A new microstructure noise index

We introduce a new microstructure noise index for financial data. This index, the computation of which is based on the p-variations of the considered asset or rate at different time scales, can be interpreted in terms of Besov smoothness spaces. We study the behavior of our new index using empirical data. It gives rise to phenomena that a classical signature plot is unable to detect. In particular, with our data set, it enables us to separate the sampling frequencies into three zones: no microstructure noise for low frequencies, increasing microstructure noise from low to high frequencies, and some kind of additional regularity on the finest scales. We then investigate the index from a theoretical point of view, under various contexts of microstructure noise, trying to reproduce the facts observed on the data. We show that this can be partially done using models involving additive correlated errors or rounding error. Accurate reproduction seems to require either both kinds of error together or some unusual form of rounding error.     

A note on Wick products and the fractional Black-Scholes model

In some recent papers (Elliott and van der Hoek 2003; Hu and Øksendal 2003) a fractional Black-Scholes model has been proposed as an improvement of the classical Black-Scholes model (see also Benth 2003; Biagini et al. 2002; Biagini and Øksendal 2004). Common to these fractional Black-Scholes models is that the driving Brownian motion is replaced by a fractional Brownian motion and that the Itô integral is replaced by the Wick integral, and proofs have been presented that these fractional Black-Scholes models are free of arbitrage. These results on absence of arbitrage complelety contradict a number of earlier results in the literature which prove that the fractional Black-Scholes model (and related models) will in fact admit arbitrage. The objective of the present paper is to resolve this contradiction by pointing out that the definition of the self-financing trading strategies and/or the definition of the value of a portfolio used in the above papers does not have a reasonable economic interpretation, and thus that the results in these papers are not economically meaningful. In particular we show that in the framework of Elliott and van der Hoek 2003, a naive buy-and-hold strategy does not in general qualify as self-financing. We also show that in Hu and Øksendal 2003, a portfolio consisting of a positive number of shares of a stock with a positive price may, with positive probability, have a negative value.Received: August 2004, Mathematics Subject Classification (2000): 91B28, 60H05JEL Classification: G10Support of the first author from the Jan Wallander and Tom Hedelius foundation is gratefully acknowledged. The research of the second author is supported by the Swedish Research Council.     

A new closed-form formula for pricing European options under a skew Brownian motion

In this paper, we present a new pricing formula based on a modified Black–Scholes (B-S) model with the standard Brownian motion being replaced by a particular process constructed with a special type of skew Brownian motions. Although Corns and Satchell [2007. “Skew Brownian Motion and Pricing European Options.” The European Journal of Finance 13 (6): 523–544] have worked on this model, the results they obtained are incorrect. In this paper, not only do we identify precisely where the errors in Although Corns and Satchell [2007. “Skew Brownian Motion and Pricing European Options”. The European Journal of Finance 13 (6): 523–544] are, we also present a new closed-form pricing formula based on a newly proposed equivalent martingale measure, called ‘endogenous risk neutral measure’, by which only endogenous risks should and can be fully hedged. The newly derived option pricing formula takes the B-S formula as a special case and it does not induce any significant additional burden in terms of numerically computing option values, compared with the effort involved in computing the B-S formula.     

A response to commentaries on a theoretical model of stakeholder perceptions of a new financial reporting system

This is a response to questions raised by Kuruppu and Lehman (2016) and Thomson (2016) on Fontes, Rodrigues and Craig’s (2016) model of Stakeholder Perceptions of a New Financial Reporting System. We clarify some matters that arise from the commentators’ concerns about the intended contribution of the model, and its conceptual foundations. We also respond to concerns raised about the need to adopt a holistic and contextualized approach; provide further insights to the complex and dynamic nature of stakeholder perceptions and their formation; and elaborate on methodological assumptions underpinning the model. We argue that interpretative-based research offers an appropriate and challenging way to further improve and extend the model. We encourage researchers to adopt critical and interpretive-based methods to foster a reflective debate that will lead to improvements in the Stakeholder Perceptions model.     

