time-series properties of aggregate stock market returns seems too low for cross-sectional asset pricing.     

商业银行内部评级体系构建的模型风险研究

自上个世纪70年代以来,风险管理模型为银行的风险量化管理提供了工具,但也同时引致了模型风险。除少数银行外,大多数商业银行在实施内部评级法时都着力构建自己的风险管理模型体系。不论是直接引入外部模型还是自我构建模型,都必然存在模型风险的问题,其模型风险主要产生于基础模型和构建过程两个方面。由于中国正处于转轨经济阶段,因此中国商业银行在内部评级体系构建中的模型风险除了来源于基础模型、模型数据以外,模型使用环境的特殊性也是一个不可忽视的因素。压力测试和极端值方法是避免模型风险的有效技术手段,而风险文化的建设则是规避模型风险的根本所在。     

An Empirical Analysis of Exchange Ratio Determination Models for Merger: A Note

This paper examines the empirical validity of two exchange ratio determination models for merger, the Larson and Gonedes (LG) PE model and the Yagil dividend growth model. These two models formulate exchange ratios as a function of a different factor: expected post-merger price-earnings multiple and expected post-merger dividend growth, respectively. While the LG model has been tested in previous studies, the Yagil model has yet been subject to empirical testing. This paper finds empirical support for the LG model but finds weak support for the Yagil model. In particular, the results show that the number of stock mergers that result in wealth gains for both acquiring and target firms and hence conform to the rationality assumption of each model is substantially greater for the LG model than for the Yagil model. Regression analysis provides confirmatory evidence on the empirical validity of the LG model that PE-related variables play a more significant role in explaining the actual exchange ratios than growth-related variables.     

Modeling and Pricing Longevity Derivatives Using Stochastic Mortality Rates and the Esscher Transform

The Lee-Carter mortality model provides a structure for stochastically modeling mortality rates incorporating both time (year) and age mortality dynamics. Their model is constructed by modeling the mortality rate as a function of both an age and a year effect. Recently the MBMM model (Mitchell et al. 2013) showed the Lee Carter model can be improved by fitting with the growth rates of mortality rates over time and age rather than the mortality rates themselves. The MBMM modification of the Lee-Carter model performs better than the original and many of the subsequent variants. In order to model the mortality rate under the martingale measure and to apply it for pricing the longevity derivatives, we adapt the MBMM structure and introduce a Lévy stochastic process with a normal inverse Gaussian (NIG) distribution in our model. The model has two advantages in addition to better fit: first, it can mimic the jumps in the mortality rates since the NIG distribution is fat-tailed with high kurtosis, and, second, this mortality model lends itself to pricing of longevity derivatives based on the assumed mortality model. Using the Esscher transformation we show how to find a related martingale measure, allowing martingale pricing for mortality/longevity risk–related derivatives. Finally, we apply our model to pricing a q-forward longevity derivative utilizing the structure proposed by Life and Longevity Markets Association.     

Bond and option pricing for interest rate model with clustering effects

This paper analyzes an interest rate model with self-exciting jumps, in which a jump in the interest rate model increases the intensity of jumps in the same model. This self-exciting property leads to clustering effects in the interest rate model. We obtain a closed-form expression for the conditional moment-generating function when the model coefficients have affine structures. Based on the Girsanov-type measure transformation for general jump-diffusion processes, we derive the evolution of the interest rate under the equivalent martingale measure and an explicit expression of the zero-coupon bond pricing formula. Furthermore, we give a pricing formula for the European call option written on zero-coupon bonds. Finally, we provide an interpretation for the clustering effects in the interest rate model within a simple framework of general equilibrium. Indeed, we construct an interest rate model, the equilibrium state of which coincides with the interest rate model with clustering effects proposed in this paper.     

Junp-Diffusion Interest Rate Process: An Empirical Examination

We investigate a jump-diffusion process, which is a mixture of an O-U process used by Vasicek (1977) and a compound Poisson jump process, for the term structure of interest rates. We develop a methodology for estimating the jump-diffusion model and complete an empirical study in comparing the model with the Vasicek model, for the US money market interest rates. The results show that when the short-term interest rate is low, both models predict an upward sloping term structure, with the jump-diffusion model fitting the actual term structure quite well and the Vasicek model overestimating significantly. When the short-term interest rate is high, both models predict a downward sloping term structure, with the jump-diffusion model underestimating the actual term structure more significantly than the Vasicek model.     

