Effects of Jumps and Small Noise in High-Frequency Financial Econometrics

Several new statistical procedures for high-frequency financial data analysis have been developed to estimate risk quantities and test the presence of jumps in the underlying continuous-time financial processes. Although the role of micro-market noise is important in high-frequency financial data, there are some basic questions on the effects of presence of noise and jump in the underlying stochastic processes. When there can be jumps and (micro-market) noise at the same time, it is not obvious whether the existing statistical methods are reliable for applications in actual data analysis. We investigate the misspecification effects of jumps and noise on some basic statistics and the testing procedures for jumps proposed by Ait-Sahalia and Jacod (Ann Stat 37–1:184–222 2009; 38–5:3093–3123 2010) as an illustration. We find that their first test (testing the presence of jumps as a null-hypothesis) is asymptotically robust in the small-noise asymptotic sense against possible misspecifications while their second test (testing no-jumps as a null-hypothesis) is quite sensitive to the presence of noise.     

A BSDE approach to fair bilateral pricing under endogenous collateralization

Nie and Rutkowski (Int. J. Theor. Appl. Finance 18:1550048, 2015; Math. Finance, 2016, to appear) examined fair bilateral pricing in models with funding costs and an exogenously given collateral. The main goal of this work is to extend results from Nie and Rutkowski (Int. J. Theor. Appl. Finance 18:1550048, 2015; Math. Finance, 2016, to appear) to the case of an endogenous margin account depending on the contract’s value for the hedger and/or the counterparty. Comparison theorems for BSDEs from Nie and Rutkowski (Theory Probab. Appl., 2016, forthcoming) are used to derive bounds for unilateral prices and to study the range for fair bilateral prices in a general semimartingale model. The backward stochastic viability property, introduced by Buckdahn et al. (Probab. Theory Relat. Fields 116:485–504, 2000), is employed to examine the bounds for fair bilateral prices for European claims with a negotiated collateral in a diffusion-type model. We also generalize in several respects the option pricing results from Bergman (Rev. Financ. Stud. 8:475–500, 1995), Mercurio (Actuarial Sciences and Quantitative Finance, pp. 65–95, 2015) and Piterbarg (Risk 23(2):97–102, 2010) by considering contracts with cash-flow streams and allowing for idiosyncratic funding costs for risky assets.     

The dispersion anomaly and analyst recommendations

The main objective of this study is to distinguish whether the forecast dispersion anomaly is due to Miller’s (J Finance 32(4):1151–1168, 1977) overpricing hypothesis or idiosyncratic risk, by conditioning the sample on “buy” and “sell” consensus recommendations. Observations on the long and short possibilities provided to the investors by the analyst stock recommendations can help us infer on the impact of short sale constraints even though they are not directly observed. This study provides strong evidence that the impact of analyst forecast dispersion is more pronounced in the group of stocks that receive the least favorable recommendations in a given period, even after controlling for the idiosyncratic risk, Fama–French factors (J Financ Econ 33(1):3–56, 1993; J Financ Econ 116(1):1–22, 2015) and even short-sale constraints. These results are consistent with Miller’s (1977) hypothesis, according to which if short-sale constraints bind, high opinion divergence stocks become overpriced and hence have low subsequent returns.     

An Empirical Comparison of Asset-Pricing Models in the Shanghai A-Share Exchange Market

This paper evaluates and compares the performance of three-asset pricing models—the capital asset pricing model of Sharpe (J Finance 19:425–442, 1964), the three-factor model of Fama and French (J Financ Econ 33:3–56, 1993), and the five-factor model (Fama and French in J Financ Econ 123:1–22, 2015)—in the Shanghai A-share exchange market. Our results do not support the superiority of the five-factor model and show that the three-factor model outperforms the other models. We also verify the redundancy of the book-to-market factor and confirm the findings of Fama and French (2015).     

