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Generalized measure Black–Scholes equation: towards option self-similar pricing
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...
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Black–Scholes–Merton Model for Option Pricing
In this chapter, we start off the discussion of option pricing or derivatives modelling with the pioneering work by Black, Scholes and Merton who...
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Efficient Numerical Scheme for Generalized Black–Scholes Equations on Piecewise Uniform Shishkin-Type Mesh
In this paper, we propose numerical techniques for solving generalized Black–Scholes partial differential equations. The proposed numerical method is...
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Black-Scholes Model for Option Pricing and Hedging Strategies
As in the previous chapters, we consider a market model consisting in two assets: one non-risky (bond), the other risky (stock). While before we...
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Pricing Models Beyond Black-Scholes
In the previous chapters we presented several pricing and hedging problems both in a discrete- and in a continuous-time setting. The basic model...
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A Robust Numerical Simulation of a Fractional Black–Scholes Equation for Pricing American Options
After the discovery of fractal structures of financial markets, fractional partial differential equations (fPDEs) became very popular in studying...
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A tempered subdiffusive Black–Scholes model
In this paper, we focus on the tempered subdiffusive Black–Scholes model. The main part of our work consists of the finite difference method as a...
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Introducing and solving generalized Black–Scholes PDEs through the use of functional calculus
We introduce some families of generalized Black–Scholes equations which involve the Riemann–Liouville and Weyl space-fractional derivatives. We prove...
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Pricing European Double Barrier Option with Moving Barriers Under a Fractional Black–Scholes Model
Analysis of financial time series shows the existence of the long memory in financial markets. Fractional stochastic models can be a suitable tool...
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Monotone methods in counterparty risk models with nonlinear Black–Scholes-type equations
A nonlinear Black–Scholes-type equation is studied within
counterparty risk models . The classical hypothesis on the uniform Lipschitz-continuity of...
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Touchard wavelet technique for solving time-fractional Black–Scholes model
The main idea of this study is to introduce a novel set of wavelet functions named Touchard wavelets for solving time-fractional Black–Scholes...
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On the Problem of Pricing a Double Barrier Option in a Modified Black-Scholes Environment
The problem of valuing double barrier options in a Black-Scholes environment has been investigated in the past, for a variety of volatility models,...
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A robust numerical solution to a time-fractional Black–Scholes equation
Dividend paying European stock options are modeled using a time-fractional Black–Scholes (tfBS) partial differential equation (PDE). The underlying...
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Numerical solution using radial basis functions for multidimensional fractional partial differential equations of type Black–Scholes
In this paper, as far as the authors know, for the first time, a one-dimensional partial differential model is generalized using fractional...
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A compact quadratic spline collocation method for the time-fractional Black–Scholes model
A compact quadratic spline collocation (QSC) method for the time-fractional Black–Scholes model governing European option pricing is presented....
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On the solution of two-dimensional fractional Black–Scholes equation for European put option
The purpose of this paper was to investigate the dynamics of the option pricing in the market through the two-dimensional time fractional-order...
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Application of Two-Dimensional Fibonacci Wavelets in Fractional Partial Differential Equations Arising in the Financial Market
This manuscript provides an efficient and high-accuracy computational technique for solving fractional Black–Scholes equations (FB–SEs) arising in...
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Black & Scholes (BS) Model
The Black & Scholes model is still topical in the market finance industry. The price of a European option is yet computed with a simple closed-form...
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Solving Black–Scholes equations using fractional generalized homotopy analysis method
This paper aims to solve the Black–Scholes (B–S) model for the European options pricing problem using a hybrid method called fractional generalized...
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Hedging with physical or cash settlement under transient multiplicative price impact
We solve the superhedging problem for European options in an illiquid extension of the Black–Scholes model, in which transactions have transient...
