Research articles for the 2020-08-23

A Dual Method For Backward Stochastic Differential Equations with Application to Risk Valuation
Andrzej Ruszczynski,Jianing Yao

We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a stochastic control problem where the control is a certain Radon-Nikodym derivative process. By exploring the maximum principle, we show that a piecewise-constant dual control provides a good approximation on a short interval. A dynamic programming algorithm extends the approximation to a finite time horizon. Finally, we illustrate the application of the procedure to financial risk management in conjunction with nested simulation and on an multidimensional portfolio valuation problem.

A Generalized Framework for Simultaneous Long-Short Feedback Trading
Joseph D. O'Brien,Mark E. Burke,Kevin Burke

We present a generalization of the Simultaneous Long-Short (SLS) trading strategy described in recent control literature wherein we allow for different parameters across the short and long sides of the controller; we refer to this new strategy as Generalized SLS (GSLS). Furthermore, we investigate the conditions under which positive gain can be assured within the GSLS setup for both deterministic stock price evolution and geometric Brownian motion. In contrast to existing literature in this area (which places little emphasis on the practical application of SLS strategies), we suggest optimization procedures for selecting the control parameters based on historical data, and we extensively test these procedures across a large number of real stock price trajectories (495 in total). We find that the implementation of such optimization procedures greatly improves the performance compared with fixing control parameters, and, indeed, the GSLS strategy outperforms the simpler SLS strategy in general.

A financial market with singular drift and no arbitrage
Nacira Agram,Bernt Øksendal

We study a financial market where the risky asset is modelled by a geometric It\^o-L\'{e}vy process, with a singular drift term. This can for example model a situation where the asset price is partially controlled by a company which intervenes when the price is reaching a certain lower barrier. See e.g. Jarrow & Protter for an explanation and discussion of this model in the Brownian motion case. As already pointed out by Karatzas & Shreve (in the continuous setting), this allows for arbitrages in the market. However, the situation in the case of jumps is not clear. Moreover, it is not clear what happens if there is a delay in the system.

In this paper we consider a jump diffusion market model with a singular drift term modelled as the local time of a given process, and with a delay \theta>0 in the information flow available for the trader. We allow the stock price dynamics to depend on both a continuous process (Brownian motion) and a jump process (Poisson random measure). We believe that jumps and delays are essential in order to get more realistic financial market models.

Using white noise calculus we compute explicitly the optimal consumption rate and portfolio in this case and we show that the maximal value is finite as long as the delay \theta> 0. This implies that there is no arbitrage in the market in that case. However, when \theta goes to 0, the value goes to infinity. This is in agreement with the above result that is an arbitrage when there is no delay.

Our model is also relevant for high frequency trading issues. This is because high frequency trading often leads to intensive trading taking place on close to infinitesimal lengths of time, which in the limit corresponds to trading on time sets of measure 0. This may in turn lead to a singular drift in the pricing dynamics. See e.g. Lachapelle et al and the references therein.

Banks, Money, and the Zero Lower Bound on Deposit Rates
Kumhof, Michael,Wang, Xuan
We develop a New Keynesian model where all payments between agents require bank deposits through deposits-in-advance constraints, bank deposits are created through disbursement of bank loans, and banks face a convex lending cost. At the zero lower bound on deposit rates (ZLBD), changes in policy rates affect activity through both real interest rates and banks’ net interest margins (NIM). At estimated credit supply elasticities, the Phillips curve is very flat at the ZLBD, because inflationary pressures increase NIM. This strongly increases credit and thereby output, but it dampens inflation by relaxing price setters’ credit rationing constraint. At the ZLBD, monetary policy has far larger effects on output relative to inflation, and Taylor rules stabilize output less effectively than rules that also respond to credit. For post-COVID-19 policy, this suggests urgency in returning inflation to targets, avoidance of negative policy rates, and a strong influence of credit conditions on rate setting.

Bookmakers' mispricing of the disappeared home advantage in the German Bundesliga after the COVID-19 break
Christian Deutscher,David Winkelmann,Marius Ötting

The outbreak of COVID-19 in March 2020 led to a shutdown of economic activities in Europe. This included the sports sector, since public gatherings were prohibited. The German Bundesliga was among the first sport leagues realising a restart without spectators. Several recent studies suggest that the home advantage of teams was eroded for the remaining matches. Our paper analyses the reaction by bookmakers to the disappearance of such home advantage. We show that bookmakers had problems to adjust the betting odds in accordance to the disappeared home advantage, opening opportunities for profitable betting strategies.

