相关论文: Numerical Solution of HCIR Equation with Transacti…

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 deals with a high-order accurate implicit finite-difference approach to the pricing of barrier options. In this way various types of barrier options are priced, including barrier options paying rebates, and options on…

We solve the problem of super-hedging European or Asian options for discrete-time financial market models where executable prices are uncertain. The risky asset prices are not described by single-valued processes but measurable selections…

In the paper written by Klibanov et al, it proposes a novel method to calculate implied volatility of a European stock options as a solution to ill-posed inverse problem for the Black-Scholes equation. In addition, it proposes a trading…

This paper addresses an important gap in rigorous numerical treatments for pricing American options under correlated two-asset jump-diffusion models using the viscosity solution framework, with a particular focus on the Merton model. The…

This paper introduces alternating-direction implicit (ADI) solvers of higher order of time-accuracy (orders two to six) for the compressible Navier-Stokes equations in two- and three-dimensional curvilinear domains. The higher-order…

In this paper we analyze a nonlinear Black--Scholes model for option pricing under variable transaction costs. The diffusion coefficient of the nonlinear parabolic equation for the price $V$ is assumed to be a function of the underlying…

We consider a standard distributed consensus optimization problem where a set of agents connected over an undirected network minimize the sum of their individual local strongly convex costs. Alternating Direction Method of Multipliers ADMM…

This paper presents a new model for options pricing. The Black-Scholes-Merton (BSM) model plays an important role in financial options pricing. However, the BSM model assumes that the risk-free interest rate, volatility, and equity premium…

We study an optimal execution problem in the infinite horizon setup. Our financial market is given by the Black-Scholes model with a linear price impact. The main novelty of the current note is that we study the constrained case where the…

This research explores the development and application of the High-Order Dynamic Integration Method for solving integro-differential equations, with a specific focus on turbulent fluid dynamics. Traditional numerical methods, such as the…

In this paper, we consider the Heston-CIR model with L\'{e}vy process for pricing in the foreign exchange (FX) market by providing a new formula that better fits the distribution of prices. To do that, first, we study the existence and…

An option market maker incurs funding costs when carrying and hedging inventory. To hedge a net long delta inventory, for example, she pays a fee to borrow stock from the securities lending market. Because of haircuts, she posts additional…

We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial…

We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops that the…

Solving Hamilton-Jacobi-Isaacs (HJI) PDEs numerically enables equilibrial feedback control in two-player differential games, yet faces the curse of dimensionality (CoD). While physics-informed neural networks (PINNs) have shown promise in…

New simulation approaches to evaluating path-dependent options without matrix inversion issues nor Euler bias are evaluated. They employ three main contributions: Stochastic approximation replaces regression in the LSM algorithm; Explicit…

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…

G-expectation, as a sublinear expectation, provides a powerful framework for modeling uncertainty in financial markets. Motivated by the need for robust valuation under model uncertainty, this work develops a unified risk-neutral valuation…

We take the holistic approach of computing an OTC claim value that incorporates credit and funding liquidity risks and their interplays, instead of forcing individual price adjustments: CVA, DVA, FVA, KVA. The resulting nonlinear…