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This paper presents a novel way to predict options price for one day in advance, utilizing the method of Quasi-Reversibility for solving the Black-Scholes equation. The Black-Scholes equation solved forwards in time with Tikhonov…

Analysis of PDEs · Mathematics 2022-03-21 Mikhail V. Klibanov , Kirill V. Golubnichiy , Andrey V. Nikitin

The Black-Scholes Option pricing model (BSOPM) has long been in use for valuation of equity options to find the prices of stocks. In this work, using BSOPM, we have come up with a comparative analytical approach and numerical technique to…

Statistical Finance · Quantitative Finance 2018-12-31 Reaz Chowdhury , M. R. C. Mahdy , Tanisha Nourin Alam , Golam Dastegir Al Quaderi

A master equation approach to the numerical solution of option pricing models is developed. The basic idea of the approach is to consider the Black--Scholes equation as the macroscopic equation of an underlying mesoscopic stochastic option…

Statistical Mechanics · Physics 2009-11-07 Daniel Faller , Francesco Petruccione

We analyze and calculate the early exercise boundary for a class of stationary generalized Black-Scholes equations in which the volatility function depends on the second derivative of the option price itself. A motivation for studying the…

Computational Finance · Quantitative Finance 2017-07-04 Maria do Rosario Grossinho , Yaser Faghan Kord , Daniel Sevcovic

It is well-known that the Black-Scholes formula has been derived under the assumption of constant volatility in stocks. In spite of evidence that this parameter is not constant, this formula is widely used by financial markets. This paper…

Pricing of Securities · Quantitative Finance 2013-06-06 Kais Hamza , Fima Klebaner , Olivia Mah

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

The author presents alternatives to the Black-Scholes european call option pricing model by incorporating different transaction cost structures in the replicating strategy. In particular, an exponentially decreasing structure is proposed…

Risk Management · Quantitative Finance 2021-12-21 F. G. Bellora , G. Mazzei , M. Maurette

We proposed classification models that utilize the result from the Quasi-Reversibility Method, which solves the Black-Scholes equation to forecast the option prices one day in advance. Combining the minimizer from QRM with our machine…

Optimization and Control · Mathematics 2025-01-28 Benjamin Jiang , Matthieu Durieux , Kirill V. Golubnichiy

We show how to derive the Black-Scholes model and its generalisation to the `exchange-option' (to exchange one asset for another) via the continuum limit of the Binomial tree. No knowledge of stochastic calculus or partial differential…

Pricing of Securities · Quantitative Finance 2023-04-04 Richard J. Martin

We deal with some generalizations on a Black--Scholes model arising in financial mathematics. As novelty in this paper, we consider a variable volatility and abstract functional boundary conditions, which allow us to treat a very large…

Classical Analysis and ODEs · Mathematics 2015-06-08 Rubén Figueroa , Maria do Rosário Grossinho

Options are financial instruments that depend on the underlying stock. We explain their non-Gaussian fluctuations using the nonextensive thermodynamics parameter $q$. A generalized form of the Black-Scholes (B-S) partial differential…

Statistical Mechanics · Physics 2009-11-07 Lisa Borland

The objective of this paper is to introduce the theory of option pricing for markets with informed traders within the framework of dynamic asset pricing theory. We introduce new models for option pricing for informed traders in complete…

Mathematical Finance · Quantitative Finance 2020-08-13 Yuan Hu , Abootaleb Shirvani , Stoyan Stoyanov , Young Shin Kim , Frank J. Fabozzi , Svetlozar T. Rachev

The classical linear Black--Scholes model for pricing derivative securities is a popular model in financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the…

Mathematical Finance · Quantitative Finance 2019-01-23 Jose Cruz , Daniel Sevcovic

We propose a novel Black-Scholes model under which the stock price processes are modeled by stochastic differential equations driven by sub-diffusions. The new framework can capture the less financial activity phenomenon during the bear…

Probability · Mathematics 2025-11-14 Shuaiqi Zhang , Zhen-Qing Chen

Report presents analysis of empirical distribution of future returns of bitcoin (BTC) from BTUSD inverse option prices. Logistic pdf is chosen as underlying distribution to fit option prices. The result is satisfactory and suggests that…

Statistical Finance · Quantitative Finance 2019-01-16 Nikolai Zaitsev

The Black-Scholes model gives vanilla Europen call option prices as a function of the volatility. We prove Lipschitz stability in the inverse problem of determining the implied volatility, which is a function of the underlying asset, from a…

Analysis of PDEs · Mathematics 2013-02-05 Mourad Bellassoued , Raymond Brummelhuis , Michel Cristofol , Eric Soccorsi

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…

Mathematical Finance · Quantitative Finance 2025-08-21 Tapan Kar , Suprio Bhar , Barun Sarkar , Sesha Meka

Option pricing models, essential in financial mathematics and risk management, have been extensively studied and recently advanced by AI methodologies. However, American option pricing remains challenging due to the complexity of…

Machine Learning · Computer Science 2024-09-30 Qiguo Sun , Hanyue Huang , XiBei Yang , Yuwei Zhang

Recent years have seen an emerging class of structured financial products based on options linked to dynamic asset allocation strategies. One of the most chosen approach is the so-called target volatility mechanism. It shifts between risky…

Pricing of Securities · Quantitative Finance 2019-02-26 Luca Di Persio , Luca Prezioso , Kai Wallbaum

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…

Pricing of Securities · Quantitative Finance 2025-09-24 Bhathiya Divelgama , Nancy Asare Nyarko , W. Brent Lindquist , Svetlozar T. Rachev , Blessing Omotade