The bias in Black-Scholes/Black implied volatility: An analysis of equity and energy markets

In this paper we examine the extent of the bias between Black and Scholes (1973)/Black (1976) implied volatility and realized term volatility in the equity and energy markets. Explicitly modeling a market price of volatility risk, we extend previous work by demonstrating that Black-Scholes is an upward-biased predictor of future realized volatility in S&P 500/S&P 100 stock-market indices. Turning to the Black options-on-futures formula, we apply our methodology to options on energy contracts, a market in which crises are characterized by a positive correlation between price-returns and volatilities: After controlling for both term-structure and seasonality effects, our theoretical and empirical findings suggest a similar upward bias in the volatility implied in energy options contracts. We show the bias in both Black-Scholes/Black implied volatilities to be related to a negative market price of volatility risk. JEL Classification G12 · G13     

Capital Allocation Using the Bootstrap

Abstract

This paper investigates the use of the bootstrap in capital allocation. In particular, for the distortion risk measure (DRM) class, we show that the exact bootstrap estimate is available in analytic form for the allocated capital. We then theoretically justify the bootstrap bias correction for the allocated capital induced from the concave DRM when the conditional mean function is strictly monotone. A numerical example shows a tradeoff exists between the bias reduction and variance increase in bootstrapping the allocated capital. However, unlike the aggregate capital case, the variance increase of the bias-corrected allocated capital estimate substantially outweighs the benefit of bias correction, making the bootstrap bias correction at the allocated capital level not as useful. Overall, the exact bootstrap without bias correction offers an efficient method for determining allocation over the ordinary resampling bootstrap estimate and the empirical counterpart.     

Anyone for Tennis (Betting)?

Abstract

The most robust anomaly noted in the literature on wagering markets is (positive) longshot bias: over a period of 50 years, it has been well documented in horse betting that higher expected returns accrue to short- than to long-odds bets. However, a few examples of betting markets with zero or negative bias have been found, for example in certain American sports. The understanding of longshot bias is likely to be informed by comparing and contrasting conditions in markets displaying positive, zero, and negative bias but, to date, relatively few markets have been examined. This paper employs a large data set on professional men's tennis matches and a new econometric approach to the estimation of the relationship between returns and odds. It finds positive bias throughout the range of odds. It discusses this finding in the context of the debate on why biases exist and persist in wagering markets, focusing particularly on bettors’ attitudes towards risk and skewness.     

Contracting with Present-Biased Consumers in Insurance Markets

Present bias challenges consumers with self-control problems when they implement precautionary efforts in insurance markets. To explore how rational insurance companies respond to this bias, this paper analyzes a contract design problem in a monopolistic insurance market with ex ante moral hazard. We consider two types of consumers with this bias: the “naifs”, who do not foresee the present bias and make decisions in a myopic way, and the “sophisticates”, who foresee the bias and incorporate it in the decision process. Relative to the benchmark case where consumers are time-consistent, we show that (i) present bias reduces the monopoly profit, regardless of the consumer type; (ii) present bias can either reduce or increase the coverage of the profit-maximizing insurance contract depending on the extent of the bias; and (iii) when present bias is severe, the insurance company can profitably exploit naifs but not sophisticates. These results still hold when consumers are heterogeneous and their types are unknown to the insurance company.     

Value-at-risk in a market subject to regime switching

Many empirical researches report that value-at-risk (VaR) measures understate the actual 1% quantile, while for Inui, K., Kijima, M. and Kitano, A., VaR is subject to a significant positive bias. Stat. Probab. Lett., 2005, 72, 299–311. proved that VaR measures overstate significantly when historical simulation VaR is applied to fat-tail distributions. This paper resolves the puzzle by developing a regime switching model to estimate portfolio VaR. It is shown that our model is able to correct the underestimation problem of risk.     

