Quantitative Finance

In recent years several trading platforms appeared which provide a backtest engine to calculate historic performance of self designed trading strategies on underlying candle data. The construction of a correct working backtest engine is, however, a subtle task as shown by Maier-Paape and Platen (cf. arXiv:1412.5558 [q-fin.TR]). Several platforms are struggling on the correctness. In this work, we discuss the problem how the correctness of backtest engines can be verified. We provide models for candles and for intra-period prices which will be applied to conduct a proof of correctness for a given backtest engine if the here provided tests on specific model candles are successful. Furthermore, we hint to algorithmic considerations in order to allow for a fast implementation of these tests necessary for the proof of correctness.

A counterparty credit limit (CCL) is a limit that is imposed by a financial institution to cap its maximum possible exposure to a specified counterparty. CCLs help institutions to mitigate counterparty credit risk via selective diversification of their exposures. In this paper, we analyze how CCLs impact the prices that institutions pay for their trades during everyday trading. We study a high-quality data set from a large electronic trading platform in the foreign exchange spot market, which enables institutions to apply CCLs. We find empirically that CCLs had little impact on the vast majority of trades in this data. We also study the impact of CCLs using a new model of trading. By simulating our model with different underlying CCL networks, we highlight that CCLs can have a major impact in some situations.

We develop a theory of bid and ask price dynamics where the two prices form due to interaction of buy and sell orders. In this model the two prices are represented by eigenvalues of a 2x2 price operator corresponding to "bid" and "ask" eigenstates. Matrix elements of price operator fluctuate in time which results in phase jitter for eigenstates. We show that the theory reflects very important characteristics of bid and ask dynamics and order density in the order book. Calibration examples are provided for stocks at various time scales. Lastly, this model allows to quantify and measure risk associated with spread and its fluctuations.

We present a model of worldwide crisis contagion based on the Google matrix analysis of the world trade network obtained from the UN Comtrade database. The fraction of bankrupted countries exhibits an \textit{on-off} phase transition governed by a bankruptcy threshold κ related to the trade balance of the countries. For κ> κ c , the contagion is circumscribed to less than 10\% of the countries, whereas, for κ< κ c , the crisis is global with about 90\% of the countries going to bankruptcy. We measure the total cost of the crisis during the contagion process. In addition to providing contagion scenarios, our model allows to probe the structural trading dependencies between countries. For different networks extracted from the world trade exchanges of the last two decades, the global crisis comes from the Western world. In particular, the source of the global crisis is systematically the Old Continent and The Americas (mainly US and Mexico). Besides the economy of Australia, those of Asian countries, such as China, India, Indonesia, Malaysia and Thailand, are the last to fall during the contagion. Also, the four BRIC are among the most robust countries to the world trade crisis.

We introduce a linear cross-impact framework in a setting in which the price of some given financial instruments (derivatives) is a deterministic function of one or more, possibly tradeable, stochastic factors (underlying). We show that a particular cross-impact model, the multivariate Kyle model, prevents arbitrage and aggregates (potentially non-stationary) traded order flows on derivatives into (roughly stationary) liquidity pools aggregating order flows traded on both derivatives and underlying. Using E-Mini futures and options along with VIX futures, we provide empirical evidence that the price formation process from order flows on derivatives is driven by cross-impact and confirm that the simple Kyle cross-impact model is successful at capturing parsimoniously such empirical phenomenology. Our framework may be used in practice for estimating execution costs, in particular hedging costs.

The composition of natural liquidity has been changing over time. An analysis of intraday volumes for the S&P500 constituent stocks illustrates that (i) volume surprises, i.e., deviations from their respective forecasts, are correlated across stocks, and (ii) this correlation increases during the last few hours of the trading session. These observations could be attributed, in part, to the prevalence of portfolio trading activity that is implicit in the growth of ETF, passive and systematic investment strategies; and, to the increased trading intensity of such strategies towards the end of the trading session, e.g., due to execution of mutual fund inflows/outflows that are benchmarked to the closing price on each day. In this paper, we investigate the consequences of such portfolio liquidity on price impact and portfolio execution. We derive a linear cross-asset market impact from a stylized model that explicitly captures the fact that a certain fraction of natural liquidity providers only trade portfolios of stocks whenever they choose to execute. We find that due to cross-impact and its intraday variation, it is optimal for a risk-neutral, cost minimizing liquidator to execute a portfolio of orders in a coupled manner, as opposed to a separable VWAP-like execution that is often assumed. The optimal schedule couples the execution of the various orders so as to be able to take advantage of increased portfolio liquidity towards the end of the day. A worst case analysis shows that the potential cost reduction from this optimized execution schedule over the separable approach can be as high as 6% for plausible model parameters. Finally, we discuss how to estimate cross-sectional price impact if one had a dataset of realized portfolio transaction records that exploits the low-rank structure of its coefficient matrix suggested by our analysis.

We extend the "No-dynamic-arbitrage and market impact"-framework of Jim Gatheral [Quantitative Finance, 10(7): 749-759 (2010)] to the multi-dimensional case where trading in one asset has a cross-impact on the price of other assets. From the condition of absence of dynamical arbitrage we derive theoretical limits for the size and form of cross-impact that can be directly verified on data. For bounded decay kernels we find that cross-impact must be an odd and linear function of trading intensity and cross-impact from asset i to asset j must be equal to the one from j to i . To test these constraints we estimate cross-impact among sovereign bonds traded on the electronic platform MOT. While we find significant violations of the above symmetry condition of cross-impact, we show that these are not arbitrageable with simple strategies because of the presence of the bid-ask spread.

Using a large database of 8 million institutional trades executed in the U.S. equity market, we establish a clear crossover between a linear market impact regime and a square-root regime as a function of the volume of the order. Our empirical results are remarkably well explained by a recently proposed dynamical theory of liquidity that makes specific predictions about the scaling function describing this crossover. Allowing at least two characteristic time scales for the liquidity (`fast' and `slow') enables one to reach quantitative agreement with the data.

Few assets in financial history have been as notoriously volatile as cryptocurrencies. While the long term outlook for this asset class remains unclear, we are successful in making short term price predictions for several major crypto assets. Using historical data from July 2015 to November 2019, we develop a large number of technical indicators to capture patterns in the cryptocurrency market. We then test various classification methods to forecast short-term future price movements based on these indicators. On both PPV and NPV metrics, our classifiers do well in identifying up and down market moves over the next 1 hour. Beyond evaluating classification accuracy, we also develop a strategy for translating 1-hour-ahead class predictions into trading decisions, along with a backtester that simulates trading in a realistic environment. We find that support vector machines yield the most profitable trading strategies, which outperform the market on average for Bitcoin, Ethereum and Litecoin over the past 22 months, since January 2018.

In recent years, the tendency of the number of financial institutions including cryptocurrencies in their portfolios has accelerated. Cryptocurrencies are the first pure digital assets to be included by asset managers. Even though they share some commonalities with more traditional assets, they have a separate nature of its own and their behaviour as an asset is still under the process of being understood. It is therefore important to summarise existing research papers and results on cryptocurrency trading, including available trading platforms, trading signals, trading strategy research and risk management. This paper provides a comprehensive survey of cryptocurrency trading research, by covering 126 research papers on various aspects of cryptocurrency trading (eg., cryptocurrency trading systems, bubble and extreme condition, prediction of volatility and return, crypto-assets portfolio construction and crypto-assets, technical trading and others). This paper also analyses datasets, research trends and distribution among research objects (contents/properties) and technologies, concluding with some promising opportunities that remain open in cryptocurrency trading.