Related papers: Deep-learning based numerical BSDE method for barr…
We investigate solving partial integro-differential equations (PIDEs) using unsupervised deep learning in this paper. To price options, assuming underlying processes follow Levy processes, we require to solve PIDEs. In supervised deep…
This paper develops a deep learning-based framework for pricing convertible bonds with path-dependent contractual features, namely downward conversion price reset and issuer call clauses under rolling-window trigger rules, which are…
Mathematically, the execution of an American-style financial derivative is commonly reduced to solving an optimal stopping problem. Breaking the general assumption that the knowledge of the holder is restricted to the price history of the…
We report two methods for solving FBSDEs of path dependent types of high dimensions. Specifically, we propose a deep learning framework for solving such problems using path signatures as underlying features. Our two methods…
We propose a deep learning algorithm for high dimensional optimal stopping problems. Our method is inspired by the penalty method for solving free boundary PDEs. Within our approach, the penalized PDE is approximated using the Deep BSDE…
The Libor market model is a mainstay term structure model of interest rates for derivatives pricing, especially for Bermudan swaptions, and other exotic Libor callable derivatives. For numerical implementation the pricing of derivatives…
Neural networks have been applied to control problems, typically by combining data, differential equation residuals, and objective costs in the training loss or by incorporating auxiliary architectural components. Instead, we propose a…
In the paper, we propose a new calculation scheme for American options in the framework of a forward backward stochastic differential equation (FBSDE). The well-known decomposition of an American option price with that of a European option…
The aim of this work is to propose an extension of the deep solver by Han, Jentzen, E (2018) to the case of forward backward stochastic differential equations (FBSDEs) with jumps. As in the aforementioned solver, starting from a discretized…
This article explores operator learning models that can deduce solutions to partial differential equations (PDEs) on arbitrary domains without requiring retraining. We introduce two innovative models rooted in boundary integral equations…
In this paper we study partial differential equations (PDEs) that can be used to model value adjustments. Different value adjustments denoted generally as xVA are nowadays added to the risk-free financial derivative values and the PDE…
In this work, we present a novel forward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs). Motivated by the fact that differential deep learning can…
Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…
This paper is devoted to the pricing of Barrier options by optimal quadratic quantization method. From a known useful representation of the premium of barrier options one deduces an algorithm similar to one used to estimate nonlinear filter…
We investigate two-barriers-reflected backward stochastic differential equations with data from rank-based stochastic differential equation. More specifically, we focus on the solution of backward stochastic differential equations…
Option pricing often requires solving partial differential equations (PDEs). Although deep learning-based PDE solvers have recently emerged as quick solutions to this problem, their empirical and quantitative accuracy remain not well…
In this paper we introduce a deep learning method for pricing and hedging American-style options. It first computes a candidate optimal stopping policy. From there it derives a lower bound for the price. Then it calculates an upper bound, a…
In this paper, we study the option pricing problems for rough volatility models. As the framework is non-Markovian, the value function for a European option is not deterministic; rather, it is random and satisfies a backward stochastic…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
We study the anticipative backward stochastic differential equations (BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H greater than 1/2. The stochastic integral used throughout the paper is the divergence…