Unlocking the black box: Non-parametric option pricing before and during COVID-19.

<sec>Under the background that stock index options urgently need launching in China, the research on stock option pricing model has important theoretical and practical significance. In the traditional B-S-M model it is assumed that the volatility remains unchanged, which differs tremendously from the market’s reality. When the market fluctuates drastically, it is difficult to realize the risk management function of stock index options. Although in the Heston model, as one of the traditional stochastic volatility option pricing models, the correlation risk between the volatility and underlying price is taken into consideration, its pricing accuracy is still to be improved. From the quantum finance perspective, in this paper we use the Feynman path integral method to explore a more practical stock index option pricing model.</sec><sec>In this paper, we construct a Feynman path integral pricing model of stock index options with stochastic volatility by taking Hang Seng index option as the research object and Heston model as the control group. It is found that the Feynman path integral pricing model is significantly superior to the Heston model either at different strike prices on the same expiration date or at different expiration dates for the same strike price. The stock index option pricing model constructed in this paper can give the numerical solution of Feynman's pricing kernel, and directly realizes the forecast of stock index option price. The pricing accuracy is significantly improved compared with the pricing accuracy given by the Heston model through using the characteristic function method.</sec><sec>The remarkable advantages of Feynman path integral stock index option pricing model are as follows. Firstly, the path integral has advantages in solving multivariate problems: the Feynman pricing kernel represents all the information about pricing and can be easily expanded from one-dimensional to multidimensional case, so the change of closing price of stock index and volatility of underlying index can be taken into account simultaneously. Secondly, based on the relationship between the Feynman path generation principle and the law of large number, the mean values of pricing kernel obtained by MATLAB not only optimizes the calculation process, but also significantly improves the pricing accuracy. Feynman path integral is the main method in quantum finance, and the research in this paper will provide reference for its further application in the pricing of financial derivatives.</sec>

Abstract: Predictive maintenance (PdM) is a technique that keeps track of the condition and performance of equipment during normal operation to reduce the possibility of failures. Accurate anomaly detection, fault diagnosis, and fault prognosis form the basis of a PdM procedure. This paper aims to explore and discuss research addressing PdM using machine learning and complications using explainable artificial intelligence (XAI) techniques. While machine learning and artificial intelligence techniques have gained great interest in recent years, the absence of model interpretability or explainability in several machine learning models due to the black-box nature requires further research. Explainable artificial intelligence (XAI) investigates the explainability of machine learning models. This article overviews the maintenance strategies, post-hoc explanations, model-specific explanations, and model-agnostic explanations currently being used. Even though machine learningbased PdM has gained considerable attention, less emphasis has been placed on explainable artificial intelligence (XAI) approaches in predictive maintenance (PdM). Based on our findings, XAI techniques can bring new insights and opportunities for addressing critical maintenance issues, resulting in more informed decisions. The results analysis suggests a viable path for future studies. Conclusion: Even though machine learning-based PdM has gained considerable attention, less emphasis has been placed on explainable artificial intelligence (XAI) approaches in predictive maintenance (PdM). Based on our findings, XAI techniques can bring new insights and opportunities for addressing critical maintenance issues, resulting in more informed decisions. The results analysis suggests a viable path for future studies.