Gibbs posterior inference on value-at-risk

ABSTRACT

Accurate estimation of value-at-risk (VaR) and assessment of associated uncertainty is crucial for both insurers and regulators, particularly in Europe. Existing approaches link data and VaR indirectly by first linking data to the parameter of a probability model, and then expressing VaR as a function of that parameter. This indirect approach exposes the insurer to model misspecification bias or estimation inefficiency, depending on whether the parameter is finite- or infinite-dimensional. In this paper, we link data and VaR directly via what we call a discrepancy function, and this leads naturally to a Gibbs posterior distribution for VaR that does not suffer from the aforementioned biases and inefficiencies. Asymptotic consistency and root-n concentration rate of the Gibbs posterior are established, and simulations highlight its superior finite-sample performance compared to other approaches.     

Random matrix models for datasets with fixed time horizons

This paper examines the use of random matrix theory as it has been applied to model large financial datasets, especially for the purpose of estimating the bias inherent in Mean-Variance portfolio allocation when a sample covariance matrix is substituted for the true underlying covariance. Such problems were observed and modeled in the seminal work of Laloux et al. [Noise dressing of financial correlation matrices. Phys. Rev. Lett., 1999, 83, 1467] and rigorously proved by Bai et al. [Enhancement of the applicability of Markowitz's portfolio optimization by utilizing random matrix theory. Math. Finance, 2009, 19, 639–667] under minimal assumptions. If the returns on assets to be held in the portfolio are assumed independent and stationary, then these results are universal in that they do not depend on the precise distribution of returns. This universality has been somewhat misrepresented in the literature, however, as asymptotic results require that an arbitrarily long time horizon be available before such predictions necessarily become accurate. In order to reconcile these models with the highly non-Gaussian returns observed in real financial data, a new ensemble of random rectangular matrices is introduced, modeled on the observations of independent Lévy processes over a fixed time horizon.     

New development: Scarcity,policy gambles,and ‘one-shot bias’—training civil servants to speak truth to power

ABSTRACT

Allocating scarce resources to meet policy objectives incurs opportunity costs. A vital element of ‘speaking truth to power’ thus involves officials advising ministers on the opportunity costs of high-risk ‘pet projects’. In democracies, the brevity of ministerial office can produce ‘one-shot bias’—radical policy-making that deploys ministers’ time-limited powers to the full, yet risks producing significant opportunity costs for public service organizations. Examples include the UK’s recent social security, healthcare and European policies. Training in the economics of organization, development of new techniques for coping with uncertainty in opportunity-cost estimates, and stronger incentives for decision-makers to consider ‘benefits foregone’ by their actions could all provide greater protection against the downsides of one-shot bias.     

Insider trading,growth opportunities and the market reaction to new financing announcements*

Abstract

This paper explores the profitability of momentum strategies, by investigating if a momentum strategy is superior to a benchmark model once the effects of data-snooping have been accounted for. Two data sets are considered. The first set of data consists of US stocks and the second one consists of Swedish stocks. For the US data strong evidence is found of a momentum effect and hence the hypothesis of weak market efficiency is rejected. Splitting the sample in two parts, it is found that the overall significance is driven by events in the earlier part of the sample. The results for the Swedish data indicate that momentum strategies based on individual stocks generate significant profits. A very weak or no momentum effect can be found when stocks are sorted into portfolios. Finally, and perhaps most importantly, results show that data-snooping bias can be very substantial. Neglecting the problem would lead to very different conclusions.     

Estimating default barriers from market information

Brockman and Turtle [J. Finan. Econ., 2003, 67, 511–529] develop a barrier option framework to show that default barriers are significantly positive. Most implied barriers are typically larger than the book value of corporate liabilities. We show theoretically and empirically that this result is biased due to the approximation of the market value of corporate assets by the sum of the market value of equity and the book value of liabilities. This approximation leads to a significant overestimation of the default barrier. To eliminate this bias, we propose a maximum likelihood (ML) estimation approach to estimate the asset values, asset volatilities, and default barriers. The proposed framework is applied to empirically examine the default barriers of a large sample of industrial firms. This paper documents that default barriers are positive, but not very significant. In our sample, most of the estimated barriers are lower than the book values of corporate liabilities. In addition to the problem with the default barriers, we find significant biases on the estimation of the asset value and the asset volatility of Brockman and Turtle.     

