In this paper, we investigate option valuation problems under the fractional Black–Scholes model. The aim is to propose a pricing formula for the European option with transaction costs, where the costs structure contains fixed costs, a cost propositional to the volume traded, and a cost proportional to the value traded. Precisely, we provide an approximate solution of the nonlinear Hoggard–Whal...

Monte Carlo simulation is one alternative for analyzing options markets when the assumptions of simpler analytical models are violated. We introduce techniques for the sensitivity analysis of option pricing which can be efficiently carried out in the simulation. In particular, using these techniques, a single run of the simulation would often provide not only an estimate of the option value but...

We characterize the price of a European option on several assets for a very risk-averse seller, in a market with small transaction costs as a solution of a nonlinear diffusion equation. This problem turns out to be one of asymptotic analysis of parabolic PDE, and the interesting feature is the role of a nonlinear PDE eigenvalue problem. In particular, we generalize previous work of Guy Barles a...

In this paper, a new radial basis function (RBF) approach is developed for solving European option pricing model. Without any simplifications, a simple discretization pattern directly leads to a system Ax = b, moreover, employing a new variable shape parameter (VSP) strategy named binary shape parameter (BSP) strategy leads to more accurat results rather than constant shape parameter (CSP) stra...

Coupon bond European and barrier options are financial derivatives that can be analyzed in the Hamiltonian formulation of quantum finance. Forward interest rates are modeled as a two-dimensional quantum field theory and its Hamiltonian and state space is defined. European and barrier options are realized as transition amplitudes of the time integrated Hamiltonian operator. The double barrier op...

Black and Scholes (1973) proved that under certain assumptions about the market place, the value of a European option, as a function of the current value of the underlying asset and time, verifies a Cauchy problem. We give new conditions for the existence and uniqueness of the value of a European option by using semigroup theory. For this, we choose a suitable space that verifies some condition...

Reduced European call and put option formulas by risk-neutral valuation are given. It is shown that the European call and put options for log-uniformjump-diffusion models are worth more than that for the Black-Scholes (diffusion) model with the common parameters. Due to the complexity of the jump-diffusion models, obtaining a closed option pricing formula like that of Black-Scholes is not tract...

The stock model and option pricing problem are central contents in modern finance. In this paper, generalized stock model for financial market is proposed and the European option pricing formula for the generalized stock model is computed.