We study and formulate arbitrage in display advertising. Real-Time Bidding (RTB) mimics stock spot exchanges and utilises computers to algorithmically buy display ads per impression via a real-time auction. Despite the new automation, the ad markets are still informationally inefficient due to the heavily fragmented marketplaces. Two display impressions with similar or identical effectiveness (e.g., measured by conversion or click-through rates for a targeted audience) may sell for quite different prices at different market segments or pricing schemes. In this paper, we propose a novel data mining paradigm called Statistical Arbitrage Mining (SAM) focusing on mining and exploiting price discrepancies between two pricing schemes. In essence, our SAMer is a meta-bidder that hedges advertisers' risk between CPA (cost per action)-based campaigns and CPM (cost per mille impressions)-based ad inventories; it statistically assesses the potential profit and cost for an incoming CPM bid request against a portfolio of CPA campaigns based on the estimated conversion rate, bid landscape and other statistics learned from historical data. In SAM, (i) functional optimisation is utilised to seek for optimal bidding to maximise the expected arbitrage net profit, and (ii) a portfolio-based risk management solution is leveraged to reallocate bid volume and budget across the set of campaigns to make a risk and return trade-off. We propose to jointly optimise both components in an EM fashion with high efficiency to help the meta-bidder successfully catch the transient statistical arbitrage opportunities in RTB. Both the offline experiments on a real-world large-scale dataset and online A B tests on a commercial platform demonstrate the effectiveness of our proposed solution in exploiting arbitrage in various model settings and market environments.
In financial markets, as a trading strategy, statistical arbitrage is a quantitative approach to security trading. It utilises statistical methods with high-frequency trading systems to detect statistical mispricing of securities caused by market inefficiency to make profit with a large number of transactions @cite_25 .
@cite_25
2108626041 2163285066 2092306038 1973081445
This paper introduces the concept of statistical arbitrage, a long horizon trading opportunity that generates a riskless profit and is designed to exploit persistent anomalies. Statistical arbitrage circumvents the "joint hypothesis" dilemma of traditional market efficiency tests because its definition is independent of any equilibrium model and its existence is incompatible with market efficiency. We provide a methodology to test for statistical arbitrage and then empirically investigate whether momentum and value trading strategies constitute statistical arbitrage opportunities. Despite controlling for transaction costs and the influence of small stocks, we find evidence that these strategies generate statistical arbitrage. Furthermore, their profitability does not appear to decline over time. We study model-driven statistical arbitrage in US equities. Trading signals are generated in two ways: using Principal Component Analysis (PCA) or regressing stock returns on sector Exchange Traded Funds (ETFs). In both cases, the idiosyncratic returns are modelled as mean-reverting processes, which leads naturally to 'contrarian' strategies. We construct, back-test and compare market-neutral PCA- and ETF-based strategies applied to the broad universe of US equities. After accounting for transaction costs, PCA-based strategies have an average annual Sharpe ratio of 1.44 over the period 1997 to 2007, with stronger performances prior to 2003. During 2003-2007, the average Sharpe ratio of PCA-based strategies was only 0.9. ETF-based strategies had a Sharpe ratio of 1.1 from 1997 to 2007, experiencing a similar degradation since 2002. We also propose signals that account for trading volume, observing significant improvement in performance in the case of ETF-based signals. ETF-strategies with volume information achieved a Sharpe ratio of 1.51 from 2003 to 2007. The paper also relates the performance of mean-reversion statistical arbitrage strategies with the stock market cycle. In particular, we study in detail the performance of the strategies during the liquidity crisis of the summer of 2007, following Khandani and Lo [Social Science Research Network (SSRN) working paper, 2007]. This paper analytically solves the portfolio optimization problem of an investor faced with a risky arbitrage opportunity (e.g. relative mispricing in equity pairs). Unlike the extant literature, which typically models mispricings through the Ornstein--Uhlenbeck (OU) process, we introduce a nonlinear generalization of OU which jointly captures several important risk factors inherent in arbitrage trading. While these factors are absent from the standard OU, we show that considering them yields several new insights into the behavior of rational arbitrageurs: Firstly, arbitrageurs recognizing these risk factors exhibit a diminishing propensity to exploit large mispricings. Secondly, optimal investment behavior in light of these risk factors precipitates the gradual unwinding of losing trades far sooner than is entailed in existing approaches including OU. Finally, an empirical application to daily FTSE100 pairs data shows that incorporating these risks renders our model's risk-management capabilities superior to both OU and a simple threshold strategy popular in the literature. These observations are useful in understanding the role of arbitrageurs in enforcing price efficiency. We study and formulate arbitrage in display advertising. Real-Time Bidding (RTB) mimics stock spot exchanges and utilises computers to algorithmically buy display ads per impression via a real-time auction. Despite the new automation, the ad markets are still informationally inefficient due to the heavily fragmented marketplaces. Two display impressions with similar or identical effectiveness (e.g., measured by conversion or click-through rates for a targeted audience) may sell for quite different prices at different market segments or pricing schemes. In this paper, we propose a novel data mining paradigm called Statistical Arbitrage Mining (SAM) focusing on mining and exploiting price discrepancies between two pricing schemes. In essence, our SAMer is a meta-bidder that hedges advertisers' risk between CPA (cost per action)-based campaigns and CPM (cost per mille impressions)-based ad inventories; it statistically assesses the potential profit and cost for an incoming CPM bid request against a portfolio of CPA campaigns based on the estimated conversion rate, bid landscape and other statistics learned from historical data. In SAM, (i) functional optimisation is utilised to seek for optimal bidding to maximise the expected arbitrage net profit, and (ii) a portfolio-based risk management solution is leveraged to reallocate bid volume and budget across the set of campaigns to make a risk and return trade-off. We propose to jointly optimise both components in an EM fashion with high efficiency to help the meta-bidder successfully catch the transient statistical arbitrage opportunities in RTB. Both the offline experiments on a real-world large-scale dataset and online A B tests on a commercial platform demonstrate the effectiveness of our proposed solution in exploiting arbitrage in various model settings and market environments.