In this paper, we present a novel approach to solving the American put options pricing model by hugely relying on a front-fixing Crank-Nicolson finite difference method. Since the American put option pricing model is a widely used financial model for valuing an option with the right to sell an underlying asset at a fated price which generally decided in advance. The method we proposed here, solves the problem of early exercise by introducing a front-fixing technique that permits for efficient and accurate valuation of an American put option. As in the comparison to other approaches in the existing literature, we can assert that this method is stable, accurate, consistent, and efficient. The results that we obtained here from the numerical experiments demonstrate not only the efficacy of the proposed method but also in consistently and accurately pricing American put options with a stable scheme. Under some appropriate conditions on the step size discretization, we also show the positivity and monotonicity of the coefficient involved in the numerical scheme used.
Despite increasing AI chatbot deployment in public discourse, empirical evidence on their capacity to foster intercultural empathy remains limited. Through a randomized experiment, we assessed how different AI deliberation approaches--cross-cultural deliberation (presenting other-culture perspectives), own-culture deliberation (representing participants' own culture), and non-deliberative control--affect intercultural empathy across American and Latin American participants. Cross-cultural deliberation increased intercultural empathy among American participants through positive emotional engagement, but produced no such effects for Latin American participants, who perceived AI responses as culturally inauthentic despite explicit prompting to represent their cultural perspectives. Our analysis of participant-driven feedback, where users directly flagged and explained culturally inappropriate AI responses, revealed systematic gaps in AI's representation of Latin American contexts that persist despite sophisticated prompt engineering. These findings demonstrate that current approaches to AI cultural alignment--including linguistic adaptation and explicit cultural prompting--cannot full
This paper studies the regularity of finite-maturity American value functions in the Heston model. Although the Heston operator is degenerate when the volatility is zero, we are able to establish C^{1,2} regularity of the American value functions in the exercise domain and the smooth-fit principle, using PDE techniques.
We study the obstacle problem associated with the American chooser option. The obstacle is given by the maximum of an American call option and an American put option, which, in turn, can be expressed as the maximum of the solutions to the corresponding obstacle problems. This structure makes the obstacle problem particularly challenging and non-trivial. Using theoretical analysis, we overcome these difficulties and establish the existence and uniqueness of a strong solution. Furthermore, we rigorously prove the monotonicity and smoothness of the free boundary arising from the obstacle problem.
Representations of AI agents in user interfaces and robotics are predominantly White, not only in terms of facial and skin features, but also in the synthetic voices they use. In this paper we explore some unexpected challenges in the representation of race we found in the process of developing an U.S. English Text-to-Speech (TTS) system aimed to sound like an educated, professional, regional accent-free African American woman. The paper starts by presenting the results of focus groups with African American IT professionals where guidelines and challenges for the creation of a representative and appropriate TTS system were discussed and gathered, followed by a discussion about some of the technical difficulties faced by the TTS system developers. We then describe two studies with U.S. English speakers where the participants were not able to attribute the correct race to the African American TTS voice while overwhelmingly correctly recognizing the race of a White TTS system of similar quality. A focus group with African American IT workers not only confirmed the representativeness of the African American voice we built, but also suggested that the surprising recognition results may
Artificial intelligence (AI) systems often reflect biases from economically advanced regions, marginalizing contexts in economically developing regions like Latin America due to imbalanced datasets. This paper examines AI representations of diverse Latin American contexts, revealing disparities between data from economically advanced and developing regions. We highlight how the dominance of English over Spanish, Portuguese, and indigenous languages such as Quechua and Nahuatl perpetuates biases, framing Latin American perspectives through a Western lens. To address this, we introduce a culturally aware dataset rooted in Latin American history and socio-political contexts, challenging Eurocentric models. We evaluate six language models on questions testing cultural context awareness, using a novel Cultural Expressiveness metric, statistical tests, and linguistic analyses. Our findings show that some models better capture Latin American perspectives, while others exhibit significant sentiment misalignment (p < 0.001). Fine-tuning Mistral-7B with our dataset improves its cultural expressiveness by 42.9%, advancing equitable AI development. We advocate for equitable AI by prioritizi
An accurate characterization of the quark-gluon plasma requires understanding of how electromagnetic effects affect the processes mediated by the strong force. All the scenarios in which the plasma emerges, either in nature or in the laboratory, involve strong electromagnetic fields. The early universe, compact astrophysical objects, or ultra-relativistic heavy-ion collisions harbor the most intense fields we know. Researches from the Latin America region have made a substantial contribution on this subject and the \lq\lq Latin American Network on Electromagnetic Effects in Strongly Interacting Matter" aims to cluster efforts to address open questions related to these systems, boosting collaborations and interaction among its members and connecting Latin American institutions with institutions from the rest of the world. In face of the upcoming experimental programs and new facilities, our mission is to bring together experimentalists, phenomenologists and theorists to better explore the properties of strongly interacting matter in the presence of intense electromagnetic fields. This document describes succinctly the recent contributions from researchers of the Latin American regio
An accurate valuation of American call options is critical in most financial decision making environments. However, traditional models like the Barone-Adesi Whaley (B-AW) and Binomial Option Pricing (BOP) methods fall short in handling the complexities of early exercise and market dynamics present in American options. This paper proposes a Modular Neural Network (MNN) model which aims to capture the key aspects of American options pricing. By dividing the prediction process into specialized modules, the MNN effectively models the non-linear interactions that drive American call options pricing. Experimental results indicate that the MNN model outperform both traditional models as well as a simpler Feed-forward Neural Network (FNN) across multiple stocks (AAPL, NVDA, QQQ), with significantly lower RMSE and nRMSE (by mean). These findings highlight the potential of MNNs as a powerful tool to improve the accuracy of predicting option prices.
