Laws of large numbers for Hayashi–Yoshida-type functionals

The main object in the statistical analysis of high-frequency financial data are sums of functionals of increments of stochastic processes, and statistical inference is based on the asymptotic behaviour of these sums as the mesh of the observation times tends to zero. Inspired by the famous Hayashi–Yoshida estimator for the quadratic covariation based on two asynchronously observed stochastic processes, we investigate similar sums for general functionals. We find that our results differ from corresponding results for synchronous observations, a case which has been well studied in the literature, and we observe that the asymptotic behaviour in the setting of asynchronous observations is not only determined by the nature of the functional, but also depends crucially on the asymptotics of the observation scheme. Several examples are discussed, including the case of \(f(x_{1},x_{2}) = |x_{1}|^{p_{1}} |x_{2}|^{p_{2}}\) which has various applications in empirical finance.

     

An enlargement of filtration formula with applications to multiple non-ordered default times

In this work, for a reference filtration \(\mathbb {F}\), we develop a method for computing the semimartingale decomposition of \(\mathbb {F}\)-martingales in a specific type of enlargement of \(\mathbb {F}\). As an application, we study the progressive enlargement of \(\mathbb {F}\) with a sequence of non-ordered default times and show how to deduce results concerning the first-to-default, \(k\)th-to-default, k-out-of-n-to-default or all-to-default events. In particular, using this method, we compute explicitly the semimartingale decomposition of \(\mathbb {F}\)-martingales under the absolute continuity condition of Jacod.     

The exact Taylor formula of the implied volatility

In a model driven by a multidimensional local diffusion, we study the behavior of the implied volatility \({\sigma}\) and its derivatives with respect to log-strike \(k\) and maturity \(T\) near expiry and at the money. We recover explicit limits of the derivatives \({\partial_{T}^{q}} \partial_{k}^{m} \sigma\) for \((T,x-k)\) approaching the origin within the parabolic region \(|x-k|\leq\lambda\sqrt{T}\), with \(x\) denoting the spot log-price of the underlying asset and where \(\lambda\) is a positive and arbitrarily large constant. Such limits yield the exact Taylor formula for the implied volatility within the parabola \(|x-k|\leq\lambda\sqrt{T}\). In order to include important models of interest in mathematical finance, e.g. Heston, CEV, SABR, the analysis is carried out under the weak assumption that the infinitesimal generator of the diffusion is only locally elliptic.     

Market completion with derivative securities

Let \(S^{F}\) be a ?-martingale representing the price of a primitive asset in an incomplete market framework. We present easily verifiable conditions on the model coefficients which guarantee the completeness of the market in which in addition to the primitive asset, one may also trade a derivative contract \(S^{B}\). Both \(S^{F}\) and \(S^{B}\) are defined in terms of the solution \(X\) to a two-dimensional stochastic differential equation: \(S^{F}_{t} = f(X_{t})\) and \(S^{B}_{t}:=\mathbb{E}[g(X_{1}) | \mathcal{F}_{t}]\). From a purely mathematical point of view, we prove that every local martingale under ? can be represented as a stochastic integral with respect to the ?-martingale \(S :=(S^{F}, S^{B})\). Notably, in contrast to recent results on the endogenous completeness of equilibria markets, our conditions allow the Jacobian matrix of \((f,g)\) to be singular everywhere on \(\mathbb{R}^{2}\). Hence they cover as a special case the prominent example of a stochastic volatility model being completed with a European call (or put) option.     

Pricing a contingent claim liability with transaction costs using asymptotic analysis for optimal investment

We price a contingent claim liability (claim for short) using a utility indifference argument. We consider an agent with exponential utility, who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of a proportional transaction cost ε>0 in two cases: with and without a claim. Using the heuristic computations of Whalley and Wilmott (Math. Finance 7:307–324, 1997), under suitable technical conditions, we provide a rigorous derivation of the asymptotic expansion of the value function in powers of \(\varepsilon^{\frac{1}{3}}\) in both cases with and without a claim. Additionally, using the utility indifference method, we derive the price of the claim at the leading order of \(\varepsilon^{\frac{2}{3}}\) . In both cases, we also obtain a “nearly optimal” strategy, whose expected utility asymptotically matches the leading terms of the value function. We also present an example of how this methodology can be used to price more exotic barrier-type contingent claims.     