Corporate bankruptcy prediction: a high dimensional analysis

Much bankruptcy research has relied on parametric models, such as multiple discriminant analysis and logit, which can only handle a finite number of predictors (Altman in The Journal of Finance 23 (4), 589–609, 1968; Ohlson in Journal of Accounting Research 18 (1), 109–131, 1980). The gradient boosting model is a statistical learning method that overcomes this limitation. The model accommodates very large numbers of predictors which can be rank ordered, from best to worst, based on their overall predictive power (Friedman in The Annals of Statistics 29 (5), 1189–1232, 2001; Hastie et al. 2009). Using a sample of 1115 US bankruptcy filings and 91 predictor variables, the study finds that non-traditional variables, such as ownership structure/concentration and CEO compensation are among the strongest predictors overall. The next best predictors are unscaled market and accounting variables that proxy for size effects. This is followed by market-price measures and financial ratios. The weakest predictors overall included macro-economic variables, analyst recommendations/forecasts and industry variables.     

Change of numeraire in the two-marginals martingale transport problem

In this paper, we apply change of numeraire techniques to the optimal transport approach for computing model-free prices of derivatives in a two-period setting. In particular, we consider the optimal transport plan constructed in Hobson and Klimmek (Finance Stoch. 19:189–214, 2015) as well as the one introduced in Beiglböck and Juillet (Ann. Probab. 44:42–106, 2016) and further studied in Henry-Labordère and Touzi (Finance Stoch. 20:635–668, 2016). We show that in the case of positive martingales, a suitable change of numeraire applied to Hobson and Klimmek (Finance Stoch. 19:189–214, 2015) exchanges forward start straddles of type I and type II, so that the optimal transport plan in the subhedging problems is the same for both types of options. Moreover, for Henry-Labordère and Touzi’s (Finance Stoch. 20:635–668, 2016) construction, the right-monotone transference plan can be viewed as a mirror coupling of its left counterpart under the change of numeraire.     

On the Price of Risk Under a Regime Switching CGMY Process

In this paper, we study option pricing under a regime-switching exponential Lévy model. Assuming that the coefficients are time-dependent and modulated by a finite state Markov chain, we generalise the work in Momeya and Morales (Method Comput Appl Probab, 2014, doi: 10.1007/s11009-014-9399-2), and Siu and Yang (Acta Mathe Appl Sin 2:369–388, 2009), that is, we use a pricing method based on the Esscher transform conditional on the information available on the Markov chain. We also carry out numerical analysis, to show the impact of the risk induced by the underlying Markov chain on the price of the option.     

Service quality in the private banking business

This paper examines the concept of service quality in private banking theoretically and empirically and identifies factors which contribute to service quality. A multidimensional and hierarchical model is developed based on the work of Rust and Oliver (in Service Quality, pp. 1–20, 1994) and Brady and Cronin (in J. Mark. 65(3):34–49, 2001). The model is then empirically tested among private banking providers with the partial least squares method. Furthermore, the developed model is compared to other approaches, including Grönroos (in Eur. J. Mark. 18(4):36–44, 1984). Another model for comparison excludes the indirect effects of Grönroos (in Eur. J. Mark. 18(4):36–44, 1984) and focuses on the direct effects on service quality. We can conclude that the model based on Rust and Oliver (in Service Quality, pp. 1–20, 1994) and Brady and Cronin (in J. Mark. 65(3):34–49, 2001) produces the best results and can best explain service quality in private banking. Finally, an analysis of various provider groups is conducted in order to identify differences between private banking providers in Germany, Switzerland, Austria and Liechtenstein and between providers with various minimum investment requirements.     

Business cycles,financial cycles and capital structure

We perform peridogram based cycle analysis of firm capital structure and find evidence that firms’ leverage is both persistent and cyclical. The cyclicality of leverage is supported by the trade-off, pecking order and market timing capital structure theories (Korajczyk and Levy in J Financ Econ 68:75–109, 2003; Bhamra et al. in Rev Financ Stud 23:645–703, 2010). Although market timing theory research supports persistence, previous literature dictates that the trade-off and pecking order theories may predict either persistent or mean reverting leverage. Our tests reject mean reversion in favor of persistent and cyclical leverage. We corroborate pecking order theory literature that predicts leverage is persistent. In these models, when firms’ investment spending is below earnings, leverage decreases. In addition, we examine whether firms change their capital structure as a result of business and financial cycles. Since financial cycles last longer than business cycles, financial cycles should have a long term effect on leverage. Our findings confirm the persistent leverage business cycle models that suggest firms change their capital structure due to financial and credit cycles (Jermann and Quadrini in Am Econ Rev 102:238–271, 2012; Azariadis et al. in Rev Econ Stud 83:1364–1405, 2016). We conclude that leverage is persistent due to the cyclicality of the financing decision.     

