Research articles for the 2019-04-07

A stochastic PDE model for limit order book dynamics
Rama Cont,Marvin S. Mueller

We propose an analytically tractable class of models for the dynamics of a limit order book, described as the solution of a stochastic partial differential equation (SPDE) with multiplicative noise. We provide conditions under which the model admits a finite dimensional realization driven by a (low-dimensional) Markov process, leading to efficient methods for estimation and computation. We study two examples of parsimonious models in this class: a two-factor model and a model in which the order book depth is mean-reverting. For each model we perform a detailed analysis of the role of different parameters, study the dynamics of the price, order book depth, volume and order imbalance, provide an intuitive financial interpretation of the variables involved and show how the model reproduces statistical properties of price changes, market depth and order flow in limit order markets.

Computational Methods for Martingale Optimal Transport problems
Gaoyue Guo,Jan Obloj

We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be approximated using linear programming (LP) problems which result from a discretisation of the marginal distributions combined with a suitable relaxation of the martingale constraint. Specialising to dimension one, we provide bounds on the convergence rate of the above scheme. We also show a stability result under only partial specification of the marginal distributions. Finally, we specialise to a particular discretisation scheme which preserves the convex ordering and does not require the martingale relaxation. We introduce an entropic regularisation for the corresponding LP problem and detail the corresponding iterative Bregman projection. We also rewrite its dual problem as a minimisation problem without constraint and solve it by computing the concave envelope of scattered data.

Earnings Management and Instances of Material Weaknesses Reported Under Sections 302 and 404
Kwon, Shin Hyoung,Deshmukh, Ashutosh
Sections 302 and 404 of the 2002 Sarbanes-Oxley Act require firms to disclose material weaknesses (MWs) in internal controls. We investigate the association of single and multiple instances of MWs with earnings management. Multiple instances are positively associated with earnings management for Section 302 and 404 firms, whereas single instances have no such association for either firm type. Thus, MWs that are not remediated within one quarter or year tend to be positively associated with earnings management and, in particular, with income- decreasing earnings management. Multiple instances of MWs for such firms can therefore provide critical information for auditors and investors.

Option pricing models without probability
John Armstrong,Claudio Bellani,Damiano Brigo,Thomas Cass

We describe the pricing and hedging practices refraining from the use of probability. We encode volatility in an enhancement of the price trajectory and we give pathwise presentations of the fundamental equations of Mathematical Finance. In particular this allows us to assess model misspecification, generalising the so-called fundamental theorem of derivative trading (see Ellersgaard et al. 2017). Our pathwise integrals and equations exhibit the role of Greeks beyond the leading-order Delta, and makes explicit the role of Gamma sensitivities.

Term Structure Modeling under Volatility Uncertainty: A Forward Rate Model driven by G-Brownian Motion
Julian Hölzermann,Qian Lin

We show how to set up a forward rate model in the presence of volatility uncertainty by using the theory of G-Brownian motion. In order to formulate the model, we extend the G-framework to integration with respect to two integrators and prove a version of Fubini's theorem for stochastic integrals. The evolution of the forward rate in the model is described by a diffusion process, which is driven by a G-Brownian motion. Within this framework, we derive a sufficient condition for the absence of arbitrage, known as the drift condition. In contrast to the traditional model, the drift condition consists of two equations and two market prices of risk, respectively, uncertainty. Furthermore, we examine the connection to short rate models and discuss some examples.

The Effect of Naïve Reinforcement Learning in the Stock Market
Park, Sunghoon,Cho, Sungzoon
Some investors who are subjected to naïve reinforcement learning create a spread between a stock’s fundamental value and its equilibrium price. Naïve learners are more likely to repurchase a stock previously sold for a gain than one sold for a loss. This causes predictable equilibrium prices. We propose a proxy for the effect of naïve learning and show the profitability of a long-short strategy based on our proxy.