‘It is all about getting the volumes down’. Organizational framings of risk in relation to waste,waste management and temporality

Abstract

Drawing on an ethnographic fieldwork at a waste facility site in the northern parts of Sweden, this article investigates organizational framings of risk (Hutter and Power 2005 Hutter, B., and M. Power. 2005. “Organizational encounters with risk: An introduction.” In Organizational Encounters with Risk, edited by B. Hutter and M. Power, 1–32. Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo: Cambridge University Press.[Crossref] , [Google Scholar]) in relation to waste and practices of waste management, employing the concept of temporality. The suggestion is that organizational framings of risk, as it contributes to steering the risk perception of the employees, also cater to a particular temporal register. In relation to the purposes of this article, the risks that my informants mentioned and/or perceived – as part of a particular organizational framework – were most often seen in terms of situated inconveniences and hazards that required technical, and logistic solutions. While this enabled them to take action, it also contributed to bounding risk and risk perception to a particular temporal register, intimately linked to what Barbara Adam (1998 Adam, B. 1998. Timescapes of Modernity: The Environment and Invisible Hazards. London and New York: Routledge. [Google Scholar]) refers to as the logics of industrial time. The logics of industrial time also suffuse formulations of current environmental policies and waste management plans, on a national as well as on an EU level where waste is seen primarily as a resource that continuously needs to be invented anew. As such, the logics of industrial time follow closely the beat of market fluctuations. Talking to representatives for the current waste facility site and observing some of their daily activities, potential risks with waste and practices of waste management were often weighed against other factors such as effectiveness, swiftness, and economic profits or losses: factors that also corresponded to short-time temporalities. While this reasoning, at first seemed to outperform any notion of risk, it actually conformed to the risks acknowledged by the organizational setting of which my informants were part.     

New development: Integration of budget and governmental accounting in Mexican states

ABSTRACT

Mexico recently introduced an accounting–budgeting framework compatible with the International Public Sector Accounting Standards (IPSAS). This article discusses the implementation of this framework, including the harmonization of information for the functional, administrative and economic budget categories for all Mexican states and for Mexico City. The author analysed public accounts and budgets prepared under the framework’s information requirements, as well as assessing the harmonization of accounts between the local, state and national levels of government. The results show an increase in both the amount and the harmonization of the public expenditure information being reported. This paper contributes to the literature of harmonization between financial reporting and budgeting processes (Dabbicco, G., & Mattei, G. (2020 Dabbicco, G. , & Mattei, G. (2020). The reconciliation of budgeting with financial reporting: A comparative study of Italy and the UK. Public Money & Management , 1–11. doi: 10.1080/09540962.2019.1708059 [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The reconciliation of budgeting with financial reporting: A comparative study of Italy and the UK. Public Money & Management, 1–11).     

Risk bounds for factor models

Recent literature has investigated the risk aggregation of a portfolio \(X=(X_{i})_{1\leq i\leq n}\) under the sole assumption that the marginal distributions of the risks \(X_{i} \) are specified, but not their dependence structure. There exists a range of possible values for any risk measure of \(S=\sum_{i=1}^{n}X_{i}\), and the dependence uncertainty spread, as measured by the difference between the upper and the lower bound on these values, is typically very wide. Obtaining bounds that are more practically useful requires additional information on dependence.Here, we study a partially specified factor model in which each risk \(X_{i}\) has a known joint distribution with the common risk factor \(Z\), but we dispense with the conditional independence assumption that is typically made in fully specified factor models. We derive easy-to-compute bounds on risk measures such as Value-at-Risk (\(\mathrm{VaR}\)) and law-invariant convex risk measures (e.g. Tail Value-at-Risk (\(\mathrm{TVaR}\))) and demonstrate their asymptotic sharpness. We show that the dependence uncertainty spread is typically reduced substantially and that, contrary to the case in which only marginal information is used, it is not necessarily larger for \(\mathrm{VaR}\) than for \(\mathrm{TVaR}\).     