BackgroundEarly detection of sepsis is essential for its successful management. Although genome-wide association studies (GWAS) have shown potential in identifying sepsis-related genetic variants, they often involve heterogeneous patient groups and use single-locus analysis methods. Here, we aim to identify new sepsis susceptibility loci in post-surgical patients using an explainable artificial intelligence (XAI) approach applied to GWAS data.MethodsGWAS was performed in 750 post-operative patients with sepsis and 3,500 population controls. We applied a novel XAI-based methodology to GWAS-derived single nucleotide polymorphisms (SNPs) to predict sepsis and prioritize new genetic variants associated with post-operative sepsis susceptibility. We also assessed functional and enrichment effects using empirical data from integrated software tools and datasets, with the top-ranked variants and associated genes.ResultsOur XAI-GWAS approach showed a notable performance in predicting post-surgical sepsis and prioritized SNPs (such as rs17653532, rs1575081785, and rs74707084) with higher contribution to post-operative sepsis prediction. It also facilitated the discovery of post-operative sepsis risk loci with important functional implications related to gene expression regulation, DNA replication, cyclic nucleotide signaling, cell proliferation, and cardiac dysfunction.ConclusionThe combination of GWAS and XAI prioritized loci associated with post-operative sepsis susceptibility. The determination of key genes, such as PRIM2, SYNPR, and RBSN, through pre-operative blood tests could enhance risk stratification, enable early detection of post-operative sepsis, and guide targeted interventions to improve patient outcomes. Further research with additional and ethnically diverse cohorts comprising sepsis and non-sepsis patients undergoing major surgery is needed to validate these exploratory findings.

We introduce canonical representation of a call option premium which solves two open problems in option pricing theory. The first problem was posed by (Kassouf, 1969, pg. 694) who sought “theoretical substantiation” for his robust option pricing power law which eschewed assumptions about risk attitudes, rejected risk neutrality, and made no assumptions about stock price distribution. The second problem was posed by (Scott, 1987, pp. 423-424) who could not find a unique solution to the call option price in his option pricing model with stochastic volatility–without appealing to an equilibrium asset pricing model posed by Hull and White (1987) – and concluded: “[w]e cannot determine the price of a call option without knowing the price of another call on the same stock”. First, we show that under certain conditions derivative assets are superstructures of the underlying. Hence any option pricing or derivative pricing model in a given number field, based on an anticipating variable in an extended field, with coefficients in a subfield containing the underlying, is admissible for option pricing and or market timing. This explains the taxonomy of variegated option pricing formulae presented in Haug and Taleb (2008) critique of the Black and Scholes (1973); Merton (1973) formula. To wit, we claim that investor sentiment is an algebraic number. Accordingly, any polynomial which satisfies those criteria is admissible for price discovery and or market timing. Therefore, at least for empirical purposes, elaborate equations of mathematical physics or otherwise are unnecessary for pricing derivatives because much simpler adaptive polynomials in suitable algebraic numbers are functionally equivalent. Second, we prove, analytically, that Kassouf (1969) power law specification for option pricing is functionally equivalent to Black and Scholes (1973); Merton (1973) in an algebraic number field containing the underlying. In fact, our canonical representation of call option price is (i) convex in time to maturity, and (ii) depends on an algebraic number for the underlying – with coefficients based on observables in a subfield. Thus, paving the way for Wold decomposition of option prices, and providing theoretical contrast with Duan (1995) heuristic GARCH option pricing model. Third, our canonical representation theory has an inherent regenerative multifactor decomposition of call option price that (1) induces a duality theorem for call option premium, and (2) permits estimation of risk factor exposure for Greeks by standard [polynomial] regression procedures. Again, providing a theoretical (a) basis for option pricing of Greeks, and (b) solving Scott’s dual call option problem a fortiori by virtue of Riesz representation theory. Moreover, we show how our regenerative decomposition extends to (Wang and Caflish, 2010, pp. 4-5) Snell‘s envelope representation of a dual [American] call option premium. Fourth, when the Wold decomposition procedure is applied we are able to construct an empirical pricing kernel for call option based on residuals from a model of risk exposure to persistent and transient risk factors. This approach is distinguished from Chernov (2003) two stage procedure.