An explicit martingale version of the one-dimensional Brenier theorem

By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge–Kantorovich mass transport problem was introduced in (Beiglböck et al. in Finance Stoch. 17:477–501, 2013; Galichon et al. in Ann. Appl. Probab. 24:312–336, 2014). Further, by suitable adaptation of the notion of cyclical monotonicity, Beiglböck and Juillet (Ann. Probab. 44:42–106, 2016) obtained an extension of the one-dimensional Brenier theorem to the present martingale version. In this paper, we complement the previous work by extending the so-called Spence–Mirrlees condition to the case of martingale optimal transport. Under some technical conditions on the starting and the target measures, we provide an explicit characterization of the corresponding optimal martingale transference plans both for the lower and upper bounds. These explicit extremal probability measures coincide with the unique left- and right-monotone martingale transference plans introduced in (Beiglböck and Juillet in Ann. Probab. 44:42–106, 2016). Our approach relies on the (weak) duality result stated in (Beiglböck et al. in Finance Stoch. 17:477–501, 2013), and provides as a by-product an explicit expression for the corresponding optimal semi-static hedging strategies. We finally provide an extension to the multiple marginals case.     

Risk measures with the CxLS property

In the present contribution, we characterise law determined convex risk measures that have convex level sets at the level of distributions. By relaxing the assumptions in Weber (Math. Finance 16:419–441, 2006), we show that these risk measures can be identified with a class of generalised shortfall risk measures. As a direct consequence, we are able to extend the results in Ziegel (Math. Finance, 2014, http://onlinelibrary.wiley.com/doi/10.1111/mafi.12080/abstract) and Bellini and Bignozzi (Quant. Finance 15:725–733, 2014) on convex elicitable risk measures and confirm that expectiles are the only elicitable coherent risk measures. Further, we provide a simple characterisation of robustness for convex risk measures in terms of a weak notion of mixture continuity.     

Erratum to: Utility maximization in incomplete markets with random endowment

K. Larsen, M. Soner and G. ?itkovi? kindly pointed out to us an error in our paper (Cvitani? et al. in Finance Stoch. 5:259–272, 2001) which appeared in 2001 in this journal. They also provide an explicit counterexample in Larsen et al. (https://arxiv.org/abs/1702.02087, 2017).In Theorem 3.1 of Cvitani? et al. (Finance Stoch. 5:259–272, 2001), it was incorrectly claimed (among several other correct assertions) that the value function \(u(x)\) is continuously differentiable. The erroneous argument for this assertion is contained in Remark 4.2 of Cvitani? et al. (Finance Stoch. 5:259–272, 2001), where it was claimed that the dual value function \(v(y)\) is strictly concave. As the functions \(u\) and \(v\) are mutually conjugate, the continuous differentiability of \(u\) is equivalent to the strict convexity of \(v\). By the same token, in Remark 4.3 of Cvitani? et al. (Finance Stoch. 5:259–272, 2001), the assertion on the uniqueness of the element \(\hat{y}\) in the supergradient of \(u(x)\) is also incorrect.Similarly, the assertion in Theorem 3.1(ii) that \(\hat{y}\) and \(x\) are related via \(\hat{y}=u'(x)\) is incorrect. It should be replaced by the relation \(x=-v'(\hat{y})\) or, equivalently, by requiring that \(\hat{y}\) is in the supergradient of \(u(x)\).To the best of our knowledge, all the other statements in Cvitani? et al. (Finance Stoch. 5:259–272, 2001) are correct.As we believe that the counterexample in Larsen et al. (https://arxiv.org/abs/1702.02087, 2017) is beautiful and instructive in its own right, we take the opportunity to present it in some detail.     

