We look at the effect of the tick size changes on the TOPIX 100 index names made by the Tokyo Stock Exchange on Jan-14-2014 and Jul-22-2104. The intended consequence of the change is price improvement and shorter time to execution. We look at security level metrics that include the spread, trading volume, number of trades and the size of trades to establish whether this goal is accomplished. An unintended effect might be the reduction in execution sizes, which would then mean that institutions with large orders would have greater difficulty in sourcing liquidity. We look at a sample of real orders to see if the execution costs have gone up across the orders since the implementation of this change.

We study the mechanisms that affect how securities are traded on an exchange, before delving into the specifics of the TSE tick size events. Some of the topics we explore are: The Venue Menu and How to Increase Revenue; To Automate or Not to Automate; Microstructure under the Microscope; The Price of Connections to High (and Faraway) Places; Speed Thrills but Kills; Pick a Size for the Perfect Tick; TSE Tick Size Experiments, Then and Now; Sergey Bubka and the Regulators; Bird`s Eye View; Deep Dive; Possibilities for a Deeper Dive; Does Tick Size Matter? Tick Size Does Matter!

In this paper we focus on the subdiffusive Black Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in the considered model. We derive the governing fractional differential equation and the related weighted numerical scheme being a generalization of the classical Crank-Nicolson scheme. The proposed method has $2-\alpha$ order of accuracy with respect to time where $\alpha\in(0,1)$ is the subdiffusion parameter, and $2$ with respect to space. Further, we provide the stability and convergence analysis. Finally, we present some numerical results.

The goal of this paper is to clarify when a stochastic partial differential equation with an affine realization admits affine state processes. This includes a characterization of the set of initial points of the realization. Several examples, as the HJMM equation from mathematical finance, illustrate our results.

The use of sequential Monte Carlo within simulation for path-dependent option pricing is proposed and evaluated. Recently, it was shown that explicit solutions and importance sampling are valuable for efficient simulation of spot price and volatility, especially for purposes of path-dependent option pricing. The resulting simulation algorithm is an analog to the weighted particle filtering algorithm that might be improved by resampling or branching. Indeed, some branching algorithms are shown herein to improve pricing performance substantially while some resampling algorithms are shown to be less suitable in certain cases. A historical property is given and explained as the distinguishing feature between the sequential Monte Carlo algorithms that work on path-dependent option pricing and those that do not. In particular, it is recommended to use the so-called effective particle branching algorithm within importance-sampling Monte Carlo methods for path-dependent option pricing. All recommendations are based upon numeric comparison of option pricing problems in the Heston model.

We present a detailed study of the performance of a trading rule that uses moving average of past returns to predict future returns on stock indexes. Our main goal is to link performance and the stochastic process of the traded asset. Our study reports short, medium and long term effects by looking at the Sharpe ratio (SR). We calculate the Sharpe ratio of our trading rule as a function of the probability distribution function of the underlying traded asset and compare it with data. We show that if the performance is mainly due to presence of autocorrelation in the returns of the traded assets, the SR as a function of the portfolio formation period (look-back) is very different from performance due to the drift (average return). The SR shows that for look-back periods of a few months the investor is more likely to tap into autocorrelation. However, for look-back larger than few months, the drift of the asset becomes progressively more important. Finally, our empirical work reports a new long-term effect, namely oscillation of the SR and propose a non-stationary model to account for such oscillations.

In this paper, we present a Longstaff-Schwartz-type algorithm for optimal stopping time problems based on the Brownian motion filtration. The algorithm is based on Le\~ao, Ohashi and Russo and, in contrast to previous works, our methodology applies to optimal stopping problems for fully non-Markovian and non-semimartingale state processes such as functionals of path-dependent stochastic differential equations and fractional Brownian motions. Based on statistical learning theory techniques, we provide overall error estimates in terms of concrete approximation architecture spaces with finite Vapnik-Chervonenkis dimension. Analytical properties of continuation values for path-dependent SDEs and concrete linear architecture approximating spaces are also discussed.

The goal of this paper is to clarify when a semilinear stochastic partial differential equation driven by L\'evy processes admits an affine realization. Our results are accompanied by several examples arising in natural sciences and economics.

Social media signals have been successfully used to develop large-scale predictive and anticipatory analytics. For example, forecasting stock market prices and influenza outbreaks. Recently, social data has been explored to forecast price fluctuations of cryptocurrencies, which are a novel disruptive technology with significant political and economic implications. In this paper we leverage and contrast the predictive power of social signals, specifically user behavior and communication patterns, from multiple social platforms GitHub and Reddit to forecast prices for three cyptocurrencies with high developer and community interest - Bitcoin, Ethereum, and Monero. We evaluate the performance of neural network models that rely on long short-term memory units (LSTMs) trained on historical price data and social data against price only LSTMs and baseline autoregressive integrated moving average (ARIMA) models, commonly used to predict stock prices. Our results not only demonstrate that social signals reduce error when forecasting daily coin price, but also show that the language used in comments within the official communities on Reddit (r/Bitcoin, r/Ethereum, and r/Monero) are the best predictors overall. We observe that models are more accurate in forecasting price one day ahead for Bitcoin (4% root mean squared percent error) compared to Ethereum (7%) and Monero (8%).