We introduce a canonical representation of call options, and propose a solution to two open problems in option pricing theory. The first problem was posed by (Kassouf, 1969, pg. 694) seeking “theoretical substantiation” for his robust option pricing power law which eschewed assumptions about risk attitudes, rejected risk neutrality, and made no assumptions about stock price distribution. The second problem was posed by (Scott, 1987, pp. 423-424) who could not find a unique solution to the call option price in his option pricing model with stochastic volatility–without appealing to an equilibrium asset pricing model by Hull and White (1987), and concluded: “[w]e cannot determine the price of a call option without knowing the price of another call on the same stock”. First, we show that under certain conditions derivative assets are superstructures of the underlying. Hence any option pricing or derivative pricing model in a given number field, based on an anticipating variable in an extended field, with coefficients in a subfield containing the underlying, is admissible for market timing. For the anticipating variable is an algebraic number that generates the subfield in which it is the root of an equation. Accordingly, any polynomial which satisfies those criteria is admissible for price discovery and or market timing. Therefore, at least for empirical purposes, elaborate models of mathematical physics or otherwise are unnecessary for pricing derivatives because much simpler adaptive polynomials in suitable algebraic numbers are functionally equivalent. Second, we prove, analytically, that Kassouf (1969) power law specification for option pricing is functionally equivalent to Black and Scholes (1973); Merton (1973) in an algebraic number field containing the underlying. In fact, we introduce a canonical polynomial representation theory of call option pricing convex in time to maturity, and algebraic number of the underlying–with coefficients based on observables in a subfield. Thus, paving the way for Wold decomposition of option prices, and subsequently laying a theoretical foundation for a GARCH option pricing model. Third, our canonical representation theory has an inherent regenerative multifactor decomposition of call option price that (1) induces a duality theorem for call option prices, and (2) permits estimation of risk factor exposure for Greeks by standard [polynomial] regression procedures. Thereby providing a theoretical (a) basis for option pricing of Greeks, and (b) solving Scott’s dual call option problem a fortiori with our duality theory in tandem with Riesz representation theory. Fourth, when the Wold decomposition procedure is applied we are able to construct an empirical pricing kernel for call option based on residuals from a model of risk exposure to persistent and transient risk factors. <div><br><div>Keywords: number theory; price discovery; derivatives pricing; asset pricing; canonical representation; Wold decomposition; empirical pricing kernel; option Greeks; dual option pricing</div></div>

We introduce a canonical representation of call options, and propose a solution to two open problems in option pricing theory. The first problem was posed by (Kassouf, 1969, pg. 694) seeking “theoretical substantiation” for his robust option pricing power law which eschewed assumptions about risk attitudes, rejected risk neutrality, and made no assumptions about stock price distribution. The second problem was posed by (Scott, 1987, pp. 423-424) who could not find a unique solution to the call option price in his option pricing model with stochastic volatility–without appealing to an equilibrium asset pricing model by Hull and White (1987), and concluded: “[w]e cannot determine the price of a call option without knowing the price of another call on the same stock”. First, we show that under certain conditions derivative assets are superstructures of the underlying. Hence any option pricing or derivative pricing model in a given number field, based on an anticipating variable in an extended field, with coefficients in a subfield containing the underlying, is admissible for market timing. For the anticipating variable is an algebraic number that generates the subfield in which it is the root of an equation. Accordingly, any polynomial which satisfies those criteria is admissible for price discovery and or market timing. Therefore, at least for empirical purposes, elaborate models of mathematical physics or otherwise are unnecessary for pricing derivatives because much simpler adaptive polynomials in suitable algebraic numbers are functionally equivalent. Second, we prove, analytically, that Kassouf (1969) power law specification for option pricing is functionally equivalent to Black and Scholes (1973); Merton (1973) in an algebraic number field containing the underlying. In fact, we introduce a canonical polynomial representation theory of call option pricing convex in time to maturity, and algebraic number of the underlying–with coefficients based on observables in a subfield. Thus, paving the way for Wold decomposition of option prices, and subsequently laying a theoretical foundation for a GARCH option pricing model. Third, our canonical representation theory has an inherent regenerative multifactor decomposition of call option price that (1) induces a duality theorem for call option prices, and (2) permits estimation of risk factor exposure for Greeks by standard [polynomial] regression procedures. Thereby providing a theoretical (a) basis for option pricing of Greeks, and (b) solving Scott’s dual call option problem a fortiori with our duality theory in tandem with Riesz representation theory. Fourth, when the Wold decomposition procedure is applied we are able to construct an empirical pricing kernel for call option based on residuals from a model of risk exposure to persistent and transient risk factors. <div><br><div>Keywords: number theory; price discovery; derivatives pricing; asset pricing; canonical representation; Wold decomposition; empirical pricing kernel; option Greeks; dual option pricing</div></div>

