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Accurately predicting the prices of financial time series is essential and challenging for the financial sector. Owing to recent advancements in deep learning techniques, deep learning models are gradually replacing traditional statistical…
This paper presents a novel way to apply mathematical finance and machine learning (ML) to forecast stock options prices. Following results from the paper Quasi-Reversibility Method and Neural Network Machine Learning to Solution of…
Deep Learning models have become dominant in tackling financial time-series analysis problems, overturning conventional machine learning and statistical methods. Most often, a model trained for one market or security cannot be directly…
We study the behavior of the critical price of an American put option near maturity in the Jump diffusion model when the underlying stock pays dividends at a continuous rate and the limit of the critical price is smaller than the stock…
The main purpose of this article is to give a general overview and understanding of the first widely used option-pricing model, the Black-Scholes model. The history and context are presented, with the usefulness and implications in the…
This paper presents a novel decision-focused framework integrating the physical energy storage model into machine learning pipelines. Motivated by the model predictive control for energy storage, our end-to-end method incorporates the prior…
An American option grants the holder the right to select the time at which to exercise the option, so pricing an American option entails solving an optimal stopping problem. Difficulties in applying standard numerical methods to complex…
We study the regularity of the stochastic representation of the solution of a class of initial-boundary value problems related to a regime-switching diffusion. This representation is related to the value function of a finite-horizon optimal…
We present a parallel algorithm that computes the ask and bid prices of an American option when proportional transaction costs apply to the trading of the underlying asset. The algorithm computes the prices on recombining binomial trees,…
We develop a model for indifference pricing in derivatives markets where price quotes have bid-ask spreads and finite quantities. The model quantifies the dependence of the prices and hedging portfolios on an investor's beliefs, risk…
Prediction markets rely on liquidity to convert trades into informative prices, yet existing mechanisms fix liquidity ex ante. This restriction enforces a static trade-off between price responsiveness and worst-case loss despite inherently…
Semi-analytical pricing of American options in a time-dependent Ornstein-Uhlenbeck model was presented in [Carr, Itkin, 2020]. It was shown that to obtain these prices one needs to solve (numerically) a nonlinear Volterra integral equation…
In this short paper, in order to price occupation-time options, such as (double-barrier) step options and quantile options, we derive various joint distributions of a mixed-exponential jump-diffusion process and its occupation times of…
Machine learning models have demonstrated remarkable efficacy and efficiency in a wide range of stock forecasting tasks. However, the inherent challenges of data scarcity, including low signal-to-noise ratio (SNR) and data homogeneity, pose…
A master equation approach to the numerical solution of option pricing models is developed. The basic idea of the approach is to consider the Black--Scholes equation as the macroscopic equation of an underlying mesoscopic stochastic option…
We develop deep learning models to learn the hedge ratio for S&P500 index options directly from options data. We compare different combinations of features and show that a feedforward neural network model with time to maturity,…
Sample selection is a straightforward technique to combat noisy labels, aiming to prevent mislabeled samples from degrading the robustness of neural networks. However, existing methods mitigate compounding selection bias either by…
This paper proposes a deep delta hedging framework for options, utilizing neural networks to learn the residuals between the hedging function and the implied Black-Scholes delta. This approach leverages the smoother properties of these…
The paper focuses on pricing European-style options on several underlying assets under the Black-Scholes model represented by a nonstationary partial differential equation. The proposed method combines the Galerkin method with…
We study continuous-time reinforcement learning (RL) for stochastic control in which system dynamics are governed by jump-diffusion processes. We formulate an entropy-regularized exploratory control problem with stochastic policies to…