Risk can be good for self-esteem: beyond self-determination theory

Abstract

Despite many decades of research that has highlighted all risk-taking sport activities as a means to satisfy sensation seeking needs (e.g., Zuckerman 1979 Zuckerman, M. 1979. Sensation Seeking: Beyond the Optimal Level of Arousal. Cambridge, UK: Cambridge University Press. [Google Scholar]), recent research has challenged that view and has revealed that some high-risk activities provide opportunities for agentic emotion regulation during participation, and are not driven by sensation-seeking needs (e.g., Barlow, Woodman, and Hardy 2013 Barlow, M., T. Woodman, and L. Hardy. 2013. “Great Expectations: Different High-Risk Activities Satisfy Different Motives.” Journal of Personality & Social Psychology 105: 458–475. doi:10.1037/a0033542.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Participation in high-risk sports is also associated with increased self-esteem (e.g., A?çi, Demirhan, and Dinç 2007 A?çi, F. H., G. Demirhan, and S. C. Dinç. 2007. “Psychological Profile of Turkish Rock Climbers: An Examination of Climbing Experience and Route Difficulty.” Perceptual and Motor Skills 104 (3): 892–900. doi:10.2466/pms.104.3.892-900.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). The aim of the present study was to investigate the link between the agentic and emotion regulation benefits of specific high-risk activities and any associated self-esteem benefits. We hypothesized that the emotion regulation and agency experiences in high-risk physical activities would mirror the elevated self-esteem derived from these activities. We examined high-risk activity (n?=?84), low-risk activity (n?=?65), and control (n?=?45) groups and found that the experience of agentic emotion regulation was greater during participation for high-risk sport participants. High-risk sport participants also had less post-activity difficulty with emotion regulation and higher self-esteem. This study provides the first support that activities that require greater agentic emotion regulation during participation also lead to elevated self-esteem. Basic psychological needs satisfaction did not account for the differences between groups, suggesting that people have other needs (e.g., the need to self-regulate) that are not incorporated into self-determination theory.     

Learning lessons: how to practice nudging around the world

Abstract

The aim of this article is to cover three things: (1) to introduce the context behind why a report prepared by the Organisation for Economic Co-operation and Development (OECD) in 2017 would be of such importance to researchers in various academic disciplines and public policy, (2) to present the details of a simple classification system that was applied to all 111 case studies of behavioural interventions (better known as nudges) referred to in the OECD (2017a OECD. 2017a. Behavioural Insights and Public Policy Lessons from Around the World.1-408 pp. OeCD Publishing. https://read.oecd-ilibrary.org/governance/behavioural-insights-and-public-policy_9789264270480-en. doi:10.1787/9789264270480-en.[Crossref] , [Google Scholar]) report, and (3) to discuss what needs to be done to help advance practitioners’ pursuit of effective behavioural interventions. This article aims to highlight the importance of accurately cataloguing the types of behavioural interventions that have been trialled/implemented across the world. By adopting an agreed classification system, researchers and practitioners can benefit from knowing what can work, and where it can work, as well as what does not work, in order to be better armed when considering the use of behavioural interventions to solve social policy issues.     

Turbo warrants under stochastic volatility

Turbo warrants have experienced huge growth since they first appeared in late 2001. In some European countries, buying and selling turbo warrants constitutes 50% of all derivative trading nowadays. In Asia, the Hong Kong Exchange and Clearing Limited (HKEx) introduced the callable bull/bear contracts, which are essentially turbo warrants, to the market in 2006. Turbo warrants are special types of barrier options in which the rebate is calculated as another exotic option. It is commonly believed that turbo warrants are less sensitive to the change in volatility of the underlying asset. Eriksson (2005 Eriksson, J. 2005. Explicit pricing formulas forturbo warrants. Uppsala Dissertation in Mathematics, 45 [Google Scholar]) has considered the pricing of turbo warrants under the Black–Scholes model. However, the pricing and characteristics of turbo warrants under stochastic volatility are not known. This paper investigates the valuation of turbo warrants considered by Eriksson (2005 Eriksson, J. 2005. Explicit pricing formulas forturbo warrants. Uppsala Dissertation in Mathematics, 45 [Google Scholar]), but extends the analysis to the CEV, the fast mean-reverting stochastic volatility and the two time-scale volatility models. We obtain analytical solutions for turbo warrants under the aforementioned models. This enables us to examine the sensitivity of turbo warrants to the implied volatility surface.     