This study conducts a comparative analysis of traditional and machine learning models for financial option pricing, using historical stock prices and interest rates data. Traditional models such as the Black-Scholes, Heston, Merton Jump-Diffusion, and GARCH are evaluated against machine learning models including Multi-Layer Perceptrons (MLPs) and Long Short-Term Memory (LSTM) networks. The analysis employs performance metrics like Mean Squared Error (MSE), Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and R value. Results indicate that the GARCH model excels in predictive accuracy due to its ability to capture volatility clustering, while machine learning models, especially the Tuned Neural Network, demonstrate superior flexibility and adaptability in managing complex non-linear relationships in financial data. Traditional models, although theoretically robust, show limitations under varying market conditions. The study underscores the potential of hybrid approaches combining traditional and machine learning techniques to leverage their respective strengths for more accurate and reliable option pricing. Future research directions include exploring advanced machine learning architectures and improving model transparency through explainable AI.

This paper presents a deep learning approach for option pricing using a long short-term memory (LSTM) neural network applied to European call options on the S&P 500 index. We utilize a rolling window approach that trains 12 instances of the LSTM model, one for each month of 2021. To gain further insight into the model performance, we use explainable artificial intelligence (XAI) through SHapley Additive Explanations (SHAP). We find that the LSTM model outperforms the Black–Scholes and the Heston models and a multilayer perceptron (MLP) neural network regarding overall pricing accuracy. Most notably, the time-sequencing nature of LSTM enables the proposed model to capture sufficient short-term volatility from recently traded options. This result is still robust when controlling for time-varying volatility dynamics. Thus, the model is less prone to measurement errors in volatility.

The need for studies connecting the machine’s explainability with granularity is very important, especially for a detailed understanding of how data is fragmented and processed according to the domain of discourse. We develop a system called RYEL based on subject-matter experts about the legal case process, facts, pieces of evidence, and how to analyze the merits of a case. Through this system, we study the Explainable Artificial Intelligence (XAI) approach using Knowledge Graphs (KG) and enforcement unsupervised algorithms which results are expressed in an Explanatory Graphical Interface (EGI). The evidence and facts of a legal case are represented as knowledge graphs. Granular Computing (GrC) techniques are applied in the graph when processing nodes and edges using object types, properties, and relations. Through RYEL we propose new definitions for Explainable Artificial Intelligence (XAI) and Interpretable Artificial Intelligence (IAI) in a much better way and will help us to cover a technological spectrum that has not yet been covered and promises to be a new area of study which we call Interpretation-Assessment/Assessment-Interpretation (IA-AI) that consists not only in explaining machine inferences but the interpretation and assessment from a user according to a context. It is proposed a new focus-centered organization in which the XAI-IAI will be able to work and will allow us to explain in more detail the method implemented by RYEL. We believe our system has an explanatory and interpretive nature and could be used in other domains of discourse, some examples are: (1) the interpretation a doctor has about a disease and the assessment of using certain medicine, (2) the interpretation a psychologist has from a patient and the assessment for a psychological application treatment, (3) or how a mathematician interprets a real-world problem and makes an assessment about which mathematical formula to use. However, now we focus on the legal domain.KeywordsRYELExplanatory Graphical Interface (EGI)Interpretation-Assessment/Assessment-Interpretation (IA-AI)Explainable Artificial Intelligence (XAI)Granular Computing (GrC)Explainable legal knowledge representationCase-Based Reasoning (CBR)

One of the central goals in finance is to find better models for pricing and hedging financial derivatives such as call and put options. We present a new semi-nonparametric approach to risk-neutral density extraction from option prices, which is based on an extension of the concept of mixture density networks. The central idea is to model the shape of the risk-neutral density in a flexible, nonlinear way as a function of the time horizon. Thereby, stylized facts such as negative skewness and excess kurtosis are captured. The approach is applied to a very large set of intraday options data on the FTSE 100 recorded at LIFFE. It is shown to yield significantly better results in terms of out-of-sample pricing accuracy in comparison to the basic and an extended Black-Scholes model. It is also significantly better than a more elaborate GARCH option pricing model which includes a time-dependent volatility process. From the perspective of risk management, the extracted risk-neutral densities provide valuable information for value-at-risk estimations.