Modelling corporate failure: A multinomial nested logit analysis for unordered outcomes

This study evaluates the theoretical and empirical significance of the multinomial nested logit (NL) model as an advanced closed-form model for the explanation and prediction of firm financial distress. Using a four-state failure model based on Australian company samples, we estimate an NL model and test its predictive performance on a holdout sample. Comparison of model fits and out-of-sample forecasts indicate that the unordered NL model statistically outperforms a standard logit model by substantial margins. NL may even be used as an effective practical alternative to more advanced open-form models such as mixed logit in the modelling of firm financial distress.     

An Empirical Analysis of Exchange Ratio Determination Models for Merger: A Note

This paper examines the empirical validity of two exchange ratio determination models for merger, the Larson and Gonedes (LG) PE model and the Yagil dividend growth model. These two models formulate exchange ratios as a function of a different factor: expected post-merger price-earnings multiple and expected post-merger dividend growth, respectively. While the LG model has been tested in previous studies, the Yagil model has yet been subject to empirical testing. This paper finds empirical support for the LG model but finds weak support for the Yagil model. In particular, the results show that the number of stock mergers that result in wealth gains for both acquiring and target firms and hence conform to the rationality assumption of each model is substantially greater for the LG model than for the Yagil model. Regression analysis provides confirmatory evidence on the empirical validity of the LG model that PE-related variables play a more significant role in explaining the actual exchange ratios than growth-related variables.     

组合预测模型在货运量预测中的应用

本文对灰色预测模型和ARIMA预测模型进行组合,建立了组合模型,并应用于货运量的预测,实证预测表明,组合模型的预测精度优于单一的预测模型,预测结果与实际货运量拟合较好。     

A self-exciting switching jump diffusion: properties,calibration and hitting time

A way to model the clustering of jumps in asset prices consists in combining a diffusion process with a jump Hawkes process in the dynamics of the asset prices. This article proposes a new alternative model based on regime switching processes, referred to as a self-exciting switching jump diffusion (SESJD) model. In this model, jumps in the asset prices are synchronized with changes of states of a hidden Markov chain. The matrix of transition probabilities of this chain is designed in order to approximate the dynamics of a Hawkes process. This model presents several advantages compared to other jump clustering models. Firstly, the SESJD model is easy to fit to time series since estimation can be performed with an enhanced Hamilton filter. Secondly, the model explains various forms of option volatility smiles. Thirdly, several properties about the hitting times of the SESJD model can be inferred by using a fluid embedding technique, which leads to closed form expressions for some financial derivatives, like perpetual binary options.     

Smooth Transition ARCH Models: Estimation and Testing

In this paper, we suggest an extension of the ARCH model, the smooth-transition autoregressive conditional heteroskedasticity (STARCH) model. STARCH models endogenously allow for time-varying shifts in the parameters of the conditional variance equation. The most general form of the model that we consider is a double smooth-transition model, the STAR-STARCH model, which permits not only the conditional variance, but also the mean, to be a function of a smooth-transition term. The threshold ARCH model, the Markov-ARCH model and the standard ARCH model are special cases of our STARCH model. We also develop Lagrange multiplier tests of the hypothesis that the smooth-transition term in the conditional variance is zero. We apply our STARCH model to excess Treasury bill returns. We find some evidence of a smooth transition in excess returns, but in contrast to previous studies, we find almost no evidence of volatility persistence once we allow for smooth transitions in the conditional variance. Thus, the apparent persistence in the conditional variance reported by many researchers could be a mere statistical artifact. We conduct in-sample tests comparing STARCH models to nested competitors; these suggest that STARCH models hold promise for improved predictions. Finally, we describe further extensions of the STARCH model and suggest issues in finance to which they might profitably be applied.     

CreditRisk+ Model with Dependent Risk Factors

The CreditRisk⁺ model is widely used in industry for computing the loss of a credit portfolio. The standard CreditRisk⁺ model assumes independence among a set of common risk factors, a simplified assumption that leads to computational ease. In this article, we propose to model the common risk factors by a class of multivariate extreme copulas as a generalization of bivariate Fréchet copulas. Further we present a conditional compound Poisson model to approximate the credit portfolio and provide a cost-efficient recursive algorithm to calculate the loss distribution. The new model is more flexible than the standard model, with computational advantages compared to other dependence models of risk factors.     

