Frontiers in Applied Mathematics and Statistics | Mathematical Finance section | New and Recent Articles
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RSS Feed for Mathematical Finance section in the Frontiers in Applied Mathematics and Statistics journal | New and Recent Articlesen-usFrontiers Feed Generator,version:12019-10-15T02:31:42.3229841+00:0060https://www.frontiersin.org/articles/10.3389/fams.2019.00049
https://www.frontiersin.org/articles/10.3389/fams.2019.00049
Did Developed and Developing Stock Markets React Similarly to Dow Jones During 2008 Crisis?2019-10-04T00:00:00ZErcan ÖzenMetin TetikThe aim of this study is to determine whether the stock indices of some developed and developing countries react similarly to the price movements in the Dow Jones Industrial Average (DJIA). In this study, the impact of DJIA on other indices during the 2008 global financial crisis, was explored by using the Vector Error Correction Model. The data used was analyzed in two periods: (1) the expansionary period; and (2) the contractionary period of the FED's policies. The results of the analysis indicate that the developed and emerging stock markets react differently to the DJIA. The results include important findings for decisions by financial investors and policy makers.]]>https://www.frontiersin.org/articles/10.3389/fams.2019.00010
https://www.frontiersin.org/articles/10.3389/fams.2019.00010
Editorial: Intertemporal Choice and Its Anomalies2019-02-11T00:00:00ZSalvador Cruz RambaudTaiki Takahashihttps://www.frontiersin.org/articles/10.3389/fams.2018.00055
https://www.frontiersin.org/articles/10.3389/fams.2018.00055
A Mathematical Analysis of the Improving Sequence Effect for Monetary Rewards2018-11-29T00:00:00ZSalvador Cruz RambaudMaría José Muñoz TorrecillasAdriana GarciaIn this paper, we mathematically formalize the concept of improving sequence effect, which is one of the main anomalies of the discounted utility model [1]. The improving sequence effect implies a preference for a given sequence of outcomes, which increase over time, and has been empirically demonstrated for both monetary and nonmonetary results (hedonic experiences and health-related outputs). Nevertheless, to date, there is no mathematical treatment of this anomaly in the context of intertemporal choice, which allows us to relate this paradox to other anomalies, such as the delay and magnitude effects. In this way, the present manuscript has filled this gap. More specifically, we have proved that the improving sequence effect for monetary rewards cannot be rationalized by using a separable discount function but only by considering a non-separable discount function. Moreover, under certain conditions, we have proved that the delay and magnitude effects are necessary conditions for the existence of the improving sequence effect.]]>https://www.frontiersin.org/articles/10.3389/fams.2018.00043
https://www.frontiersin.org/articles/10.3389/fams.2018.00043
How Are Individual Time Preferences Aggregated in Groups? A Laboratory Experiment on Intertemporal Group Decision-Making2018-10-02T00:00:00ZManami TsurutaKeigo InukaiThe study of intertemporal decision-making is an interdisciplinary scientific topic of economics, psychology, and neuroscience. Most of these studies focus on individual intertemporal decisions, but little is known about the relationship between groups and individual time preferences. As a result, we intend to assess the role of group intertemporal decision-making. We experimentally investigate how to aggregate individual time preferences by clarifying who has the most influence on group decisions among heterogeneous group members. We formulate two hypotheses. The first is the multilateral bargaining hypothesis, which is based on the multilateral bargaining model. If people employ this model to reach agreement, the most patient member in a group has the greatest impact on group choices. The second is the median voter hypothesis, which is based on the median voter model. When people employ this model to reach agreement, the median patient member in a group has the greatest impact on group choices. Here, we find that the median patient member in a group has a significant impact on group decisions in an unstructured bargaining situation. This finding suggests that people use the majority voting rule during group intertemporal decision-making. Thus, our findings support the median voter hypothesis. Furthermore, the results of a chat analysis show that this result is partially due to people's conformity with the majority opinion.]]>https://www.frontiersin.org/articles/10.3389/fams.2018.00037
https://www.frontiersin.org/articles/10.3389/fams.2018.00037