Detecting and repairing arbitrage in traded option prices
Samuel N. Cohen,Christoph Reisinger,Sheng Wang

Option price data are used as inputs for model calibration, risk-neutral density estimation and many other financial applications. The presence of arbitrage in option price data can lead to poor performance or even failure of these tasks, making pre-processing of the data to eliminate arbitrage necessary. Most attention in the relevant literature has been devoted to arbitrage-free smoothing and filtering (i.e. removing) of data. In contrast to smoothing, which typically changes nearly all data, or filtering, which truncates data, we propose to repair data by only necessary and minimal changes. We formulate the data repair as a linear programming (LP) problem, where the no-arbitrage relations are constraints, and the objective is to minimise prices' changes within their bid and ask price bounds. Through empirical studies, we show that the proposed arbitrage repair method gives sparse perturbations on data, and is fast when applied to real world large-scale problems due to the LP formulation. In addition, we show that removing arbitrage from prices data by our repair method can improve model calibration with enhanced robustness and reduced calibration error.

Estimation of the number of irregular foreigners in Poland using non-linear count regression models
Maciej Beręsewicz,Katarzyna Pawlukiewicz

Population size estimation requires access to unit-level data in order to correctly apply capture-recapture methods. Unfortunately, for reasons of confidentiality access to such data may be limited. To overcome this issue we apply and extend the hierarchical Poisson-Gamma model proposed by Zhang (2008), which initially was used to estimate the number of irregular foreigners in Norway.

The model is an alternative to the current capture-recapture approach as it does not require linking multiple sources and is solely based on aggregated administrative data that include (1) the number of apprehended irregular foreigners, (2) the number of foreigners who faced criminal charges and (3) the number of foreigners registered in the central population register. The model explicitly assumes a relationship between the unauthorized and registered population, which is motivated by the interconnection between these two groups. This makes the estimation conditionally dependent on the size of regular population, provides interpretation with analogy to registered population and makes the estimated parameter more stable over time.

In this paper, we modify the original idea to allow for covariates and flexible count distributions in order to estimate the number of irregular foreigners in Poland in 2019. We also propose a parametric bootstrap for estimating standard errors of estimates. Based on the extended model we conclude that in as of 31.03.2019 and 30.09.2019 around 15,000 and 20,000 foreigners and were residing in Poland without valid permits. This means that those apprehended by the Polish Border Guard account for around 15-20% of the total.

Focused Bayesian Prediction
Ruben Loaiza-Maya,Gael M. Martin,David T. Frazier

We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After observing data, we update the prior to a posterior over these models, via a criterion that captures a user-specified measure of predictive accuracy. Under regularity, this update yields posterior concentration onto the element of the predictive class that maximizes the expectation of the accuracy measure. In a series of simulation experiments and empirical examples we find notable gains in predictive accuracy relative to conventional likelihood-based prediction.

GA-MSSR: Genetic Algorithm Maximizing Sharpe and Sterling Ratio Method for RoboTrading
Zezheng Zhang,Matloob Khushi

Foreign exchange is the largest financial market in the world, and it is also one of the most volatile markets. Technical analysis plays an important role in the forex market and trading algorithms are designed utilizing machine learning techniques. Most literature used historical price information and technical indicators for training. However, the noisy nature of the market affects the consistency and profitability of the algorithms. To address this problem, we designed trading rule features that are derived from technical indicators and trading rules. The parameters of technical indicators are optimized to maximize trading performance. We also proposed a novel cost function that computes the risk-adjusted return, Sharpe and Sterling Ratio (SSR), in an effort to reduce the variance and the magnitude of drawdowns. An automatic robotic trading (RoboTrading) strategy is designed with the proposed Genetic Algorithm Maximizing Sharpe and Sterling Ratio model (GA-MSSR) model. The experiment was conducted on intraday data of 6 major currency pairs from 2018 to 2019. The results consistently showed significant positive returns and the performance of the trading system is superior using the optimized rule-based features. The highest return obtained was 320% annually using 5-minute AUDUSD currency pair. Besides, the proposed model achieves the best performance on risk factors, including maximum drawdowns and variance in return, comparing to benchmark models. The code can be accessed at