Equilibrium leadership in tax competition models with capital ownership: a rejoinder

This paper reconciles two opposite results in the tax competition literature. Kempf and Rota-Graziosi (J Public Econ 94(9–10):768–776, 2010) and Hindriks and Nishimura (J Public Econ 121:66–68, 2015) have shown that the two Stackelberg outcomes prevail as the subgame perfect equilibria when capital is entirely owned by nonresidents. However, Ogawa (Int Tax Public Finance 20(3):474–484, 2013) has shown that the simultaneous-move outcome prevails when capital is entirely owned by residents. We develop a model in which capital ownership can vary freely between these two polar cases. We show that there exists a unique degree of residential capital ownership such that the equilibrium switches from the Stackelberg to the simultaneous-move outcomes. The chance for the simultaneous-move outcome to prevail increases with the extent of production asymmetry between regions. Partial ownership also induces a novel effect of tax leadership that we call the preference reversion effect.     

Audit firms face downward-sloping demand curves and the audit market is far from perfectly competitive

We discuss the discrete choice demand estimation methods applied by Guo et al. (2017) in the audit setting. We then review insights into audit market competition that demand estimation has already provided. We conclude that the audit market is far from perfectly competitive.     

Indirect tax reform and the specification of demand: the case of Ireland

This paper examines the sensitivity of marginal tax reform analysis to changes in the underlying demand system. In particular, we analyse the sensitivity of results from Ahmad and Stern’s (J Publ Econ 25(3):259–298, 1984) marginal tax reform model to different specifications of Deaton and Muellbauer’s (Am Econ Rev 70(3):312–326, 1980) Almost Ideal Demand System (AIDS) and Banks et al.’s (Rev Econ Stat 79(4):527–539, 1997) Quadratic AIDS. Using Irish Household Budget Survey data, we show that tax reform results exhibit a low degree of sensitivity to changes in the underlying demand system. An adjustment for a mass of observed zero-expenditures in the data for certain goods produces most sensitivity in the tax reform results. Even in these cases, many of the tax reform recommendations remain constant. Including demerit good arguments in the tax reform model can substantially alter the tax reform recommendations relating to demerit goods. Notably though, when we include these arguments in the tax reform model, the results are particularly insensitive to changes in the underlying demand system.     

The leverage effect puzzle: the case of European sovereign credit default swap market

One of the stylized facts about the behaviour of time series is that their volatility exhibits asymmetrical responses to good and bad news. In the case of stock markets, volatility seems to rise when the stock price decreases and fall when the stock price increases. This so-called “leverage effect” was first described by Black (Proceedings of the 1976 meeting of the business and economic statistics section, pp 177–181, 1976). The concept is not new and has already been comprehensively studied and implemented in many volatility models (GARCH and SV) in the form of an additional parameter in the volatility equation. However, there is no study or a theoretical explanation of the leverage effect in sovereign credit default swap spreads (hereinafter: sCDS). In this article, we discuss the possible behaviour of sCDS volatility and explain it by way of reference to the Prospect Theory by Kahneman and Tversky (Econometrica 47(2):263–292, 1979). We estimate a series of stochastic volatility models with the leverage effect, proposed by Yu (J Econom 127(2):165–178, 2005). In this model, the “leverage effect” is, in fact, the same as a coefficient of the correlation between the current return of an asset and its expected future volatility. We show that the effect does exist and differs across markets. As far as the safe European markets are concerned, the parameter is negative; in the case of extremely risky economies—it is positive. In markets of medium risk the effect varies depending on the relationship between the perceived risk and the value of the sCDS premium.     