Understanding the World Economy in Terms of Networks: A Survey of Data-Based Network Science Approaches on Economic Networks2018-08-28T00:00:00ZFrank Emmert-StreibShailesh TripathiOlli Yli-HarjaMatthias DehmerThe purpose of this paper is to survey studies for estimating and analyzing different types of economic networks We focus on data-based approaches that allow the direct estimation of the networks from empirical data without the need of relying on theoretical assumptions. Due to the fact that there is a large variety of different economic networks, e.g., interbank, investment, director, ownership, financial, product or trade networks, we present a systematic categorization of these by the meaning of the “nodes” within these networks. These can correspond to banks, firms, investors, products, stocks etc. Furthermore, we review practical methods for graphically exploring such networks and discuss useful databases for obtaining the empirical data for the computational construction of economic networks.]]>https://www.frontiersin.org/articles/10.3389/fams.2018.00036
https://www.frontiersin.org/articles/10.3389/fams.2018.00036
The Magnitude and “Peanuts” Effects: Searching Implications2018-08-17T00:00:00ZSalvador Cruz RambaudAna M. Sánchez PérezThe framework of this paper is the field of decision-making processes in which people face the choice between probabilistic and dated rewards. Traditionally, the preferences for probabilistic outcomes have been analyzed by the Expected Utility (EU) model whilst the preferences for dated rewards have been studied by the Discounted Utility (DU) model. Nevertheless, recent empirical findings have revealed the existence of several anomalies or paradoxes in both contexts. Specifically, EU and DU models exhibit an anomaly affecting the amount of the reward, viz the “peanuts” and the magnitude effects, respectively, which seem to go in opposite directions. The aim of this paper is to analyze both effects jointly in a wide setting involving choices subject to risk and over a period of time, and thereby identify and consider the implications of one anomaly on the other.]]>https://www.frontiersin.org/articles/10.3389/fams.2018.00027
https://www.frontiersin.org/articles/10.3389/fams.2018.00027
Performance in Multi-Armed Bandit Tasks in Relation to Ambiguity-Preference Within a Learning Algorithm2018-07-25T00:00:00ZSong-Ju KimTaiki TakahashiEllsberg paradox in decision theory posits that people will inevitably choose a known probability of winning over an unknown probability of winning even if the known probability is low [1]. One of the prevailing theories that addresses the Ellsberg paradox is known as “ambiguity-aversion.” In this study, we investigated the properties of ambiguity-aversion in four distinct types of reinforcement learning algorithms: ucb1-tuned [2], modified ucb1-tuned, softmax [3], and tug-of-war [4, 5]. We took the following scenario as our sample, in which there were two slot machines and each machine dispenses a coin according to a probability that is generated by its own probability density function (PDF). We then investigated the choices of a learning algorithm in such multi-armed bandit tasks. There were different reactions in multi-armed bandit tasks, depending on the ambiguity-preference in the learning algorithms. Notably, we discovered a clear performance enhancement related to ambiguity-preference in a learning algorithm. Although this study does not directly address the issue of ambiguity-aversion theory highlighted in Ellsberg paradox, the differences among different learning algorithms suggest that there is room for further study regarding the Ellsberg paradox and the decision theory.]]>https://www.frontiersin.org/articles/10.3389/fams.2018.00020
https://www.frontiersin.org/articles/10.3389/fams.2018.00020
Mean-ETL Optimization in HorseRace Competition2018-06-11T00:00:00ZBarret P. ShaoIn this paper, we present the methodology and results of the portfolios submitted to the HorseRace competition. The nine portfolios were constructed by applying the Mean-ETL optimization approach. The Mean-ETL optimization approach uses three fundamental variables (CTEF, MQ, and REG10) and three stock universes (GL, XUS, and EM), with each of the three fundamental variables applied one at a time to one of the three universes. This study assesses the return of the nine portfolios, and we report that all of these Mean-ETL portfolios produce positive active returns and most of them are statistically significant. Additionally, MQ variable is found to be the best among these three variables in the Mean-ETL portfolio construction.]]>https://www.frontiersin.org/articles/10.3389/fams.2018.00017
https://www.frontiersin.org/articles/10.3389/fams.2018.00017
Effective Stock Selection and Portfolio Construction Within US, International, and Emerging Markets2018-05-24T00:00:00ZBijan BeheshtiIn this paper, we explore the ex-post attributes of 120 simulated portfolios across the U.S., International, and Emerging Markets. We estimate expected returns using a given global stock selection model employing Global Equity Rating (GLER) and Consensus Temporary Earnings Forecasting (CTEF) signals. Our portfolios are constructed under the Markowitz optimization framework and constrained at various tracking error levels. Further, an alpha alignment factor is applied to aid in portfolio construction. As a result of our research, we present the reader with three key findings. First, GLER and CTEF signals employed as the primary inputs to security selection result in portfolios with superior risk adjusted returns relative to the Russell 3000, MSCI AC World ex. US, and MSCI Emerging Markets benchmarks which they are measured against. Second, expanding the investment universe outside the U.S. increases the opportunity set yielding higher risk adjusted performance. Third, the incorporation of an alpha alignment factor within the portfolio construction process improves risk forecasts resulting in ex-post tracking error aligning more closely to ex-ante, and ultimately improving information ratios.]]>https://www.frontiersin.org/articles/10.3389/fams.2018.00016
