Black-Scholes equation as one of the most celebrated mathematical models has an explicit analytical solution known formula. Later variations equation, such fractional or nonlinear equations, do not have a closed form expression for corresponding In that case, will need asymptotic expansions, homotopy perturbation method, to give approximate solution. However, is non-smooth at special point. We ...

This paper analyses the model of Black–Scholes option pricing from point view group theoretic approach. The study identified new independent variables that lead to transformation equation. Furthermore, corresponding determining equations were constructed and symmetries found. As a result, findings demonstrate integrability present an invariant solution for Ornstein–Uhlenbeck stochastic process.

We present a new nonlinear version of the well-known Black-Scholes model for option pricing in financial mathematics. The partial differential equation is based on quasilinear diffusion term with p-Laplace operator \(\Delta_p\) \(1 < p \infty\). existence and uniqueness weak solution weighted Sobolev space proved, first, by methods parabolic problems using Gel'fand triplet and, alternatively...

A family of local spectral evolution kernels (LSEKs) are derived for analytically integrating a class of partial differential equations (PDEs) 0021-9 doi:10. * Co E-m o ot u 1⁄4 AðtÞ o 2 ox2 þ BðtÞ o ox þ CðtÞ u: The LSEK can solve the above PDEs with x-independent coefficients in a single step. They are utilized in operator splitting schemes to arrive at a local spectral time-splitting (LSTS) ...

This paper considered the notion of European option which is geared towards solving analytical and numerical solutions. In particular, we examined Black-Scholes closed form solution modified (MBS) partial differential equation using Crank-Nicolson finite difference method. These equations were approximated to obtain Call Put prices. The explicit price both options found accordingly. solutions c...

A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the disc...

A generalized option-pricing formula is found, based on a nonGaussian stock price model. The dynamics of the underlying stock are assumed to follow a stochastic process with anomalous nonlinear diffusion, phenomenologically modelled as a statistical feedback process within the framework of the generalized thermostatistics proposed by Tsallis. A generalized form of the Black-Scholes differential...