No arbitrage of the first kind and local martingale numéraires

A supermartingale deflator (resp. local martingale deflator) multiplicatively transforms nonnegative wealth processes into supermartingales (resp. local martingales). A supermartingale numéraire (resp. local martingale numéraire) is a wealth process whose reciprocal is a supermartingale deflator (resp. local martingale deflator). It has been established in previous works that absence of arbitrage of the first kind (\(\mbox{NA}_{1}\)) is equivalent to the existence of the (unique) supermartingale numéraire, and further equivalent to the existence of a strictly positive local martingale deflator; however, under \(\mbox{NA}_{1}\), a local martingale numéraire may fail to exist. In this work, we establish that under \(\mbox{NA}_{1}\), a supermartingale numéraire under the original probability \(P\) becomes a local martingale numéraire for equivalent probabilities arbitrarily close to \(P\) in the total variation distance.     

New solvable stochastic volatility models for pricing volatility derivatives

In this paper we discuss a new approach to extend a class of solvable stochastic volatility models (SVM). Usually, classical SVM adopt a CEV process for instantaneous variance where the CEV parameter γ takes just few values: 0—the Ornstein–Uhlenbeck process, 1/2—the Heston (or square root) process, 1—GARCH, and 3/2—the 3/2 model. Some other models, e.g. with γ = 2 were discovered in Henry-Labordére (Analysis, geometry, and modeling in finance: advanced methods in option pricing. Chapman & Hall/CRC Financial Mathematics Series, London, 2009) by making connection between stochastic volatility and solvable diffusion processes in quantum mechanics. In particular, he used to build a bridge between solvable superpotentials (the Natanzon superpotentials, which allow reduction of a Schrödinger equation to a Gauss confluent hypergeometric equation) and existing SVM. Here we propose some new models with ${\gamma \in \mathbb{R}}$ and demonstrate that using Lie’s symmetries they could be priced in closed form in terms of hypergeometric functions. Thus obtained new models could be useful for pricing volatility derivatives (variance and volatility swaps, moment swaps).     

Optimal dividend policies for a class of growth-restricted diffusion processes under transaction costs and solvency constraints

In this paper, we consider a company whose surplus follows a rather general diffusion process and whose objective is to maximize expected discounted dividend payments. With each dividend payment, there are transaction costs and taxes, and it is shown in Paulsen (Adv. Appl. Probab. 39:669?C689, 2007) that under some reasonable assumptions, optimality is achieved by using a lump sum dividend barrier strategy, i.e., there is an upper barrier $\bar{u}^{*}$ and a lower barrier $\underline{u}^{*}$ so that whenever the surplus reaches $\bar{u}^{*}$ , it is reduced to $\underline{u}^{*}$ through a dividend payment. However, these optimal barriers may be unacceptably low from a solvency point of view. It is argued that, in that case, one should still look for a barrier strategy, but with barriers that satisfy a given constraint. We propose a solvency constraint similar to that in Paulsen (Finance Stoch. 4:457?C474, 2003); whenever dividends are paid out, the probability of ruin within a fixed time T and with the same strategy in the future should not exceed a predetermined level ??. It is shown how optimality can be achieved under this constraint, and numerical examples are given.     

Do financial returns have finite or infinite variance? A paradox and an explanation

One of the major points of contention in studying and modelling financial returns is whether or not the variance of the returns is finite or infinite (sometimes referred to as the Bachelier–Samuelson Gaussian world versus the Mandelbrot stable world). A different formulation of the question asks how heavy the tails of the financial returns are. The available empirical evidence can be, and has been, interpreted in more than one way. The apparent paradox, which has puzzled many a researcher, is that the tails appear to become less heavy for less frequent (e.g. monthly) returns than for more frequent (e.g. daily) returns, a phenomenon not easily explainable by the standard models. Inspired by the prelimit theorems of Klebanov, Rachev and Szekely (1999 Klebanov, L, Rachev, S and Szekely, G. 1999. Pre-limit theorems and their applications. Acta Applicandae Mathematicae, 58: 159–174.  [Google Scholar]) and Klebanov, Rachev and Safarian (2000 Klebanov, L, Rachev, S and Safarian, M. 2000. Local prelimit theorems and their applications to finance. Appl. Math. Lett., 13: 73–78.  [Google Scholar]), we provide an explanation of this paradox. We show that, for financial returns, a natural family of models are those with tempered heavy tails. These models can generate observations that appear heavy tailed for a wide range of aggregation levels before becoming clearly light tailed at even larger aggregation scales. Important examples demonstrate the existence of a natural scale associated with the model at which such an apparent shift in the tails occurs.     