https://www.frontiersin.org/articles/10.3389/fams.2018.00016
Decreasing Impatience for Health Outcomes and Its Relation With Healthy Behavior2018-05-23T00:00:00ZArthur E. AttemaStefan A. LipmanThere is a growing amount of literature suggesting people tend to behave inconsistently over time, which is driven by decreasing impatience. In addition, many studies have found relations between discounting estimates from experiments and field behavior, such as smoking cessation and dieting. However, these studies often did not separate time inconsistency from other factors such as utility curvature or the level of discounting. In order to establish the relation between field behavior and the degree of time inconsistency, it is therefore necessary to obtain a pure measure of the latter that is not distorted by these other factors. The present study implements a recently introduced measure of deviations from constant impatience, called the “Decreasing Impatience (DI)-index,” to estimate the degree to which people deviate from constant impatience. We provide the first extension of DI to health outcomes, both for individual and societal discounting using three different starting points. Moreover, we include a survey gathering information about several health-related behaviors, in order to test for the relationship between the amount of decreasing impatience and healthy behavior. We observe that decreasing impatience is the modal preference, although constant and increasing impatience are no exceptions, and, hence, these types of discounters should not be neglected. Furthermore, the DI-index is higher for individual health outcomes than for societal health outcomes, but is not distributed differently among the three classes of discounters. The DI-index decreases with starting period for individual health outcomes, but not for societal health outcomes. Very few significant relations between time inconsistency and self-reported health-related behavior were found.]]>https://www.frontiersin.org/articles/10.3389/fams.2018.00010
https://www.frontiersin.org/articles/10.3389/fams.2018.00010
The Amnesiac Lookback Option: Selectively Monitored Lookback Options and Cryptocurrencies2018-05-22T00:00:00ZHo-Chun Herbert ChangKevin LiThis study proposes a strategy to make the lookback option cheaper and more practical, and suggests the use of its properties to reduce risk exposure in cryptocurrency markets through blockchain enforced smart contracts and correct for informational inefficiencies surrounding prices and volatility. This paper generalizes partial, discretely-monitored lookback options that dilute premiums by selecting a subset of specified periods to determine payoff, which we call amnesiac lookback options. Prior literature on discretely-monitored lookback options considers the number of periods and assumes equidistant lookback periods in pricing partial lookback options. This study by contrast considers random sampling of lookback periods and compares resulting payoff of the call, put and spread options under floating and fixed strikes. Amnesiac lookbacks are priced with Monte Carlo simulations of Gaussian random walks under equidistant and random periods. Results are compared to analytic and binomial pricing models for the same derivatives. Simulations show diminishing marginal increases to the fair price as the number of selected periods is increased. The returns correspond to a Hill curve whose parameters are set by interest rate and volatility. We demonstrate over-pricing under equidistant monitoring assumptions with error increasing as the lookback periods decrease. An example of a direct implication for event trading is when shock is forecasted but its timing uncertain, equidistant sampling produces a lower error on the true maximum than random choice. We conclude that the instrument provides an ideal space for investors to balance their risk, and as a prime candidate to hedge extreme volatility. We discuss the application of the amnesiac lookback option and path-dependent options to cryptocurrencies and blockchain commodities in the context of smart contracts.]]>https://www.frontiersin.org/articles/10.3389/fams.2018.00004
https://www.frontiersin.org/articles/10.3389/fams.2018.00004