Dynamic Fund Protection

Abstract

Dynamic fund protection provides an investor with a floor level of protection during the investment period. This feature generalizes the concept of a put option, which provides only a floor value at a particular time. The dynamic protection feature ensures that the fund value is upgraded if it ever falls below a certain threshold level. Gerber and Pafumi (2000) have recently derived a closed-form expression for the price of this protection when the basic portfolio follows geometric Brownian motion. In this paper we examine the pricing of this feature under the constant elasticity of variance process. Two approaches are used to obtain numerical results. First, we show how to extend the basic Monte Carlo approach to handle the particular features of dynamic protection. When a discrete-time simulation approach is used to value a derivative that is subject to continuous monitoring, there is a bias. We show how to remove this bias. Second, a partial differential equation approach is used to price dynamic protection. We demonstrate that the price of the dynamic protection is sensitive to the investment assumptions. We also discuss a discrete time modification of the dynamic protection feature that is suitable for practical implementation. The paper deals just with pricing and does not consider the important question of reserving for these contracts.     

Accrual mispricing: Evidence from European sovereign debt crisis

PurposeThis paper examines the accrual anomaly on the European market and the impact of the financial crisis on its dynamics.Design/methodology/approachUsing a sample of public European firms, during the period 2005-2016, this paper follows Sloan (1996) seminal work and measures accruals as Dechow, Sloan and Sweeney (1995).FindingsThere is no evidence that accrual anomaly persists on European markets. The study shows that, contrary to previous research, investors are not underweighting the accrual component of earnings and that accruals are not a good predictor of future stock returns.Research limitations/implicationsOur study has two limitations. First, due to the lack of data, the original sample was reduced to about one third. Second, results must be interpreted carefully since the sample period may be seen as an outlier case attributed to the crisis. Research on future years may unveil a conclusion on this.Practical implicationsResults suggest that transaction costs and idiosyncratic risk are no longer a barrier to investors. Results also point toward a possible new outcome in investor´s behaviour during crisis. Economically, given the lower returns that can be obtained on today markets, it makes sense that investors may reduce their risk aversion levels to get more returns.Originality/valueThis study contributes to the ongoing debate about accruals anomaly and market efficiency. To the best of our knowledge, it provides an original contribution to the literature by framing the accrual anomaly during the European debt crisis.     

No-arbitrage bounds for the forward smile given marginals

We explore the robust replication of forward-start straddles given quoted (Call and Put options) market data. One approach to this problem classically follows semi-infinite linear programming arguments, and we propose a discretisation scheme to reduce its dimensionality and hence its complexity. Alternatively, one can consider the dual problem, consisting in finding optimal martingale measures under which the upper and the lower bounds are attained. Semi-analytical solutions to this dual problem were proposed by Hobson and Klimmek [Financ. Stochastics, 2015, 19, 189–214] and by Hobson and Neuberger [Math. Financ., 2012, 22, 31–56]. We recast this dual approach as a finite-dimensional linear program, and reconcile numerically, in the Black–Scholes and in the Heston model, the two approaches.     

The impact of monetary policy on the financing behaviour of firms in the Euro area and the UK

Abstract

According to the ‘broad credit view’ bank-dependent firms are more strongly affected by monetary contractions than firms with access to non-bank forms of external finance. Within the credit view the bank lending channel focuses on the special role of bank loans, and predicts that monetary contractions reduce loan supply to firms facing information problems. However, the ‘relationship lending channel’ argues that, especially in bank-based economies, bank-dependent firms have close ties with banks, which may reduce the sensitivity of their use of bank debt to monetary shocks. The sensitivity of corporate debt structures to changes in the monetary policy stance is analysed using a sample of 22,000 firms in the Euro area and the UK. Evidence is found for the credit view, the relationship lending channel, but not for the bank lending channel.     