The Cox-Ross-Rubinstein (CRR) market model is one of the simplest and easiest ways to analyze the option pricing model. CRR has been employed to evaluate a European Option Pricing (call options) model without complex elements, including dividends, stocks, and stock indexes. Instead, it considers only a continuous dividend yield, futures, and currency options. The CRR model is simple but strong enough to describe the general economic intuition behind option pricing and its principal techniques. Also, it gives us basic ideas on how to develop financial products based on current deviations and volatilities. The paper investigates the CRR model using numerical approaches with python code. It provides a practical event using the mathematical model to demonstrate the application of the model in the financial market. First, the paper provides a simple example to figure out the basic concept of the model. Only a two-period binomial model based on the introductory definitions of the call options makes us understand the concept more easily and quickly. Next, we used actual data on Tesla stock fluctuations from the Nasdaq website (See section 3). We developed the python code to make it easier to understand figures, including tables and graphs. The code allows us to visualize and simplify the model and output data. The code analyzes the stock data to evaluate the probability of the stock’s price increasing or decreasing. Then, it used the CRR model to estimate all possible cases for the stock’s prices and investigate the call and put option pricing. The code was based on the introductory code of binomial option pricing, but we improved it to get more information and provide more detailed results from the data. The detailed codes are provided in section 3 of the paper. As a result, we believe the CRR model is a fundamental formula, but the improved python code can suggest a new direction for evaluating the probability and investigating the value of the stocks. Also, we expect to develop the code to extend the Black Scholes Pricing model, increasing the number of periods.

This article elaborates upon the intuition underlying Doherty and Garven's (1986) option pricing model and extends its basic results to a further consideration of the implications of limited liability and asymmetric taxes for pricing and incentives in property-liability insurance. When compared with CAPM-based models of the insurer, a number of important insights emerge. First, the option pricing framework is shown to encompass the CAPM framework as a special case and may help to explain a number of empirical phenomena. Second, the option pricing framework is used to develop a risk hypothesis which suggests that limited liability and asymmetric taxes provide mutuals with greater disincentives for riskbearing than stock companies, even in the absence of owner/manager conflicts. Although the property-liability insurance industry has been subject to price regulation for many years, researches have only recently derived valuation formulas for property-liability insurance firms. To date, the most promising approaches apply financial theories such as the capital asset pricing model (CAPM) (see Biger and Kahane, 1978; Fairley, 1979; Hill, 1979; Hill and Modigliani, 1987; and Myers and Cohn, 1987) and the option pricing model (see Doherty and Garven, 1986; Cummins, 1988b; and Derrig, 1989). Although details vary, these models are generally organized around the principle that the rate of underwriting profit must be set so as to produce a fair, or competitive rate of return on equity.(1) In spite of their common origins, CAPM and option-based insurance pricing models produce substantially different predictions concerning pricing and incentives for property-liability insurance. It will be shown that these differences are primarily due to the manner in which the effects of insolvency and taxes are modeled. Essentially, CAPM-based models implicitly assume that shareholders have unlimited liability, whereas option-based models assume that shareholders' liability is limited. Similarly, by assuming that losses are rebated at the same rate at which gains are taxed, CAPM-based models effectively assign unlimited liability to the government, whereas option-based models limit the government's liability by assuming that gains and losses are taxed in an asymmetric fashion. This article elaborates upon the intuition underlying Doherty and Garven's (1986) option pricing model and extends its basic results to a further consideration of the implications of limited liability and asymmetric taxes for pricing and incentives in property-liability insurance. This is accomplished by comparing and contrasting option-based with CAPM-based models of the insurance firm. This analysis yields a number of important insights, such as the fact that the option pricing framework encompasses the CAPM framework as a special case. The option pricing model also has several practical advantages over the CAPM. For example, it is not plagued by the CAPM's well-known parameter estimation problems; indeed, it may help to explain the causes of these problems.(2) The option pricing model also provides an explicit linkage between fair return and the risks of insolvency and tax shield underutilization, whereas the CAPM totally ignores these effects. The option pricing model also calls attention to some important incentive effects concerning risk-bearing that are not captured by the CAPM. Under the CAPM, asset and liability is not particularly important so long as these claims are priced to yield appropriate risk-adjusted rates of return. However, under the option pricing model, the extent to which firms will seek to increase or avoid through their investment and underwriting policy choices depends upon the likelihood of being taxed or becoming insolvent. Consequently, the application of the option pricing framework makes it possible to develop a risk hypothesis which predicts that mutual insurers will seek less exposure to than stock companies. …