Ruin time and aggregate claim amount up to ruin time for the perturbed risk process

We consider the classical Sparre-Andersen risk process perturbed by a Wiener process, and study the joint distribution of the ruin time and the aggregate claim amounts until ruin by determining its Laplace transform. This is first done when the claim amounts follow respectively an exponential/Phase-type distribution, in which case we also compute the distribution of recovery time and study the case of a barrier dividend. Then the general distribution is considered when ruin occurs by oscillation, in which case a renewal equation is derived.     

A note on the existence of unique equivalent martingale measures in a Markovian setting

Simple sufficient conditions for the existence of a unique equivalent martingale measure are provided. Furthermore, these conditions give us a handle on situations where an equivalent martingale measure cannot exist. The existence of a unique equivalent martingale measure is of relevance to problems in mathematical finance. Two examples of models for which the question of existence was unresolved are studied. By means of our results existence of a unique equivalent measure up to an explosion time is proved.     

A note on myopic loss aversion and the equity premium puzzle

In 1995, Benartzi and Thaler introduced the concept myopic loss aversion to explain the equity premium puzzle. They provided empirical evidence to support their arguments. Recently, Durand et al. criticized this empirical analysis. They propose an approach which not only rejects the significance of the earlier findings but also suggests a reversal of the original findings. In contrast to their approach, we implement a bootstrap approach and find results in line with the results of Benartzi and Thaler. We further show that the significance of the effect strongly depends on somewhat arbitrary assumptions about the length of data history.     

A note on the interaction effects of non-financial measures of performance

Using principal-agent analyses, the effect of the interactions between two non-financial measures of performance in an agent’s incentive compensation scheme is studied. The agent can allocate effort between “meeting output targets” and “getting output that needs no rework.” The principal trades off (1) a penalty for not meeting output targets, and (2) cost of reworking output that is defective when initially produced. In a compensation mechanism that includes incentives based on measures of output that needs no rework, as well as total output, it is shown that the agent may respond to an increased weight on output that needs no rework by reducing effort allocated towards it. This occurs when the increased weight on the output that needs no rework is accompanied by a sufficiently steep decrease in the weight on total output in the compensation mechanism, leading to a reduction of all effort, and all output. Numerical analyses and implications for the use of multiple measures of performance-based incentives are provided.     

Forward-looking portfolio selection with multivariate non-Gaussian models

In this study, we suggest a portfolio selection framework based on time series of stock log-returns, option-implied information, and multivariate non-Gaussian processes. We empirically assess a multivariate extension of the normal tempered stable (NTS) model and of the generalized hyperbolic (GH) one by implementing an estimation method that simultaneously calibrates the multivariate time series of log-returns and, for each margin, the univariate observed one-month implied volatility smile. To extract option-implied information, the connection between the historical measure P and the risk-neutral measure Q, needed to price options, is provided by the multivariate Esscher transform. The method is applied to fit a 50-dimensional series of stock returns, to evaluate widely known portfolio risk measures and to perform a forward-looking portfolio selection analysis. The proposed models are able to produce asymmetries, heavy tails, both linear and non-linear dependence and, to calibrate them, there is no need for liquid multivariate derivative quotes.     

A note on robust testing by indexing the parameter space

1. Introduction

A preliminary test is sometimes performed to obtain a simple model with few parameters. This should ostensibly result in a better performance in the subsequent treatment of the observations. For obvious reasons such a procedure is questionable. It is felt that one should keep to the original a priori model with the original parameter vector θ. In this note a third method is proposed. Adhere to original parameters θ, but concentrate attention on an index φ(θ) which sums up some essential features of the model. (This principle has been advocated by Goldstein (1981).)     