Industry cost of equity capital: European evidence for multifactor models

We estimate the costs of equity capital for 117 industries from 16 European countries employing the CAPM and 8 multifactor asset pricing models as well as a variety of different econometric techniques. In doing so, we extend previous research on cost of equity estimation in mainly two ways. First, our study involves European instead of US or UK industries, which are investigated in previous research, and we find that cost of equity estimates obtained from the CAPM or multifactor asset pricing models are as imprecise for European industries as for US and UK industries. Second, in addition to the CAPM, the Fama and French [1993 Fama, Eugene F., and Kenneth R. French. 1993. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics 33: 3–56. doi: 10.1016/0304-405X(93)90023-5[Crossref], [Web of Science ®] , [Google Scholar]. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics 33: 3–56] three-factor model, and the Carhart [1997 Carhart, Mark M. 1997. “On Persistence in Mutual Fund Performance.” The Journal of Finance 52 (1): 57–82. doi: 10.1111/j.1540-6261.1997.tb03808.x[Crossref], [Web of Science ®] , [Google Scholar]. “On Persistence in Mutual Fund Performance.” The Journal of Finance 52 (1): 57–82] four-factor model, which are usually employed, our study includes six multifactor models that have not yet been examined on their ability to provide precise estimates of the costs of equity: the five-factor model of Fama and French [1993 Fama, Eugene F., and Kenneth R. French. 1993. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics 33: 3–56. doi: 10.1016/0304-405X(93)90023-5[Crossref], [Web of Science ®] , [Google Scholar]. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics 33: 3–56] as well as the multifactor models of Pástor and Stambaugh [2003 Pástor, Lubos, and Robert F. Stambaugh. 2003. “Liquidity Risk and Expected Stock Returns.” Journal of Political Economy 111 (3): 642–685. doi: 10.1086/374184[Crossref], [Web of Science ®] , [Google Scholar]. “Liquidity Risk and Expected Stock Returns.” Journal of Political Economy 111 (3): 642–685]; Campbell and Vuolteenaho [2004 Campbell, John Y., and Tuomo Vuolteenaho. 2004. “Bad Beta, Good Beta.” American Economic Review 94 (5): 1249–1275. doi: 10.1257/0002828043052240[Crossref], [Web of Science ®] , [Google Scholar]. “Bad Beta, Good Beta.” American Economic Review 94 (5): 1249–1275]; Hahn and Lee [2006 Hahn, Jaehoon, and Hangyong Lee. 2006. “Yield Spreads as Alternative Risk Factors for Size and Book-To-Market.” Journal of Financial &; Quantitative Analysis 41 (2): 245–269. doi: 10.1017/S0022109000002052[Crossref], [Web of Science ®] , [Google Scholar]. “Yield Spreads as Alternative Risk Factors for Size and Book-To-Market.” Journal of Financial &; Quantitative Analysis 41 (2): 245–269]; Petkova [2006 Petkova, Ralitsa. 2006. “Do the Fama–French Factors Proxy for Innovations in Predictive Variables?” The Journal of Finance 61 (2): 581–612. doi: 10.1111/j.1540-6261.2006.00849.x[Crossref], [Web of Science ®] , [Google Scholar]. “Do the Fama–French Factors Proxy for Innovations in Predictive Variables?” The Journal of Finance 61 (2): 581–612]; and Koijen, Lustig, and van Nieuwerburgh [2010 Koijen, Ralph S., Hanno N. Lustig, and Stijn G. van Nieuwerburgh. 2010. “The Cross-Section and Time-Series of Stock and Bond Returns.” Working Paper, University of Chicago, University of California at Los Angeles, New York University. [Google Scholar]. “The Cross-Section and Time-Series of Stock and Bond Returns.” Working Paper, University of Chicago, University of California at Los Angeles, New York University]. Our results suggest that these models provide even more imprecise cost of equity estimates. One main reason for these inaccurate estimates is the large temporal variation of the risk loadings on the non-traded factors in these models.