This study introduces an explainable artificial intelligence (XAI) approach of convolutional neural networks (CNNs) for classification in vibration signals analysis. First, vibration signals are transformed into images by short-time Fourier transform (STFT). A CNN is applied as classification model, and Gradient class activation mapping (Grad-CAM) is utilized to generate the attention of model. By analyzing the attentions, the explanation of classification models for vibration signals analysis can be carried out. Finally, the verifications of attention are introduced by neural networks, adaptive network-based fuzzy inference system (ANFIS), and decision trees to demonstrate the proposed results. By the proposed methodology, the explanation of model using highlighted attentions is carried out.

In this work we propose a workflow to deal with overlaid images—images with superimposed text and company logos—, which is very common in underwater monitoring videos and surveillance camera footage. It is demonstrated that it is possible to use Explaining Artificial Intelligence to improve deep learning models performance for image classification tasks in general. A deep learning model trained to classify metal surface defect, which previously had a low performance, is then evaluated with Layer-wise relevance propagation—an Explaining Artificial Intelligence technique—to identify problems in a dataset that hinder the training of deep learning models in a wide range of applications. Thereafter, it is possible to remove this unwanted information from the dataset—using different approaches: from cutting part of the images to training a Generative Inpainting neural network model—and retrain the model with the new preprocessed images. This proposed methodology improved F1 score in 20% when compared to the original trained dataset, validating the proposed workflow.

Autonomous driving has reached significant milestones in research and development over the last few decades. There is growing attention in the area as the utilization of autonomous vehicles (AVs) assurances safer and more environmentally-friendly transportation systems. Adverse environmental conditions like dust or sandstorms, fog, heavy snow, and rain conditions are unsafe limitations on the function of the cameras by decreasing visibility and influencing driving safety. These limitations affect the performance of tracking and detection methods applied in traffic surveillance systems and autonomous driving applications. Using the fast development in mathematically powerful artificial intelligence (AI) approaches, AVs could sense their atmosphere using higher accuracy, make safer real-world decisions, and work consistently without user intervention. Therefore, this paper proposes a Complex Data Analysis for Adverse Weather Detection in Autonomous Vehicles Using Explainable Artificial Intelligence (CDAAWD-AVXAI) approach. The CDAAWD-AVXAI approach improves the safety and reliability of AVs by ensuring robust weather detection. Initially, the presented CDAAWD-AVXAI approach applies image pre-processing by utilizing the median filter (MF) model to reduce noise and enhance the quality of input images. The CapsNet model is employed for feature extraction to recognize spatial hierarchies and capture intricate patterns from complex visual data. Moreover, the temporal convolutional network (TCN) model detects adverse weather conditions. To further enhance performance, the hyperparameter tuning of the TCN model is performed by implementing the improved dung beetle optimization (IDBO) model. Finally, the XAI using LIME provides transparency and interpretability, allowing stakeholders to understand the decision-making process behind weather condition predictions. The stimulation study of the CDAAWD-AVXAI technique is performed under the DAWN dataset. The experimental validation of the CDAAWD-AVXAI technique portrayed a superior accuracy value of 98.83% over existing methods.