A Case Study of Forecasted Earnings Acceleration and Stock Selection in Global and Emerging Stock Markets2018-04-27T00:00:00ZJohn GuerardAnureet SaxenaThe allocation of scarce economic resources so as to maximize societal good is at the very core of human economic development. The key contribution of Markowitz [1] was to view this age-old activity in a scientifically rigorous manner, and bring three key elements to the forefront, namely, risk, return and correlations. Since the publication of Markowitz' seminal paper, investment professionals have expensed significant resources in identifying, understanding, and monetizing new sources of uncorrelated returns. This paper moves forward that narrative by focusing on Emerging Markets (EM) and demonstrating the effectiveness of earnings acceleration factors in building significantly better mean-variance optimized portfolios.]]>https://www.frontiersin.org/articles/10.3389/fams.2017.00027
https://www.frontiersin.org/articles/10.3389/fams.2017.00027
Uncertainty of Volatility Estimates from Heston Greeks2018-01-10T00:00:00ZOliver PfanteNils BertschingerVolatility is a widely recognized measure of market risk. As volatility is not observed it has to be estimated from market prices, i.e., as the implied volatility from option prices. The volatility index VIX making volatility a tradeable asset in its own right is computed from near- and next-term put and call options on the S&P 500 with more than 23 days and less than 37 days to expiration and non-vanishing bid. In the present paper we quantify the information content of the constituents of the VIX about the volatility of the S&P 500 in terms of the Fisher information matrix. Assuming that observed option prices are centered on the theoretical price provided by Heston's model perturbed by additive Gaussian noise we relate their Fisher information matrix to the Greeks in the Heston model. We find that the prices of options contained in the VIX basket allow for reliable estimates of the volatility of the S&P 500 with negligible uncertainty as long as volatility is large enough. Interestingly, if volatility drops below a critical value of roughly 3%, inferences from option prices become imprecise because Vega, the derivative of a European option w.r.t. volatility, and thereby the Fisher information nearly vanishes.]]>https://www.frontiersin.org/articles/10.3389/fams.2016.00022
https://www.frontiersin.org/articles/10.3389/fams.2016.00022
Disentangling the Information Content of Government Bonds and Credit Default Swaps: An Empirical Analysis on Sovereigns and Banks2016-12-02T00:00:00ZMichele L. BianchiMarco RoccoWe propose a multi-factor Gaussian model to analyze the dynamics of sovereign bond yields, as well as sovereign and banks CDS quotes. This paper has three objectives (all of them with relevant implications from a supervisory perspective): (1) disentangling the credit risk component of sovereign bonds from the interest rate component; (2) exploring the sovereign CDS-bond basis, i.e., the difference between sovereign CDS quotes and the corresponding bond yields; (3) inferring from CDS quotes the idiosyncratic component of a bank credit risk and analyzing its relation with sovereign risk. We cast the model in a state-space form with linear measurement function. To calibrate the model we consider a maximum likelihood estimation together with a Kalman filter method in which both the gradient vector and the Hessian matrix to be used in the optimization can be computed in closed form.]]>https://www.frontiersin.org/articles/10.3389/fams.2016.00016
https://www.frontiersin.org/articles/10.3389/fams.2016.00016
Interpretable Multiclass Models for Corporate Credit Rating Capable of Expressing Doubt2016-10-06T00:00:00ZLennart ObermannStephan WaackCorporate credit rating is a process to classify commercial enterprises based on their creditworthiness. Machine learning algorithms can construct classification models, but in general they do not tend to be 100% accurate. Since they can be used as decision support for experts, interpretable models are desirable. Unfortunately, interpretable models are provided by only few machine learners. Furthermore, credit rating often is a multiclass problem with more than two rating classes. Due to this fact, multiclass classification is often achieved via meta-algorithms using multiple binary learners. However, most state-of-the-art meta-algorithms destroy the interpretability of binary models. In this study, we present Thresholder, a binary interpretable threshold-based disjunctive normal form (DNF) learning algorithm in addition to modifications of popular multiclass meta-algorithms which maintain the interpretability of our binary classifier. Furthermore, we present an approach to express doubt in the decision of our model. Performance and model size are compared with other interpretable approaches for learning DNFs (RIPPER) and decision trees (C4.5) as well as non-interpretable models like random forests, artificial neural networks, and support vector machines. We evaluate their performances on three real-life data sets divided into three rating classes. In this case study all threshold-based and interpretable models perform equally well and significantly better than other methods. Our new Thresholder algorithm builds the smallest models while its performance is as good as the best methods of our case study. Furthermore, Thresholder marks many potential misclassifications in advance with a doubt label without increasing the classification error.]]>https://www.frontiersin.org/articles/10.3389/fams.2015.00014
