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The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as \begin{equation*}…

Mathematical Finance · Quantitative Finance 2021-03-05 Jonas Al-Hadad , Zbigniew Palmowski

In this paper we investigate a nonlinear generalization of the Black-Scholes equation for pricing American style call options in which the volatility term may depend on the underlying asset price and the Gamma of the option. We propose a…

Computational Finance · Quantitative Finance 2018-06-14 Maria do Rosario Grossinho , Yaser Faghan Kord , Daniel Sevcovic

We propose an efficient and easy-to-implement gradient-enhanced least squares Monte Carlo method for computing price and Greeks (i.e., derivatives of the price function) of high-dimensional American options. It employs the sparse Hermite…

Computational Finance · Quantitative Finance 2025-09-01 Jiefei Yang , Guanglian Li

It is well known that the Black-Scholes-Merton model suffers from several deficiencies. Jump-diffusion and Levy models have been widely used to partially alleviate some of the biases inherent in this classical model. Unfortunately, the…

Computational Engineering, Finance, and Science · Computer Science 2007-05-23 Kenneth R. Jackson , Sebastian Jaimungal , Vladimir Surkov

Pricing a multi-asset derivative is an important problem in financial engineering, both theoretically and practically. Although it is suitable to numerically solve partial differential equations to calculate the prices of certain types of…

Quantum Physics · Physics 2022-07-05 Kenji Kubo , Koichi Miyamoto , Kosuke Mitarai , Keisuke Fujii

In the paper we consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follow the classical multidimensional Black and Scholes model. We provide a general early exercise premium…

Probability · Mathematics 2016-03-01 Tomasz Klimsiak , Andrzej Rozkosz

In this paper we consider the problem of finding bounds on the prices of options depending on multiple assets without assuming any underlying model on the price dynamics, but only the absence of arbitrage opportunities. We formulate this as…

Optimization and Control · Mathematics 2022-06-06 Didier Henrion , Felix Kirschner , Etienne de Klerk , Milan Korda , Jean-Bernard Lasserre , Victor Magron

Contrary to the common view that exact pricing is prohibitive owing to the curse of dimensionality, this study proposes an efficient and unified method for pricing options under multivariate Black-Scholes-Merton (BSM) models, such as the…

Pricing of Securities · Quantitative Finance 2018-05-09 Jaehyuk Choi

We introduce a modular framework that extends the signature method to handle American option pricing under evolving volatility roughness. Building on the signature-pricing framework of Bayer et al. (2025), we add three practical…

Mathematical Finance · Quantitative Finance 2025-08-13 Roshan Shah

Barrier options are one of the most widely traded exotic options on stock exchanges. In this paper, we develop a new stochastic simulation method for pricing barrier options and estimating the corresponding execution probabilities. We show…

Pricing of Securities · Quantitative Finance 2018-03-29 Keegan Mendonca , Vasileios E. Kontosakos , Athanasios A. Pantelous , Konstantin M. Zuev

We introduce a stacking version of the Monte Carlo algorithm in the context of option pricing. Introduced recently for aeronautic computations, this simple technique, in the spirit of current machine learning ideas, learns control variates…

Computational Finance · Quantitative Finance 2019-03-27 Antoine Jacquier , Emma R. Malone , Mugad Oumgari

We present a comprehensive quantum algorithm tailored for pricing autocallable options, offering a full implementation and experimental validation. Our experiments include simulations conducted on high-performance computing (HPC) hardware,…

We present an adaptive approach for valuing the European call option on assets with stochastic volatility. The essential feature of the method is a reduction of uncertainty in latent volatility due to a Bayesian learning procedure. Starting…

Other Condensed Matter · Physics 2008-12-02 Sergei Fedotov , Stephanos Panayides

We study an American option pricing problem with liquidity risks and transaction fees. As endogenous transaction costs, liquidity risks of the underlying asset are modeled by a mean-reverting process. Transaction fees are exogenous…

Mathematical Finance · Quantitative Finance 2025-09-08 Dong Yan , Xin-Jie Huang , Guiyuan Ma , Xin-Jiang He

The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…

Numerical Analysis · Mathematics 2023-07-03 Alexander Hvatov , Tatiana Tikhonova

This paper presents a Monte-Carlo-based artificial neural network framework for pricing Bermudan options, offering several notable advantages. These advantages encompass the efficient static hedging of the target Bermudan option and the…

Computational Finance · Quantitative Finance 2024-02-27 Vikranth Lokeshwar Dhandapani , Shashi Jain

Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…

Optimization and Control · Mathematics 2024-03-15 Nazanin Abolfazli , Ruichen Jiang , Aryan Mokhtari , Erfan Yazdandoost Hamedani

In this paper we introduce a new algorithm for American Monte Carlo that can be used either for American-style options, callable structured products or for computing counterparty credit risk (e.g. CVA or PFE computation). Leveraging least…

Computational Finance · Quantitative Finance 2014-04-07 Calypso Herrera , Louis Paulot

Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in…

Pricing of Securities · Quantitative Finance 2012-05-15 Jean-Pierre Fouque , Sebastian Jaimungal , Matthew Lorig

Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need to be minimized…

Computational Engineering, Finance, and Science · Computer Science 2014-04-30 Snehanshu Saha , Swati Routh , Bidisha Goswami