Related papers: Physics-Informed Convolutional Transformer for Pre…

Volatility is a natural risk measure in finance as it quantifies the variation of stock prices. A frequently considered problem in mathematical finance is to forecast different estimates of volatility. What makes it promising to use deep…

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…

Black-Scholes implied volatility is a quantile. The insight follows from the normalized option price being a probability on the variance scale, with the inverse Gaussian distribution providing the link. It enables analytically exact and…

Accurate option pricing is essential for effective trading and risk management in financial markets, yet it remains challenging due to market volatility and the limitations of traditional models like Black-Scholes. In this paper, we…

Events such as the Financial Crisis of 2007-2008 or the COVID-19 pandemic caused significant losses to banks and insurance entities. They also demonstrated the importance of using accurate equity risk models and having a risk management…

Black-Scholes (BS) is the standard mathematical model for option pricing in financial markets. Option prices are calculated using an analytical formula whose main inputs are strike (at which price to exercise) and volatility. The BS…

In financial mathematics, it is a typical approach to approximate financial markets operating in discrete time by continuous-time models such as the Black Scholes model. Fitting this model gives rise to difficulties due to the discrete…

We consider a non-stochastic online learning approach to price financial options by modeling the market dynamic as a repeated game between the nature (adversary) and the investor. We demonstrate that such framework yields analogous…

The implied volatility smile surface is the basis of option pricing, and the dynamic evolution of the option volatility smile surface is difficult to predict. In this paper, attention mechanism is introduced into LSTM, and a volatility…

Volatility modelling has become a significant area of research within Financial Mathematics. Wiener process driven stochastic volatility models have become popular due their consistency with theoretical arguments and empirical observations.…

In this paper, a new numerical method based on adaptive gradient descent optimizers is provided for computing the implied volatility from the Black-Scholes (B-S) option pricing model. It is shown that the new method is more accurate than…

Recent work in financial machine learning has shown the virtue of complexity: the phenomenon by which deep learning methods capable of learning highly nonlinear relationships outperform simpler approaches in financial forecasting. While…

We consider the supervised learning problem of learning the price of an option or the implied volatility given appropriate input data (model parameters) and corresponding output data (option prices or implied volatilities). The majority of…

This paper proposes a physics-informed learning framework for a class of recurrent neural networks tailored to large-scale and networked systems. The approach aims to learn control-oriented models that preserve the structural and stability…

This paper deals with an extension of the so-called Black-Scholes model in which the volatility is modeled by a linear combination of the components of the solution of a differential equation driven by a fractional Brownian motion of Hurst…

With the rapid advancement of neural networks, methods for option pricing have evolved significantly. This study employs the Black-Scholes-Merton (B-S-M) model, incorporating an additional variable to improve the accuracy of predictions…

Volatility models of price fluctuations are well studied in the econometrics literature, with more than 50 years of theoretical and empirical findings. The recent advancements in neural networks (NN) in the deep learning field have…

We present a new numerical method to price vanilla options quickly in time-changed Brownian motion models. The method is based on rational function approximations of the Black-Scholes formula. Detailed numerical results are given for a…

We present a deep learning framework for pricing options based on market-implied volatility surfaces. Using end-of-day S\&P 500 index options quotes from 2018-2023, we construct arbitrage-free volatility surfaces and generate training data…

Transition prediction is an important aspect of aerodynamic design because of its impact on skin friction and potential coupling with flow separation characteristics. Traditionally, the modeling of transition has relied on correlation-based…