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Control of the Black–Scholes equation

Computers & Mathematics with Applications, 2017
There are hundreds of papers dealing with the Black-Scholes equation. Yet, no one seems to have ever used the scaling invariance coming from the heat equation. And there appears to be very few studies on the "control aspect" of the equation. In previous works, J.Y. Chemin and Cl.
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Revisiting the Black-Scholes equation [PDF]

, 1998
In common finance literature, Black-Scholes partial differential equation of option pricing is usually derived with no-arbitrage principle. Considering an asset market, Merton applied the Hamilton-Jacobi-Bellman techniques of his continuous-time consumption-portfolio problem, deriving general equilibrium relationships among the securities in the asset ...
openaire   +2 more sources

Financial Statement Information and Equity Value: The Role of Real Options Characteristics

Financial Management, EarlyView.
ABSTRACT This paper examines whether firm‐specific real options characteristics are equity value‐relevant beyond valuation estimates anchored in financial statements. Using extensive historical data for the United Kingdom, we assess and compare the forecast accuracy and explanatory power for stock prices of equity valuation models based on residual ...
Mingyu (Chandler) Chen, Colin Clubb, Tarik Driouchi   +2 more
wiley   +1 more source

Qualitative financial modelling in fractal dimensions

Financial Innovation
The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets. The Black–Scholes model for pricing stock options has been applied to various payoff structures, and
Rami Ahmad El-Nabulsi, Waranont Anukool
doaj   +1 more source

Comparison: Binomial model and Black Scholes model

Quantitative Finance and Economics, 2018
The Binomial Model and the Black Scholes Model are the popular methods that are used to solve the option pricing problems. Binomial Model is a simple statistical method and Black Scholes model requires a solution of a stochastic differential equation ...
Amir Ahmad Dar, N. Anuradha
doaj   +1 more source

Novel Approaches for Getting the Solution of the Fractional Black–Scholes Equation Described by Mittag-Leffler Fractional Derivative

Discrete Dynamics in Nature and Society, 2020
The value of an option plays an important role in finance. In this paper, we use the Black–Scholes equation, which is described by the nonsingular fractional-order derivative, to determine the value of an option. We propose both a numerical scheme and an
Ndolane Sene, Babacar Sène, Seydou Nourou Ndiaye, Awa Traoré   +3 more
doaj   +1 more source

Symmetries of the Black-Scholes equation [PDF]

Methods and Applications of Analysis, 2012
We determine the algebra of isovectors for the Black--Scholes equation. As a consequence, we obtain some previously unknown families of transformations on the solutions.
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Cubic Spline Method for a Generalized Black‐Scholes Equation [PDF]

Mathematical Problems in Engineering, 2014
We develop a numerical method based on cubic polynomial spline approximations to solve a a generalized Black‐Scholes equation. We apply the implicit Euler method for the time discretization and a cubic polynomial spline method for the spatial discretization.
Jian Huang, Zhongdi Cen
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The Role of Index Fund Ownership in the Era of Say‐on‐Pay

Financial Management, EarlyView.
ABSTRACT We examine whether and how index funds influence executive compensation in the post‐Say‐on‐Pay era. Using the annual reconstitution of the Russell indexes as a source of exogenous variation in index fund ownership, we document a causal effect of index ownership on CEO pay structure.
Kiseo Chung, Hwanki Brian Kim
wiley   +1 more source

Using a Mix of Finite Difference Methods and Fractional Differential Transformations to Solve Modified Black–Scholes Fractional Equations

Mathematics
This paper discusses finding solutions to the modified Fractional Black–Scholes equation. As is well known, the options theory is beneficial in the stock market.
Agus Sugandha, Endang Rusyaman, Sukono, Ema Carnia   +3 more
doaj   +1 more source