Market illiquidity, feedback e ects, presence of transaction costs, risk from unprotected portfolio Note 1: In the title, insert “a” or “the” before “Analytical”? and other nonlinear e ects in PDE-based option pricing models can be described by solutions to the generalized Black–Scholes parabolic equation with a di usion term nonlinearly depending on the option price itself. In this paper, di e...

Nonstandard finite difference schemes for the Black-Scholes partial differential equation preserving the positivity property are proposed. Computationally simple schemes are derived by using a nonlocal approximation in the reaction term of the Black-Scholes equation. Unlike the standard methods, the solutions of new proposed schemes are positive and free of the spurious oscillations.

nonstandard finite difference schemes for the black-scholes partial differential equation preserving the positivity property are proposed. computationally simple schemes are derived by using a nonlocal approximation in the reaction term of the black-scholes equation. unlike the standard methods, the solutions of new proposed schemes are positive and free of the spurious oscillations.

A closed form option pricing formula is obtained, based on a stochastic model with statistical feedback. The fluctuations evolve according to a Tsallis distribution which fits empirical data for stock returns. A generalized form of the Black-Scholes PDE is derived, parametrized by the Tsallis entropic index q. We also derive a martingale representation which allows us to use concepts of risk-fr...

In this paper two different methods are presented to approximate the solution of the fractional Black-Scholes equation for valuation of barrier option. Also, the two schemes need less computational work in comparison with the traditional methods. In this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the appli...

in this paper, we try and valuate preemption rights by modifying the black-scholes model, which is widely used to valuate options and other derivatives. here we first present the basics of the black-scholes model and then we discus modification of the model to be fit for preemption right valuation. at the end, we valuate four of the preemptive rights using the proposed model

in this paper, the pricing of a european call option on the underlying asset is performed by using a monte carlo method, one of the powerful simulation methods, where the price development of the asset is simulated and value of the claim is computed in terms of an expected value. the proposed approach, applied in monte carlo simulation, is based on the black-scholes equation which generally def...

Abstract Dividend paying European stock options are modeled using a time-fractional Black–Scholes (tfBS) partial differential equation (PDE). The underlying fractional stochastic dynamics explored in this work appropriate for capturing market fluctuations which random white noise has the potential to accurately estimate put option premiums while providing good numerical convergence. aim of pape...

We present a method of deriving analytical solutions for two-dimensional Black-Scholes-Merton equation. The consists three changes variables in order to reduce the original partial differential equation (PDE) normal form and then solve it. Analytical two cases option pricing on minimum maximum assets are derived using our shown agree with previously published results. advantage solution procedu...