A note on some properties of the hypergeometric function with the last argument unity

Abstract

In this note some interrelationships between, and inequalities involving, the gamma and beta functions and the hyper geometric function with the last argument unity are established.     

地方政府债务违约的博弈理论分析

伴随着财政分权,世界范围内,地方公共债务的日渐膨胀以及拖欠或违约已不是个别现象, 情况严重的甚至引发了一国宏观经济的不稳定。但是,要全面考察地方政府债务违约和中央政府救助动机绝非易事。本文试图梳理解释地方政府债务违约的博弈理论,分析地方债务违约博弈中,双方的动机,以探索控制地方政府债务违约的制度、经济、政治等方面的基本因素。     

Ruin probability at a given time for a model with liabilities of the fractional Brownian motion type: A partial differential equation approach

In this paper we study the ruin probability at a given time for liabilities of diffusion type, driven by fractional Brownian motion with Hurst exponent in the range (0.5, 1). Using fractional Itô calculus we derive a partial differential equation the solution of which provides the ruin probability. An analytical solution is found for this equation and the results obtained by this approach are compared with the results obtained by Monte-Carlo simulation.     

A note on deficit analysis in dependency models involving Coxian claim amounts

In this paper, we consider a fairly large class of dependent Sparre Andersen risk models where the claim sizes belong to the class of Coxian distributions. We analyze the Gerber–Shiu discounted penalty function when the penalty function depends on the deficit at ruin. We show that the system of equations needed to solve for this quantity is surprisingly simple. Various applications of this result are also considered.     

A note on takeover success prediction

A takeover success prediction model attempts to use information that is publicly available at the time of the announcement in order to predict the probability that a takeover attempt will succeed. This paper develops a takeover success prediction model by comparing two techniques: the traditional logistic regression model and the artificial neural network technology. To alleviate the problem of bias from the sampling variation, we validate our results through re-sampling. Our empirical results indicate that 1). Arbitrage spread, target resistance, deal structure and transaction size are the dominating factors that have impacts on the outcome of a takeover attempt. 2). Neural network model outperforms logistic regression in predicting failed takeover attempts and performs as well as logistic regression in predicting successful takeover attempts.     

A note on the forward measure

For a Markov process , the forward measure over the time interval is defined by the Radon-Nikodym derivative , where is a given non-negative function and is the normalizing constant. In this paper, the law of under the forward measure is identified when is a diffusion process or, more generally, a continuous-path Markov process.     

The Valuation of Executive Stock Options in an Intensity-Based Framework

This paper presents a general intensity-based framework to value executive stock options (ESOs). It builds upon the recent advances in the credit risk modeling arena. The early exercise or forfeiture due to voluntary or involuntary employment termination and the early exercise due to the executive's desire for liquidity or diversification are modeled as an exogenous point process with random intensity dependent on the stock price.Two analytically tractable specifications are given where the ESO value, expected time of exercise or forfeiture, and the expected stock price at the time of exercise or forfeiture are calculated in closed-form.     

The institutional determinants of IPO firm prospectus length in a developing context: A research note

This study focuses on the impact of institutional quality on the amount of disclosure in IPO firms listing prospectuses using the six well established World Bank Governance indices, namely corruption control, government effectiveness in promotion of private sector development, political stability and absence from terrorism, regulatory quality, rule of law and lastly democratic voice and accountability. Using a unique hand-collected sample of 165 IPO firms from across Africa from 2000 to 2011 I find evidence that enhanced rule of law and regulatory quality impact on the amount of disclosure by firms, reflected in length of IPO listings prospectuses. In addition I find evidence that founder-led entrepreneurial firms are more likely to disclose more alongside firms in extractive and technology industries that rely on local stock exchanges as a source of external finance. In contrast IPO firms that have significant long term foreign partners or are subsidiaries of foreign Multinational Enterprises are likely to disclose less than other types of firm underscoring their apathy to domestic investors and relative lack of dependence on indigenous stock markets as a viable source of external finance.