We introduce a modular framework that extends the signature method to handle American option pricing under evolving volatility roughness. Building on the signature-pricing framework of Bayer et al. (2025), we add three practical innovations. First, we train a gradient-boosted ensemble to estimate the time-varying Hurst parameter H(t) from rolling windows of recent volatility data. Second, we feed these forecasts into a regime switch that chooses either a rough Bergomi or a calibrated Heston simulator, depending on the predicted roughness. Third, we accelerate signature-kernel evaluations with Random Fourier Features (RFF), cutting computational cost while preserving accuracy. Empirical tests on S&P 500 equity-index options reveal that the assumption of persistent roughness is frequently violated, particularly during stable market regimes when H(t) approaches or exceeds 0.5. The proposed hybrid framework provides a flexible structure that adapts to changing volatility roughness, improving performance over fixed-roughness baselines and reducing duality gaps in some regimes. By integrating a dynamic Hurst parameter estimation pipeline with efficient kernel approximations, we propo
In this paper we propose a semi-analytic approach to pricing American options for time-dependent jump-diffusions models with exponential jumps The idea of the method is to further generalize our approach developed for pricing barrier, [Itkin et al., 2021], and American, [Carr and Itkin, 2021; Itkin and Muravey, 2023], options in various time-dependent one factor and even stochastic volatility models. Our approach i) allows arbitrary dependencies of the model parameters on time; ii) reduces solution of the pricing problem for American options to a simpler problem of solving a system of an algebraic nonlinear equation for the exercise boundary and a linear Fredholm-Volterra equation for the the option price; iii) the options Greeks solve a similar Fredholm-Volterra linear equation obtained by just differentiating Eq. (25) by the required parameter. Once done, the American option price is presented in close form.
COVID-19 has aided the spread of racism, as well as national insecurity, distrust of immigrants, and general xenophobia, both of which may be linked to the rise in anti-Asian hate crimes during the pandemic. Coronavirus Disease 2019(COVID19) is thought to have originated in late December 2019 in Wuhan, China, and quickly spread across the world during the spring months of 2020. Asian Americans recorded in increase in racially based hate crimes including physical abuse and intimidation as COVID-19 spread throughout the United States. This research study was conducted by high school students in the Bay Area to compare the intention and characteristics of hate crimes against Asian Americans to hate crimes against African Americans. According to studies of both victim-related and most offender-related variables, hate crimes against Asian Americans have been rapidly growing in the United States and vary from those against African Americans. This leads to an investigation into the racial disparity between Asian American offenders and those of other races. The nature and characteristics of hate crimes against Asian Americans are compared to those of hate crimes against African Americans i
We conducted a global comparative analysis of the coverage of American topics in different language versions of Wikipedia, using over 90 million Wikidata items and 40 million Wikipedia articles in 58 languages. Our study aimed to investigate whether Americanization is more or less dominant in different regions and cultures and to determine whether interest in American topics is universal.
Since most of the traded options on individual stocks is of American type it is of interest to generalize the results obtained in semi-static trading to the case when one is allowed to statically trade American options. However, this problem has proved to be elusive so far because of the asymmetric nature of the positions of holding versus shorting such options. Here we provide a unified framework and generalize the fundamental theorem of asset pricing (FTAP) and hedging dualities in arXiv:1502.06681 (to appear in Annals of Applied Probability) to the case where the investor can also short American options. Following arXiv:1502.06681, we assume that the longed American options are divisible. As for the shorted American options, we show that the divisibility plays no role regarding arbitrage property and hedging prices. Then using the method of enlarging probability spaces proposed in arXiv:1604.05517, we convert the shorted American options to European options, and establish the FTAP and sub- and super-hedging dualities in the enlarged space both with and without model uncertainty.