The challenges of longitudinal surveys in the flood risk domain

Abstract

There has been much research regarding the perceptions, preferences, behaviour, and responses of people exposed to flooding and other natural hazards. Cross-sectional surveys have been the predominant method applied in such research. While cross-sectional data can provide a snapshot of a respondent’s behaviour and perceptions, it cannot be assumed that the respondent’s perceptions are constant over time. As a result, many important research questions relating to dynamic processes, such as changes in risk perceptions, adaptation behaviour, and resilience cannot be fully addressed by cross-sectional surveys. To overcome these shortcomings, there has been a call for developing longitudinal (or panel) datasets in research on natural hazards, vulnerabilities, and risks. However, experiences with implementing longitudinal surveys in the flood risk domain (FRD), which pose distinct methodological challenges, are largely lacking. The key problems are sample recruitment, attrition rate, and attrition bias. We present a review of the few existing longitudinal surveys in the FRD. In addition, we investigate the potential attrition bias and attrition rates in a panel dataset of flood-affected households in Germany. We find little potential for attrition bias to occur. High attrition rates across longitudinal survey waves are the larger concern. A high attrition rate rapidly depletes the longitudinal sample. To overcome high attrition, longitudinal data should be collected as part of a multisector partnership to allow for sufficient resources to implement sample retention strategies. If flood-specific panels are developed, different sample retention strategies should be applied and evaluated in future research to understand how much-needed longitudinal surveying techniques can be successfully applied to the study of individuals threatened by flooding.     

Corporate social responsibility reports: topic analysis and big data approach

ABSTRACT

This paper performs topic modeling using all publicly available CSR (Corporate Social Responsibility) reports for all constituent firms of the major stock market indices of 15 industrialized countries included in MSCI Europe for the sample period from 1999 to 2016. Our text mining results and LDA analyses indicate that ‘employees safety’, ‘employees training support’, ‘carbon emission’, ‘human right’, ‘efficient power’, and ‘healthcare medicines’ are the common topics reported by publicly listed companies in Europe and the UK. There is a clear sector bias with industrial firms emphasizing ‘employee safety’, Utilities concentrating on ‘efficient power’ while consumer discretionary and consumer staples highlighting ‘food waste’ and ‘food packaging.’ To produce these results, we used a battery of python code to organize the hundreds of reports downloaded from Bloomberg and the internet, the latest R-algorithm to estimate LDA (Latent Dirichlet Allocation) model and the LDAvis interactive tool to visualize and refine the LDA model.     

The home bias is here to stay

Over the last 15 years, dramatically decreasing foreign investment costs have not reduced the home bias. We show that the home bias induced by a given cost is proportional to the factor ρ/(1 − ρ), where ρ is the average correlation between markets. This factor is very sensitive to the correlation, especially when the correlation is high. Empirically, correlations have been steadily increasing from 0.4 in the 90’s to about 0.9 today. Thus, the decreasing extra costs are increasingly magnified, explaining the persistence of the home bias, and predicting its continuation.     

A Hermite-spline model of post-retirement mortality

ABSTRACT

We present a model for post-retirement mortality where differentials automatically reduce with increasing age, but without the fitted mortality rates for subgroups crossing over. Selection effects are catered for, as are age-modulated time trends and seasonal variation in mortality. Central to the model are Hermite splines, which permit parsimonious modelling of complex risk factors in even modest-sized portfolios. The model is therefore suitable for the stand-alone analysis of experience data for reinsurance, bulk annuities and longevity swaps. We also illustrate the contrast between the statistical significance of a risk factor and its financial significance and discuss reasons why one might include risk factors like season that are not directly financially significant.     

Does Government Subsidy Affect Firm Survival? Evidence from Chinese Manufacturing Firms

ABSTRACT

This article applies a matching approach to deal with the selection bias and use the complementary log-log model to analyze the impacts of subsidy on Chinese manufacturing firms’ survival from 1998 to 2007. Our empirical results show that government subsidies significantly decrease the likelihood of firm exit. However, the effect decreases as the level of subsidies increases for private and foreign firms, but displays a nonlinear relationship across subsidy levels for SOEs. We also show the effects vary across the levels of institutional quality measured by the prevalence of rent seeking and government intervention. Further results suggest that the potential channels include increased investment in intangible and fixed assets as well as enhanced profitability.     

Public and private funding in new urban public transport

Pressures to reduce urban traffic pollution in the UK have not yet resulted in new policies to provide attractive alternatives to the private car. With growing pressure on public sector investment funds, this article considers ways in which the private sector could work in partnership with the public sector to create new light rail systems.