Daily Papers

This paper studies the use of randomized neural networks for the estimation of exposure profiles and unilateral CVA of American options within a Monte Carlo framework. The analysis is carried out separately under both Black-Scholes and Heston dynamics, combining American option valuation, expected exposure and potential future exposure estimation, and unilateral CVA calculation with portfolio netting effects. The numerical experiment compares this approach with the classical Least-Squares Monte Carlo (LSM) used as a benchmark in both low-dimensional single-asset and high-dimensional multi-asset scenarios, and also includes a path convergence test and a sensitivity analysis. The results show that the randomized feedforward neural network approach preserves convergence to the LSM benchmark when it is extended from pricing to exposure and CVA estimation, while its main advantage appears in high-dimensional problems, where it scales more efficiently and leads to lower computational cost. These results support the use of randomized neural networks as a useful alternative for exposure and CVA estimation in high-dimensional American-style options.

We apply a physics-informed deep-learning approach the PINN approach to the Black-Scholes equation for pricing American and European options. We test our approach on both simulated as well as real market data, compare it to analytical/numerical benchmarks. Our model is able to accurately capture the price behaviour on simulation data, while also exhibiting reasonable performance for market data. We also experiment with the architecture and learning process of our PINN model to provide more understanding of convergence and stability issues that impact performance.

In this work, we introduce amortizing perpetual options (AmPOs), a fungible variant of continuous-installment options suitable for exchange-based trading. Traditional installment options lapse when holders cease their payments, destroying fungibility across units of notional. AmPOs replace explicit installment payments and the need for lapsing logic with an implicit payment scheme via the decay of the claimable notional. This amortization ensures all units evolve identically, preserving fungibility. We demonstrate that AmPO valuation can be reduced to an equivalent vanilla perpetual American option on a dividend-paying asset. This enables analytical expressions for the exercise boundaries and risk-neutral valuations for calls and puts. These formulas and relations allow us to derive the Greeks and study comparative statics with respect to the amortization rate. Illustrative numerical case studies demonstrate how the amortization rate shapes option behavior and reveal the resulting tradeoffs in the effective volatility sensitivity.

We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.

Researchers have been using Neural Networks and other related machine-learning techniques to price options since the early 1990s. After three decades of improvements in machine learning techniques, computational processing power, cloud computing, and data availability, this paper is able to provide a comparison of using Google Cloud's AutoML Regressor, TensorFlow Neural Networks, and XGBoost Gradient Boosting Decision Trees for pricing European Options. All three types of models were able to outperform the Black Scholes Model in terms of mean absolute error. These results showcase the potential of using historical data from an option's underlying asset for pricing European options, especially when using machine learning algorithms that learn complex patterns that traditional parametric models do not take into account.

The optimal stopping problem is a category of decision problems with a specific constrained configuration. It is relevant to various real-world applications such as finance and management. To solve the optimal stopping problem, state-of-the-art algorithms in dynamic programming, such as the least-squares Monte Carlo (LSMC), are employed. This type of algorithm relies on path simulations using only the last price of the underlying asset as a state representation. Also, the LSMC was thinking for option valuation where risk-neutral probabilities can be employed to account for uncertainty. However, the general optimal stopping problem goals may not fit the requirements of the LSMC showing auto-correlated prices. We employ a data-driven method that uses Monte Carlo simulation to train and test artificial neural networks (ANN) to solve the optimal stopping problem. Using ANN to solve decision problems is not entirely new. We propose a different architecture that uses convolutional neural networks (CNN) to deal with the dimensionality problem that arises when we transform the whole history of prices into a Markovian state. We present experiments that indicate that our proposed architecture improves results over the previous implementations under specific simulated time series function sets. Lastly, we employ our proposed method to compare the optimal exercise of the financial options problem with the LSMC algorithm. Our experiments show that our method can capture more accurate exercise opportunities when compared to the LSMC. We have outstandingly higher (above 974\% improvement) expected payoff from these exercise policies under the many Monte Carlo simulations that used the real-world return database on the out-of-sample (test) data.

One of the most discussed problems in the financial world is stock option pricing. The Black-Scholes Equation is a Parabolic Partial Differential Equation which provides an option pricing model. The present work proposes an approach based on Neural Networks to solve the Black-Scholes Equations. Real-world data from the stock options market were used as the initial boundary to solve the Black-Scholes Equation. In particular, times series of call options prices of Brazilian companies Petrobras and Vale were employed. The results indicate that the network can learn to solve the Black-Sholes Equation for a specific real-world stock options time series. The experimental results showed that the Neural network option pricing based on the Black-Sholes Equation solution can reach an option pricing forecasting more accurate than the traditional Black-Sholes analytical solutions. The experimental results making it possible to use this methodology to make short-term call option price forecasts in options markets.

