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Related papers: A master equation approach to option pricing

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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 2014-02-12 Aishwarya B U , Mohammed Saaqib A , Rajashree H R , Vigasini B

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…

Pricing of Securities · Quantitative Finance 2026-01-13 Francesco Romaggi

Based on the analog between the stochastic dynamics and quantum harmonic oscillator, we propose a market force driving model to generalize the Black-Scholes model in finance market. We give new schemes of option pricing, in which we can…

Risk Management · Quantitative Finance 2026-01-05 Pengpeng Li , Shi-Dong Liang

The Black-Scholes model (sometimes known as the Black-Scholes-Merton model) gives a theoretical estimate for the price of European options. The price evolution under this model is described by the Black-Scholes formula, one of the most…

General Finance · Quantitative Finance 2018-08-15 Rajeshwari Majumdar , Phanuel Mariano , Lowen Peng , Anthony Sisti

Optimal pricing of European call option is described by linear stochastic differential equation. Trading strategy given by a twin of stochastic variables was integrated w.r.t. Black-Scholes formula to adopt optimal pricing to tarading…

Optimization and Control · Mathematics 2007-05-23 Toshio Fukumi

A new mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock as well as new initial and boundary conditions. Conventional notions of…

Mathematical Finance · Quantitative Finance 2015-03-13 Michael V. Klibanov , Andrey V. Kuzhuget

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

The Black-Scholes formula for pricing options on stocks and other securities has been generalized by Merton and Garman to the case when stock volatility is stochastic. The derivation of the price of a security derivative with stochastic…

Condensed Matter · Physics 2009-10-30 B. E. Baaquie

An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and…

Statistical Mechanics · Physics 2009-11-07 G. Montagna , O. Nicrosini , N. Moreni

This research addresses accurate option pricing by employing models beyond the traditional Black-Scholes framework. While Black-Scholes provides a closed-form solution, it is limited by assumptions of constant volatility, no dividends, and…

Computational Finance · Quantitative Finance 2026-04-08 Karmanpartap Singh Sidhu , Pranshi Saxena

This paper explores the use of the multinode Shepard method for the numerical solution of the two-dimensional Black-Scholes equation. The proposed approach integrates a spatial approximation via the multinode Shepard operator with a…

Numerical Analysis · Mathematics 2025-08-12 Francesco Dell'Accio , Filomena Di Tommaso , Elisa Francomano , Clara Lorenzi

One of the most discussed problems in the financial world is stock option pricing. The Black-Scholes Equation is a Parabolic Partial Differential Equation which provides an option pricing model. The present work proposes an approach based…

Machine Learning · Computer Science 2024-05-12 Daniel de Souza Santos , Tiago Alessandro Espinola Ferreira

We present a novel method for the numerical pricing of American options based on Monte Carlo simulation and the optimization of exercise strategies. Previous solutions to this problem either explicitly or implicitly determine so-called…

Computational Finance · Quantitative Finance 2019-08-13 Christian Bayer , Raúl Tempone , Sören Wolfers

The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range…

Other Condensed Matter · Physics 2008-12-02 Sergei Fedotov , Abby Tan

Options financial instruments designed to protect investors from the stock market randomness. In 1973, Fisher Black, Myron Scholes and Robert Merton proposed a very popular option pricing method using stochastic differential equations…

Physics and Society · Physics 2009-11-06 J. Perello , J. M. Porra , M. Montero , J. Masoliver

We investigate qualitative and quantitative behavior of a solution of the mathematical model for pricing American style of perpetual put options. We assume the option price is a solution to the stationary generalized Black-Scholes equation…

Mathematical Finance · Quantitative Finance 2017-11-09 Maria do Rosario Grossinho , Yaser Kord Faghan , Daniel Sevcovic

Assuming that price of the underlying stock is moving in range bound, the Black-Scholes formula for options pricing supports a separation of variables. The resulting time-independent equation is solved employing different behavior of the…

Pricing of Securities · Quantitative Finance 2013-07-24 Ovidiu Racorean

We consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty…

Mathematical Finance · Quantitative Finance 2017-01-13 Hanno Gottschalk , Elpida Nizami , Marius Schubert

Options have provided a field of much study because of the complexity involved in pricing them. The Black-Scholes equations were developed to price options but they are only valid for European styled options. There is added complexity when…

Computational Engineering, Finance, and Science · Computer Science 2007-05-23 Michael Maio Pires , Tshilidzi Marwala

In this work, we give a generalized formulation of the Black-Scholes model. The novelty resides in considering the Black-Scholes model to be valid on 'average', but such that the pointwise option price dynamics depends on a measure…

Mathematical Finance · Quantitative Finance 2024-04-09 Nizar Riane , Claire David
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