Geographic Proximity and Insider Trading: Evidence from COVID-19
Henry, Erin,Plesko, George A.,Rawson, Caleb
We examine the role of geographic proximity and attentiveness on insider stock sales during the initial phases of the COVID-19 pandemic. We expect that insiders of firms with operational connections to China (“China insiders”) were more attentive to, and better understood, the implications of publicly available information about COVID-19 and acted upon it sooner than insiders at firms without operational connections to China (“non-China insiders”). We find that the stock sales of China insiders exhibit a significantly larger increase in profitability following the beginning of the pandemic than those of non-China insiders, largely driven by China insiders selling stock more frequently and earlier in the COVID-19 period than non-China insiders. Our results are consistent with China insiders anticipating declines in their firms’ stock that were driven by the systematic effects of COVID-19 ahead of other market participants. Our paper contributes to the insider trading literature which has otherwise found little evidence that corporate insider stock sales precede a market-driven stock price decline. The results also contribute to the emerging literature examining the economic and financial market effects of the COVID-19 pandemic.

Is COVID Revealing a CMBS Virus?
Griffin, John M.,Priest, Alex
Commercial loan valuations crucially depend on accurate loan income, but we find that underwritten income is commonly overstated when compared to actual property income. Consistent with these differences being purposeful, income overstatement varies widely and consistently across originators, is priced by originators, predictable ex-ante, and accompanied by clear inflation of past financials. Income overstatement is highly predictive of pre- and COVID-period loan distress, even after controlling for loan characteristics and geographic and time fixed effects. We document appraisal aggressiveness and abnormally low capitalization rates that are also related to current distress. Overall, aggressive CMBS underwriting practices appear to be revealing themselves in the current crisis.

Learning low-frequency temporal patterns for quantitative trading
Joel da Costa,Tim Gebbie

We consider the viability of a modularised mechanistic online machine learning framework to learn signals in low-frequency financial time series data. The framework is proved on daily sampled closing time-series data from JSE equity markets. The input patterns are vectors of pre-processed sequences of daily, weekly and monthly or quarterly sampled feature changes. The data processing is split into a batch processed step where features are learnt using a stacked autoencoder via unsupervised learning, and then both batch and online supervised learning are carried out using these learnt features, with the output being a point prediction of measured time-series feature fluctuations. Weight initializations are implemented with restricted Boltzmann machine pre-training, and variance based initializations. Historical simulations are then run using an online feedforward neural network initialised with the weights from the batch training and validation step. The validity of results are considered under a rigorous assessment of backtest overfitting using both combinatorially symmetrical cross validation and probabilistic and deflated Sharpe ratios. Results are used to develop a view on the phenomenology of financial markets and the value of complex historical data-analysis for trading under the unstable adaptive dynamics that characterise financial markets.

Not all Gold Shines in Crisis Times - COVID-19 Evidence
Baur, Dirk G.,Trench, Allan
This paper analyses the impact of the coronavirus pandemic on the share prices of gold firms, whose activities are spread across gold exploration, project development and gold mining with markedly different risk characteristics. We find evidence for COVID-induced stock market contagion leading to a decoupling of gold companies from the price of gold illustrating that gold shares are not a safe haven. The equity market and gold exposures differ significantly between explorers, developers and producers in normal times and are higher and more similar in crisis times. Our findings demonstrate that investors treat different firms differently in normal times and more equally in crisis times leading to mispricing and profit opportunities.

Robust fundamental theorems of asset pricing in discrete time
Huy N. Chau

This paper is devoted to the study of robust fundamental theorems of asset pricing in discrete time and finite horizon settings. The new concept "robust pricing system" is introduced to rule out the existence of model independent arbitrage opportunities. Superhedging duality and strategy are obtained.

Using detrended deconvolution foreign exchange network to identify currency status
Pengfei Xi,Shiyang Lai,Xueying Wang,Weiqiang Huang

This article proposed a hybrid detrended deconvolution foreign exchange network construction method (DDFEN), which combined the detrended cross-correlation analysis coefficient (DCCC) and the network deconvolution method together. DDFEN is designed to reveal the `true' correlation of currencies by filtering indirect effects in the foreign exchange networks (FXNs). The empirical results show that DDFEN can reflect the change of currency status in the long term and also perform more stable than traditional network construction methods.