Option valuation with long-run and short-run volatility components

This paper presents a new model for the valuation of European options, in which the volatility of returns consists of two components. One is a long-run component and can be modeled as fully persistent. The other is short-run and has a zero mean. Our model can be viewed as an affine version of Engle and Lee [1999. A permanent and transitory component model of stock return volatility. In: Engle, R., White, H. (Eds.), Cointegration, Causality, and Forecasting: A Festschrift in Honor of Clive W.J. Granger. Oxford University Press, New York, pp. 475–497], allowing for easy valuation of European options. The model substantially outperforms a benchmark single-component volatility model that is well established in the literature, and it fits options better than a model that combines conditional heteroskedasticity and Poisson–normal jumps. The component model's superior performance is partly due to its improved ability to model the smirk and the path of spot volatility, but its most distinctive feature is its ability to model the volatility term structure. This feature enables the component model to jointly model long-maturity and short-maturity options.     

A New Approach to International Arbitrage Pricing

This paper uses a nonlinear arbitrage-pricing model, a conditional linear model, and an unconditional linear model to price international equities, bonds, and forward currency contracts. Unlike linear models, the nonlinear arbitrage-pricing model requires no restrictions on the payoff space, allowing it to price payoffs of options, forward contracts, and other derivative securities. Only the nonlinear arbitrage-pricing model does an adequate job of explaining the time series behavior of a cross section of international returns.     

A STATISTICAL MODEL OF CHANGES IN ASSET PRICES EMPLOYING INTRADAY DATA: A RECURSIVE APPROACH

This paper develops a statistical model of changes in asset prices employing intraday data. The procedure proposed in this paper is an alternative to the Hausman, Lo, and MacKinlay (1992) ordered probit model. Similar to the ordered probit model, our model also contains the linear regression model as a special case. However, compared to the ordered probit model, our specification is parsimonious. Parsimony does come at a cost, but for certain applications where, for example, a benchmark return is needed in intraday studies, there is value in terms of the computational effort required and the method's robustness to various empirical microstructure phenomena. The parsimony is achieved when statistical implications arising from intraday structural changes, which may due to such factors as concentrated trading patterns, are incorporated into a statistical model.     

Option pricing under stochastic volatility and tempered stable Lévy jumps

The purpose of this paper is to introduce a stochastic volatility model for option pricing that exhibits Lévy jump behavior. For this model, we derive the general formula for a European call option. A well known particular case of this class of models is the Bates model, for which the jumps are modeled by a compound Poisson process with normally distributed jumps. Alternatively, we turn our attention to infinite activity jumps produced by a tempered stable process. Then we empirically compare the estimated log-return probability density and the option prices produced from this model to both the Bates model and the Black–Scholes model. We find that the tempered stable jumps describe more precisely market prices than compound Poisson jumps assumed in the Bates model.     

Regime-switching stochastic volatility and short-term interest rates

In this paper, we introduce regime switching in a two-factor stochastic volatility (SV) model to explain the behavior of short-term interest rates. We model the volatility of short-term interest rates as a stochastic volatility process whose mean is subject to shifts in regime. We estimate the regime-switching stochastic volatility (RSV) model using a Gibbs Sampling-based Markov Chain Monte Carlo algorithm. In-sample results strongly favor the RSV model in comparison to the single-state SV model and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) family of models. Out-of-sample results are mixed and, overall, provide weak support for the RSV model.     

A nonparametric approach to measuring the sensitivity of an asset’s return to the market

In the market model the return on an asset is modeled as a linear function of the return on a market index with slope parameter beta. The coefficient beta is often used as a measure of the sensitivity of the asset’s return to the market and to measure the component of the variance of the return that is explained by the market. However, both of these interpretations require the additional assumption that the error term in the market model has mean 0 conditional on the return on the market index, an assumption that is often difficult to verify in practice. In this paper, a nonparametric version of the market model is proposed that does not require such an assumption. This nonparametric model replaces the beta coefficient of the market model with a “beta curve” describing the relationship between the asset’s return and that of the market locally near a given value of the market return. The proposed model is applied to stock returns, as well as to returns on mutual funds. Corresponding tests of the market model are given and it is shown that the nonparametric model often provides an improvement over the standard parametric market model.