Related papers: Option pricing for Barndorff-Nielsen and Shephard …

We develop several deep learning algorithms for approximating families of parametric PDE solutions. The proposed algorithms approximate solutions together with their gradients, which in the context of mathematical finance means that the…

We consider the problem of pricing basket options in a multivariate Black Scholes or Variance Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high dimensional numerical integration problems with…

In this paper, we focus on the tempered subdiffusive Black-Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in the considered model. We derive the governing…

We extend the application of the Cherny-Shiryaev-Yor invariance principle to a unified Bachelier-Black-Scholes-Merton (BBSM) dynamic pricing model. This extension incorporates the influence of the history of the dynamics (i.e., the path…

We present an uncertainty-aware, physics-informed neural network (PINN) for option pricing that solves the Black--Scholes (BS) partial differential equation (PDE) as a mesh-free, global surrogate over $(S,t)$. The model embeds the BS…

Neural networks with sufficiently smooth activation functions can approximate values and derivatives of any smooth function, and they are differentiable themselves. We improve the approximation capability of neural networks by utilizing the…

Using the option delta systematically, we derive tighter lower and upper bounds of the Black-Scholes implied volatility than those in Tehranchi [SIAM J. Financ. Math. 7 (2016), 893-916]. As an application, we propose a Newton-Raphson…

The Black-Scholes option pricing model remains a cornerstone in financial mathematics, yet its application is often challenged by the need for accurate hedging strategies, especially in dynamic market environments. This paper presents a…

We develop a novel deep learning approach for pricing European basket options written on assets that follow jump-diffusion dynamics. The option pricing problem is formulated as a partial integro-differential equation, which is approximated…

This paper uses deep learning to value derivatives. The approach is broadly applicable, and we use a call option on a basket of stocks as an example. We show that the deep learning model is accurate and very fast, capable of producing…

Following the foundational work of the Black--Scholes model, extensive research has been developed to price the option by addressing its underlying assumptions and associated pricing biases. This study introduces a novel framework for…

The key objective of this paper is to develop an empirical model for pricing SPX options that can be simulated over future paths of the SPX. To accomplish this, we formulate and rigorously evaluate several statistical models, including…

We analyze approximation rates by deep ReLU networks of a class of multi-variate solutions of Kolmogorov equations which arise in option pricing. Key technical devices are deep ReLU architectures capable of efficiently approximating tensor…

We propose a new cognitive framework for option price modelling, using quantum neural computation formalism. Briefly, when we apply a classical nonlinear neural-network learning to a linear quantum Schr\"odinger equation, as a result we get…

Predicting volatility is important for asset predicting, option pricing and hedging strategies because it cannot be directly observed in the financial market. The Black-Scholes option pricing model is one of the most widely used models by…

Pricing of financial derivatives, in particular early exercisable options such as Bermudan options, is an important but heavy numerical task in financial institutions, and its speed-up will provide a large business impact. Recently,…

We derive quantitative error bounds for deep neural networks (DNNs) approximating option prices on a $d$-dimensional risky asset as functions of the underlying model parameters, payoff parameters and initial conditions. We cover a general…

We give an exposition and numerical studies of upper hedging prices in multinomial models from the viewpoint of linear programming and the game-theoretic probability of Shafer and Vovk. We also show that, as the number of rounds goes to…

We develop a theory for option pricing with perfect hedging in an inefficient market model where the underlying price variations are autocorrelated over a time tau. This is accomplished by assuming that the underlying noise in the system is…

We introduce a variant of the Barndorff-Nielsen and Shephard stochastic volatility model where the non Gaussian Ornstein-Uhlenbeck process describes some measure of trading intensity like trading volume or number of trades instead of…