Three state-of-the-art language-and-image AI models, CLIP, SLIP, and BLIP, are evaluated for evidence of a bias previously observed in social and experimental psychology: equating American identity with being White. Embedding association tests (EATs) using standardized images of self-identified Asian, Black, Latina/o, and White individuals from the Chicago Face Database (CFD) reveal that White individuals are more associated with collective in-group words than are Asian, Black, or Latina/o individuals. In assessments of three core aspects of American identity reported by social psychologists, single-category EATs reveal that images of White individuals are more associated with patriotism and with being born in America, but that, consistent with prior findings in psychology, White individuals are associated with being less likely to treat people of all races and backgrounds equally. Three downstream machine learning tasks demonstrate biases associating American with White. In a visual question answering task using BLIP, 97% of White individuals are identified as American, compared to only 3% of Asian individuals. When asked in what state the individual depicted lives in, the model r
We consider the problem of pricing American Exchange options driven by a Lévy process. We study the properties of American Exchange options, we represented it as the sum of the price of the corresponding European exchange option price and an early exercise premium. Secondly, we show some properties of the free boundary and give an approximative formula of an American Exchange option.
We study the upper and lower bounds for prices of European and American style options with the possibility of an external termination, meaning that the contract may be terminated at some random time. Under the assumption that the underlying market model is incomplete and frictionless, we obtain duality results linking the upper price of a vulnerable European option with the price of an American option whose exercise times are constrained to times at which the external termination can happen with a non-zero probability. Similarly, the upper and lower prices for an vulnerable American option are linked to the price of an American option and a game option, respectively. In particular, the minimizer of the game option is only allowed to stop at times which the external termination may occur with a non-zero probability.
This pilot study explored physiological responses to playing and listening to the Native American flute. Autonomic, electroencephalographic (EEG), and heart rate variability (HRV) metrics were recorded while participants (N = 15) played flutes and listened to several styles of music. Flute playing was accompanied by an 84% increase in HRV (p < .001). EEG theta (4-8 Hz) activity increased while playing flutes (p = .007) and alpha (8-12 Hz) increased while playing lower-pitched flutes (p = .009). Increase in alpha from baseline to the flute playing conditions strongly correlated with experience playing Native American flutes (r = +.700). Wide-band beta (12-25 Hz) decreased from the silence conditions when listening to solo Native American flute music (p = .013). The findings of increased HRV, increasing slow-wave rhythms, and decreased beta support the hypothesis that Native American flutes, particularly those with lower pitches, may have a role in music therapy contexts. We conclude that the Native American flute may merit a more prominent role in music therapy and that a study of the effects of flute playing on clinical conditions, such as post-traumatic stress disorder (PTSD),
Binomial tree methods (BTM) and explicit difference schemes (EDS) for the variational inequality model of American options with time dependent coefficients are studied. When volatility is time dependent, it is not reasonable to assume that the dynamics of the underlying asset's price forms a binomial tree if a partition of time interval with equal parts is used. A time interval partition method that allows binomial tree dynamics of the underlying asset's price is provided. Conditions under which the prices of American option by BTM and EDS have the monotonic property on time variable are found. Using convergence of EDS for variational inequality model of American options to viscosity solution the decreasing property of the price of American put options and increasing property of the optimal exercise boundary on time variable are proved. First, put options are considered. Then the linear homogeneity and call-put symmetry of the price functions in the BTM and the EDS for the variational inequality model of American options with time dependent coefficients are studied and using them call options are studied.
A variational inequality for pricing the perpetual American option and the corresponding difference equation are considered. First, the maximum principle and uniqueness of the solution to variational inequality for pricing the perpetual American option are proved. Then the maximum principle, the existence and uniqueness of the solution to the difference equation corresponding to the variational inequality for pricing the perpetual American option and the solution representation are provided and the fact that the solution to the difference equation converges to the viscosity solution to the variational inequality is proved. It is shown that the limits of the prices of variational inequality and BTM models for American Option when the maturity goes to infinity do not depend on time and they become the prices of the perpetual American option.
American options are the reference instruments for the model calibration of a large and important class of single stocks. For this task, a fast and accurate pricing algorithm is indispensable. The literature mainly discusses pricing methods for American options that are based on Monte Carlo, tree and partial differential equation methods. We present an alternative approach that has become popular under the name de-Americanization in the financial industry. The method is easy to implement and enjoys fast run-times. Since it is based on ad hoc simplifications, however, theoretical results guaranteeing reliability are not available. To quantify the resulting methodological risk, we empirically test the performance of the de-Americanization method for calibration. We classify the scenarios in which de-Americanization performs very well. However, we also identify the cases where de-Americanization oversimplifies and can result in large errors.