We show that wealth processes in the block-shaped order book model of Obizhaeva/Wang converge to their counterparts in the reduced-form model proposed by Almgren/Chriss, as the resilience of the order book tends to infinity. As an application of this
limit theorem, we explain how to reduce portfolio choice in highly-resilient Obizhaeva/Wang models to the corresponding problem in an Almgren/Chriss setup with small quadratic trading costs.
We describe the impact of the intra-day activity pattern on the autocorrelation function estimator. We obtain an exact formula relating estimators of the autocorrelation functions of non-stationary process to its stationary counterpart. Hence, we pro
ved that the day seasonality of inter-transaction times extends the memory of as well the process itself as its absolute value. That is, both processes relaxation to zero is longer.
The call auction is a widely used trading mechanism, especially during the opening and closing periods of financial markets. In this paper, we study a standard call auction problem where orders are submitted according to Poisson processes, with rando
m prices distributed according to a general distribution, and may be cancelled at any time. We compute the analytical expressions of the distributions of the traded volume, of the lower and upper bounds of the clearing prices, and of the price range of these possible clearing prices of the call auction. Using results from the theory of order statistics and a theorem on the limit of sequences of random variables with independent random indices, we derive the weak limits of all these distributions. In this setting, traded volume and bounds of the clearing prices are found to be asymptotically normal, while the clearing price range is asymptotically exponential. All the parameters of these distributions are explicitly derived as functions of the parameters of the incoming orders flows.
We present a Hawkes model approach to foreign exchange market in which the high frequency price dynamics is affected by a self exciting mechanism and an exogenous component, generated by the pre-announced arrival of macroeconomic news. By focusing on
time windows around the news announcement, we find that the model is able to capture the increase of trading activity after the news, both when the news has a sizeable effect on volatility and when this effect is negligible, either because the news in not important or because the announcement is in line with the forecast by analysts. We extend the model by considering non-causal effects, due to the fact that the existence of the news (but not its content) is known by the market before the announcement.
We generalize the reaction-diffusion model A + B -> 0 in order to study the impact of an excess of A (or B) at the reaction front. We provide an exact solution of the model, which shows that linear response breaks down: the average displacement of th
e reaction front grows as the square-root of the imbalance. We argue that this model provides a highly simplified but generic framework to understand the square-root impact of large orders in financial markets.
Using non-linear machine learning methods and a proper backtest procedure, we critically examine the claim that Google Trends can predict future price returns. We first review the many potential biases that may influence backtests with this kind of d
ata positively, the choice of keywords being by far the greatest culprit. We then argue that the real question is whether such data contain more predictability than price returns themselves: our backtest yields a performance of about 17bps per week which only weakly depends on the kind of data on which predictors are based, i.e. either past price returns or Google Trends data, or both.
In financial markets, the order flow, defined as the process assuming value one for buy market orders and minus one for sell market orders, displays a very slowly decaying autocorrelation function. Since orders impact prices, reconciling the persiste
nce of the order flow with market efficiency is a subtle issue. A possible solution is provided by asymmetric liquidity, which states that the impact of a buy or sell order is inversely related to the probability of its occurrence. We empirically find that when the order flow predictability increases in one direction, the liquidity in the opposite side decreases, but the probability that a trade moves the price decreases significantly. While the last mechanism is able to counterbalance the persistence of order flow and restore efficiency and diffusivity, the first acts in opposite direction. We introduce a statistical order book model where the persistence of the order flow is mitigated by adjusting the market order volume to the predictability of the order flow. The model reproduces the diffusive behaviour of prices at all time scales without fine-tuning the values of parameters, as well as the behaviour of most order book quantities as a function of the local predictability of order flow.
Prospect theory is widely viewed as the best available descriptive model of how people evaluate risk in experimental settings. According to prospect theory, people are risk-averse with respect to gains and risk-seeking with respect to losses, a pheno
menon called loss aversion. Despite of the fact that prospect theory has been well developed in behavioral economics at the theoretical level, there exist very few large-scale empirical studies and most of them have been undertaken with micro-panel data. Here we analyze over 28.5 million trades made by 81.3 thousand traders of an online financial trading community over 28 months, aiming to explore the large-scale empirical aspect of prospect theory. By analyzing and comparing the behavior of winning and losing trades and traders, we find clear evidence of the loss aversion phenomenon, an essence in prospect theory. This work hence demonstrates an unprecedented large-scale empirical evidence of prospect theory, which has immediate implication in financial trading, e.g., developing new trading strategies by minimizing the effect of loss aversion. Moreover, we introduce three risk-adjusted metrics inspired by prospect theory to differentiate winning and losing traders based on their historical trading behavior. This offers us potential opportunities to augment online social trading, where traders are allowed to watch and follow the trading activities of others, by predicting potential winners statistically based on their historical trading behavior rather than their trading performance at any given point in time.
We develop a probabilistic consumer choice framework based on information asymmetry between consumers and firms. This framework makes it possible to study market competition of several firms by both quality and price of their products. We find Nash m
arket equilibria and other optimal strategies in various situations ranging from competition of two identical firms to firms of different sizes and firms which improve their efficiency.
We examine the dynamics of the bid and ask queues of a limit order book and their relationship with the intensity of trade arrivals. In particular, we study the probability of price movements and trade arrivals as a function of the quote imbalance at
the top of the limit order book. We propose a stochastic model in an attempt to capture the joint dynamics of the top of the book queues and the trading process, and describe a semi-analytic approach to calculate the relative probability of market events. We calibrate the model using historical market data and discuss the quality of fit and practical applications of the results.
