In the realm of option pricing, existing models are typically classified into principle-driven methods, such as solving partial differential equations (PDEs) that pricing function satisfies, and data-driven approaches, such as machine learning (ML) techniques that parameterize the pricing function directly. While principle-driven models offer a rigorous theoretical framework, they often rely on unrealistic assumptions, such as asset processes adhering to fixed stochastic differential equations (SDEs). Moreover, they can become computationally intensive, particularly in high-dimensional settings when analytical solutions are not available and thus numerical solutions are needed. In contrast, data-driven models excel in capturing market data trends, but they often lack alignment with core financial principles, raising concerns about interpretability and predictive accuracy, especially when dealing with limited or biased datasets. This work proposes a hybrid approach to address these limitations by integrating the strengths of both principled and data-driven methodologies. Our framework combines the theoretical rigor and interpretability of PDE-based models with the adaptability of machine learning techniques, yielding a more versatile methodology for pricing a broad spectrum of options. We validate our approach across different volatility modeling approaches-both with constant volatility (Black-Scholes) and stochastic volatility (Heston), demonstrating that our proposed framework, Finance-Informed Neural Network (FINN), not only enhances predictive accuracy but also maintains adherence to core financial principles. FINN presents a promising tool for practitioners, offering robust performance across a variety of market conditions.

Estimator Vectors: OOV Word Embeddings based on Subword and Context Clue Estimates Raj Patel Carlotta Domeniconi † Abstract Semantic representations of words have been successfully extracted from unlabeled corpuses using neural network models like word2vec. These representations are generally high quality and are computationally inexpensive to train, making them popular. However, these approaches generally fail to approximate out of vocabulary (OOV) words, a task humans can do quite easily, using word roots and context clues. This paper proposes a neural network model that learns high quality word representations, subword representations, and context clue representations jointly. Learning all three types of representations together enhances the learning of each, leading to enriched word vectors, along with strong estimates for OOV words, via the combination of the corresponding context clue and subword embeddings. Our model, called Estimator Vectors (EV), learns strong word embed-dings and is competitive with state of the art methods for OOV estimation. 1 Introduction Semantic representations of words are useful for many natural language processing (NLP) tasks. While there exists many ways to learn them, models like word2vec [11] and GloVe [15] have been shown to be very efficient at producing high quality word embeddings. These embeddings not only capture similarity between words, but also capture some algebraic relationships between words. These models, though, also have some downsides. One major drawback is that they can only learn embeddings for words in the vocabulary, determined by the corpus they were trained on. Although common words are typically captured, most existing approaches are unable to learn the meaning of new words, known as out of vocabulary (OOV) words, a task humans can do easily.