UK food prices after Brexit, with implications for poverty and health
Martine J Barons,Willy Aspinall

A key driver of household food insecurity is the balance between household disposable income and food prices. In the UK in recent years, many households have relied on charitable food banks in order to eat. The UK exit of the EU (Brexit) is expected to have significant influence across the economy, including on employment, wages and prices. We use structured expert judgement to quantify food prices and associated uncertainties in a principled manner under two scenarios: a Brexit deal broadly similar to the present situation and Brexit without a deal. Here we show that consumer prices index (CPI) food prices will rise faster than previously under both scenarios (6% and 24% respectively) and that the uncertainty is significantly larger under no-deal (a plausible worst-case of 43% compared to 14% ). Under a Brexit deal, a family with two adults and two children, one at pre-school and one at primary school, buying healthy diets will suffer median increases in food costs of {\pounds}6 per week (with a plausible worst case of {\pounds}16 per week). Under a no-deal scenario, this family will suffer a median increase of {\pounds}23 per week (plausible worst-case {\pounds}45 per week). The Lancet reported that poor diet is linked to 20% of all deaths worldwide, though association with disease. Rising food prices in a condition of static UK incomes is likely to add to demand pressure on the NHS. Our results demonstrate that uncertainty analysis associated with expected changes in food costs are vital to inform policies that allow households to afford a food basket that meets their needs.

Why People Buy Insurance: A Modern Answer to an Old Question
Fels, Markus
In this essay, I revisit the question of which motive underlies insurance demand. I draw on the literature of state-dependent utility and on the literature of imperfectly divisible consumption to argue that the general purpose of insurance is not a risk transfer, but meeting a conditional need. I discuss how this understanding of insurance extends the traditional view of insurance and I show how this extension has implications for our discipline’s research agenda and policy advice.

Ð"иагностирование инсайдерской торговли на российском фондовом рынке перед важными корпоративными событиями (Testing for the Insider Trading Prior to the Significant Corporate Events)
Petrov, Vladislav
Russian Abstract: Ð' статье представлены результаты исследования инсайдерской торговли в периоды, предшествую-щие случаям административного давления на бизнес, на российском фондовом рынке в 2000â€"2014 годах. Исследование базируется на анализе накопленной избыточной доходности в период до пу-бликации соответствующего новостного события. в рамках исследования мы проанализировали 71 новость. Нами не было диагностировано значительной по масштабам инсайдерской торговли в периоды, предшествовавшие случаям административного давления на бизнес со стороны пред-ставителей исполнительной и законодательной властей российской федерации. размер избыточ-ной доходности в данном случае составил -0,4%...-0,6% в зависимости от применяемой модели. Мы обнаружили наличие значительной по масштабам инсайдерской торговли в периоды, предше-ствовавшие случаям административного давления на бизнес со стороны представителей силовых структур (-8,2%...-10,4%). реакция рынка в обоих случаях была значительной. Мы диагностирова-ли наличие меньшей по масштабам инсайдерской торговли, чем в случае действий представителей силовых структур, в периоды, предшествовавшие случаям административного давления на бизнес со стороны представителей таких служб исполнительной власти, как фНс и фас (-2,3%...-4,4% и -3,9%...-4,4% соответственно). при этом рынок слабо реагировал на случаи административного давления со стороны представителей данных государственных органов. кроме того, мы пришли к выводу, что ужесточение законодательства российской федерации в сфере противодействия инсай-дерской торговле в 2010â€"2013 гг. не дало желаемого результата и масштабы инсайдерской торговли на российском фондовом рынке увеличились.English Abstract: This article presents the results of a study of insider trading prior to the cases of administrative pressure on the Russian public companies. The study is based on an analysis of cumulative abnormal returns during the period prior to the publication of a news. In the study we analyzed 71 news about the administrative pressure.we have not found the presence of a large-scale insider trading prior to the administrative pressure on business by the representatives of executive and legislative authorities of the Russian Federation. The cumulative abnormal return (CAR) amounted -0,4% â€" -0,6% depending on utilized model. We found a large-scale insider trading prior to the to the administrative pressure on business by the representatives of security agencies (CAR = -8,2% â€" -10,4%). Market reaction was significant in both cases. Also we detected a small-scale insider trading prior to the administrative pressure on business by the representatives of Federal Tax Service and Federal Antimonopoly Service (-2,3% â€" -4,4% and -3,9% â€" -4,4% respectively). Meanwhile, the market reaction was insignificant in both of these cases.