https://www.frontiersin.org/articles/10.3389/fams.2015.00014
Investing in Global Markets: Big Data and Applications of Robust Regression2016-02-24T00:00:00ZJohn B. GuerardIn this analysis of the risk and return of stocks in global markets, we apply several applications of robust regression techniques in producing stock selection models and several optimization techniques in portfolio construction in global stock universes. We find that (1) that robust regression applications are appropriate for modeling stock returns in global markets; and (2) mean-variance techniques continue to produce portfolios capable of generating excess returns above transactions costs and statistically significant asset selection. We estimate expected return models in a global equity markets using a given stock selection model and generate statistically significant active returns from various portfolio construction techniques.]]>https://www.frontiersin.org/articles/10.3389/fams.2015.00013
https://www.frontiersin.org/articles/10.3389/fams.2015.00013
A Markov Chain Approximation for American Option Pricing in Tempered Stable-GARCH Models2016-01-08T00:00:00ZXiang ShiLihua ZhangYoung S. A. KimThis paper considers the American option pricing problem under the stochastic volatility models. In particular, we introduce the GARCH model with two heavy-tailed distributions: classical tempered stable (CTS) and normal tempered stable (NTS) distribution. Then we apply the Markov chain approach to compute the prices of American style options under these two models. Minimal entropy provides a convenient way to construct equivalent martingale measure (EMM) and allows us to overcome the difficulties in incorporating the Markov chain approximation. The convergence of the approximation is also proved. Both numerical and empirical results are analyzed to show the advantages and drawbacks of our approach.]]>https://www.frontiersin.org/articles/10.3389/fams.2015.00011
https://www.frontiersin.org/articles/10.3389/fams.2015.00011
The role of incompleteness in commodity futures markets2015-10-26T00:00:00ZTakashi KanamuraThis paper proposes a convenience yield-based pricing for commodity futures, which embeds incompleteness of commodity futures markets in convenience yields. By using the pricing method, we conduct empirical analyses of the prices of WTI crude oil, heating oil, and natural gas futures traded on the NYMEX in order to assess the incompleteness of energy futures markets. We show that the fluctuation from the incompleteness is partly driven by the fluctuation from convenience yields. In addition, it is shown that the incompleteness of natural gas futures market is more highlighted than the incompleteness of WTI crude oil and heating oil futures markets. We apply the implied market price of risk from the NYMEX data to pricing an Asian call option written on WTI crude oil futures. Finally, we try to apply the market incompleteness analysis to the post-crisis periods after 2009.]]>https://www.frontiersin.org/articles/10.3389/fams.2015.00010
https://www.frontiersin.org/articles/10.3389/fams.2015.00010
A novel view of suprathreshold stochastic resonance and its applications to financial markets2015-10-08T00:00:00ZGui CitovskySergio FocardiWe introduce an original application of Suprathreshold Stochastic Resonance (SSR). Given a noise-corrupted signal, we induce SSR in effort to filter the effect of the corrupting noise. This will yield a clearer version of the signal we desire to detect. We propose a financial application that can help forecast returns generated by big orders. We assume there exist return signals that correspond to big orders, which are hidden by noise from small scale traders. We induce SSR in an attempt to reveal these return signals.]]>https://www.frontiersin.org/articles/10.3389/fams.2015.00008
https://www.frontiersin.org/articles/10.3389/fams.2015.00008
General equilibrium pricing with information asymmetry2015-08-26T00:00:00ZYuzhong ZhangFangfei DongWe propose a general equilibrium model for asset pricing that incorporates asymmetric information as the key element determining security prices. In our setting, the concepts of completeness, arbitrage, state price and equivalent martingale measure are extended to the case of asymmetric information. Our model shows that in a so-called quasi-complete market, agents with differential information can reach an agreement on an universal equilibrium price. The corresponding state price and martingale measure are derived. The key intuition is that agents evaluate consumption choices conditioned on their private information and the public information generated by the price. As a consequence, information asymmetry can lead to mispricing as well.]]>