In this study, we develop a deterministic nonlinear filtering algorithm based on a high-dimensional version of Kitagawa (1987) to evaluate the likelihood function of models that allow for stochastic volatility and jumps whose arrival intensity is also stochastic. We show numerically that the deterministic filtering method is precise and much faster than the particle filter, in addition to yielding a smooth function over the parameter space. We then find the maximum likelihood estimates of various models that include stochastic volatility, jumps in the returns and variance, and also stochastic jump arrival intensity with the S&P 500 daily returns. During the Great Recession, the jump arrival intensity increases significantly and contributes to the clustering of volatility and negative returns.

In this note we propose a new approach towards solving numerically optimal stopping problems via reinforced regression based Monte Carlo algorithms. The main idea of the method is to reinforce standard linear regression algorithms in each backward induction step by adding new basis functions based on previously estimated continuation values. The proposed methodology is illustrated by a numerical example from mathematical finance.

In this paper we extend the existing literature on xVA along three directions. First, we extend existing BSDE-based xVA frameworks to include initial margin by following the approach of Cr\'epey (2015a) and Cr\'epey (2015b). Next, we solve the consistency problem that arises when the front-office desk of the bank uses trade-specific discount curves that differ from the discount curve adopted by the xVA desk. Finally, we address the existence of multiple aggregation levels for contingent claims in the portfolio between the bank and the counterparty by providing suitable extensions of our proposed single-claim xVA framework.

From the stock markets of six countries with high GDP, we study the stock indices, S&P 500 (NYSE, USA), SSE Composite (SSE, China), Nikkei (TSE, Japan), DAX (FSE, Germany), FTSE 100 (LSE, Britain) and NIFTY (NSE, India). The daily mean growth of the stock values is exponential. The daily price fluctuations about the mean growth are Gaussian, but with a finite asymptotic convergence. The growth of the monthly average of stock values is statistically self-similar to their daily growth. The monthly fluctuations of the price follow a Wiener process, with a decline of the volatility. The mean growth of the daily volume of trade is exponential. These observations are globally applicable and underline regularities across global stock markets.

In this study, we construct two tests for the weights of the global minimum variance portfolio (GMVP) in a high-dimensional setting, namely, when the number of assets $p$ depends on the sample size $n$ such that $\frac{p}{n}\to c \in (0,1)$ as $n$ tends to infinity. In the case of a singular covariance matrix with rank equal to $q$ we assume that $q/n\to \tilde{c}\in(0, 1)$ as $n\to\infty$. The considered tests are based on the sample estimator and on the shrinkage estimator of the GMVP weights. We derive the asymptotic distributions of the test statistics under the null and alternative hypotheses. Moreover, we provide a simulation study where the power functions and the receiver operating characteristic curves of the proposed tests are compared with other existing approaches. We observe that the test based on the shrinkage estimator performs well even for values of $c$ close to one.

Carr and Wu (2004), henceforth CW, developed a framework that encompasses almost all of the continuous-time models proposed in the option pricing literature. Their framework hinges on the stopping time property of the time changes. By analyzing the measurability of the time changes with respect to the underlying filtration, we show that all models CW proposed for the time changes fail to satisfy this assumption.

We study a series of static and dynamic portfolios of VIX futures and their effectiveness to track the VIX index. We derive each portfolio using optimization methods, and evaluate its tracking performance from both empirical and theoretical perspectives. Among our results, we show that static portfolios of different VIX futures fail to track VIX closely. VIX futures simply do not react quickly enough to movements in the spot VIX. In a discrete-time model, we design and implement a dynamic trading strategy that adjusts daily to optimally track VIX. The model is calibrated to historical data and a simulation study is performed to understand the properties exhibited by the strategy. In addition, comparing to the volatility ETN, VXX, we find that our dynamic strategy has a superior tracking performance.

Planning and execution of clinical research and publication of results should conform to the highest ethical standards, given that human lives are at stake. However, economic incentives can generate conflicts of interest for investigators, who may be inclined to withhold unfavorable results or even tamper with the data. Analyzing p-values reported to the ClinicalTrials.gov registry with two different methodologies, we find suspicious patterns only for results from trials conducted by smaller industry sponsors, with presumably less reputation at stake. First, a density discontinuity test reveals an upward jump at the classical threshold for statistical significance for Phase 3 results by small industry sponsors, suggesting some selective reporting. Second, we find an excess mass of significant results in Phase 3 compared to Phase 2. However, we can explain almost completely this excess mass for large industry sponsors, once we account for the incentives to selectively continue research through a novel technique linking trials across phases. In contrast, for trials sponsored by small pharmaceutical companies, selective continuation of trials economizing on research costs only explains one third of the increase in the number of significant results from Phase 2 to Phase 3. The different pattern depending on the type of sponsor suggests that reputational concerns can mitigate the short-run economic incentives that undermine integrity in reporting results of clinical research.