Autodeleveraging (ADL) is a last-resort loss socialization mechanism for perpetual futures venues. It is triggered when solvency-preserving liquidations fail. Despite the dominance of perpetual futures in the crypto derivatives market, with over \60 trillion of volume in 2024, there has been no formal study of ADL. In this paper, we provide the first rigorous model of ADL. We prove that ADL mechanisms face a fundamental trilemma: no policy can simultaneously satisfy exchange solvency, revenue, and fairness to traders. This impossibility theorem implies that as participation scales, a novel form of moral hazard grows asymptotically, rendering `zero-loss' socialization impossible. On the positive side, we show that three classes of ADL mechanisms can optimally navigate this trilemma to provide fairness, robustness to price shocks, and maximal exchange revenue. We analyze these mechanisms on the Hyperliquid dataset from October 10, 2025, when ADL was used repeatedly to close 2.1 billion of positions in 12 minutes. By comparing production ADL to transparent benchmark allocations, we find that Hyperliquid's production algorithm overshot the minimum trader profit haircut required to cover the shortfall. Our methodology suggests the excess profits lost by profitable traders is between \45.0M and 51.7M. In terms of the positions liquidated, this corresponds to roughly \$653.6M of positions being closed. This comparison also suggests that Binance overutilized ADL far more than Hyperliquid. Our results show both theoretically and empirically that optimized ADL mechanisms can dramatically reduce losses of trader profitability while maintaining exchange solvency.

We propose a deep hedging framework for index option portfolios, grounded in a realistic market simulator that captures the joint dynamics of S&P 500 returns and the full implied volatility surface. Our approach integrates surface-informed decisions with multiple hedging instruments and explicitly accounts for transaction costs. The hedging strategy also considers the variance risk premium embedded in the hedging instruments, enabling more informed and adaptive risk management. Tested on a historical out-of-sample set of straddles from 2020 to 2023, our method consistently outperforms traditional delta-gamma hedging strategies across a range of market conditions.

Portfolio management is an essential component of investment strategy that aims to maximize returns while minimizing risk. This paper explores several portfolio management strategies, including asset allocation, diversification, active management, and risk management, and their importance in optimizing portfolio performance. These strategies are examined individually and in combination to demonstrate how they can help investors maximize alpha and minimize beta. Asset allocation is the process of dividing a portfolio among different asset classes to achieve the desired level of risk and return. Diversification involves spreading investments across different securities and sectors to minimize the impact of individual security or sector-specific risks. Active management involves security selection and risk management techniques to generate excess returns while minimizing losses. Risk management strategies, such as stop-loss orders and options strategies, aim to minimize losses in adverse market conditions. The importance of combining these strategies for optimizing portfolio performance is emphasized in this paper. The proper implementation of these strategies can help investors achieve their investment goals over the long-term, while minimizing exposure to risks. A call to action for investors to utilize portfolio management strategies to maximize alpha and minimize beta is also provided.

Automatic Adjustment Mechanisms (AAM) are legal instruments that help social security systems respond to demographic and economic changes. In Brazil, the Social Security Factor (SSF) was introduced in the late 1990s as an AAM to link retirement benefits to life expectancy at the retirement age, with the hope of promoting contributory justice and discouraging early retirement. Recent research has highlighted the limitations of right-censored life tables, such as those used in Brazil. It has recommended using the gamma-Gompertz-Makeham (GGM) model to estimate adult and old-age mortality. This study investigated the impact of right-censoring on the SSF by comparing the official SSF and other social security metrics with a counterfactual scenario computed based on fitted GGM models. The results indicate that from 2004 to 2012, official life tables may have negatively impacted retirees' income, particularly for those who delayed their retirement. Furthermore, the GGM-fitted models' life expectancies had more stable paths over time, which could have helped with long-term planning. This study's findings are significant for policymakers as they highlight the importance of using appropriate mortality metrics in AAMs to ensure accurate retirement benefit payments. They also underscore the need to consider the potential impacts of seemingly innocuous hypotheses on public action outcomes. Overall, this study provides valuable insights for public planners and policymakers looking to enhance the effectiveness and fairness of social security systems.

We introduce a novel approach to options trading strategies using a highly scalable and data-driven machine learning algorithm. In contrast to traditional approaches that often require specifications of underlying market dynamics or assumptions on an option pricing model, our models depart fundamentally from the need for these prerequisites, directly learning non-trivial mappings from market data to optimal trading signals. Backtesting on more than a decade of option contracts for equities listed on the S&P 100, we demonstrate that deep learning models trained according to our end-to-end approach exhibit significant improvements in risk-adjusted performance over existing rules-based trading strategies. We find that incorporating turnover regularization into the models leads to further performance enhancements at prohibitively high levels of transaction costs.

We consider two data driven approaches, Reinforcement Learning (RL) and Deep Trajectory-based Stochastic Optimal Control (DTSOC) for hedging a European call option without and with transaction cost according to a quadratic hedging P&L objective at maturity ("variance-optimal hedging" or "final quadratic hedging"). We study the performance of the two approaches under various market environments (modeled via the Black-Scholes and/or the log-normal SABR model) to understand their advantages and limitations. Without transaction costs and in the Black-Scholes model, both approaches match the performance of the variance-optimal Delta hedge. In the log-normal SABR model without transaction costs, they match the performance of the variance-optimal Barlett's Delta hedge. Agents trained on Black-Scholes trajectories with matching initial volatility but used on SABR trajectories match the performance of Bartlett's Delta hedge in average cost, but show substantially wider variance. To apply RL approaches to these problems, P&L at maturity is written as sum of step-wise contributions and variants of RL algorithms are implemented and used that minimize expectation of second moments of such sums.