The holdings markup behavior of mutual funds: evidence from an emerging market

This paper uncovers a seasonal mutual fund holdings markup pattern in Taiwan’s market. Specifically, we find that fund’s equity holdings jump up significantly at the quarter-ends and year-end while drop back immediately to the previous level in the following month. While the holdings markup pattern found in this paper may look similar to the price markup phenomenon found by Carhart et al. (J Finance 57:661–693, 2002), the mechanism used by fund managers in the performance inflation may be quite different. In specific, while Carhart et al. (J Finance 57:661–693, 2002) document that fund managers use the stocks currently held in their portfolio to mark up the fund performance, we find that fund managers in fact use both the stocks already held in their portfolio and the new stocks to mark up their holdings. Furthermore, Carhart et al. (J Finance 57:661–693, 2002) do not explicitly examine if there exists a holdings markup in addition to the price markup. In this study, we fill this gap by directly exploring the holdings markup behavior by the fund managers. We also identify the specific stock characteristics that fund managers prefer in their holdings markup. In specific, fund managers prefer to trade growth stocks, stocks with larger market capitalization, higher institutional ownership, higher quality of earnings, and stocks in the high-tech industry, to inflate the fund performance. We also find that fund managers tend to avoid stocks that are herded by other funds.     

A four-factor stochastic volatility model of commodity prices

The number of factors driving the uncertain dynamics of commodity prices has been a central consideration in financial literature. While the majority of empirical studies relies on the assumption that up to three factors are sufficient to explain all relevant uncertainty inherent in commodity spot, futures, and option prices, evidence from Trolle and Schwartz (Rev Financ Stud 22(11):4423–4461, 2009b) and Hughen (J Futures Mark 30(2):101–133, 2010) indicates a need for additional risk factors. In this article, we propose a four-factor maximal affine stochastic volatility model that allows for three independent sources of risk in the futures term structure and an additional, potentially unspanned stochastic volatility process. The model principally integrates the insights from Hughen (2010) and Tang (Quant Finance 12(5):781–790, 2012) and nests many well-known models in the literature. It can account for several stylized facts associated with commodity dynamics such as mean reversion to a stochastic level, stochastic volatility in the convenience yield, a time-varying correlation structure, and time-varying risk-premia. In-sample and out-of-sample tests indicate a superior model fit to futures and options data as well as lower hedging errors compared to three-factor benchmark models. The results also indicate that three factors are not sufficient to model the joint dynamics of futures and option prices accurately.     

Tukey’s transformational ladder for portfolio management

Over the past half-century, the empirical finance community has produced vast literature on the advantages of the equally weighted Standard and Poor (S&P 500) portfolio as well as the often overlooked disadvantages of the market capitalization weighted S&P 500’s portfolio (see Bloomfield et al. in J Financ Econ 5:201–218, 1977; DeMiguel et al. in Rev Financ Stud 22(5):1915–1953, 2009; Jacobs et al. in J Financ Mark 19:62–85, 2014; Treynor in Financ Anal J 61(5):65–69, 2005). However, portfolio allocation based on Tukey’s transformational ladder has, rather surprisingly, remained absent from the literature. In this work, we consider the S&P 500 portfolio over the 1958–2015 time horizon weighted by Tukey’s transformational ladder (Tukey in Exploratory data analysis, Addison-Wesley, Boston, 1977): \(1/x^2,\,\, 1/x,\,\, 1/\sqrt{x},\,\, \text {log}(x),\,\, \sqrt{x},\,\, x,\,\, \text {and} \,\, x^2\), where x is defined as the market capitalization weighted S&P 500 portfolio. Accounting for dividends and transaction fees, we find that the 1/\(x^2\) weighting strategy produces cumulative returns that significantly dominate all other portfolio returns, achieving a compound annual growth rate of 18% over the 1958–2015 horizon. Our story is furthered by a startling phenomenon: both the cumulative and annual returns of the \(1/x^2\) weighting strategy are superior to those of the 1 / x weighting strategy, which are in turn superior to those of the \(1/\sqrt{x}\) weighted portfolio, and so forth, ending with the \(x^2\) transformation, whose cumulative returns are the lowest of the seven transformations of Tukey’s transformational ladder. The order of cumulative returns precisely follows that of Tukey’s transformational ladder. To the best of our knowledge, we are the first to discover this phenomenon.