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...

the option-pricing problem is always an important part in modern finance. assuming that the stock diffusion is a constant, some literature has introduced many stock models and given corresponding option pricing formulas within the framework of the uncertainty theory. in this paper, we propose a new stock model with uncertain stock diffusion for uncertain markets. some option pricing formulas on...

This thesis examines the performance of five option pricing models with respect to the pricing of barrier options. The models include the Black-Scholes model and four stochastic volatility models ranging from the single-factor stochastic volatility model first proposed by Heston (1993) to a multi-factor stochastic volatility model with jumps in the spot price process. The stochastic volatility ...

in this paper, a new identification of the lagrange multipliers by means of the sumudu transform, is employed to  btain a quick and accurate solution to the fractional black-scholes equation with the initial condition for a european option pricing problem. undoubtedly this model is the most well known model for pricing financial derivatives. the fractional derivatives is described in caputo sen...

The option-pricing problem is always an important part in modern finance. Assuming that the stock diffusion is a constant, some literature has introduced many stock models and given corresponding option pricing formulas within the framework of the uncertainty theory. In this paper, we propose a new stock model with uncertain stock diffusion for uncertain markets. Some option pricing formulas on...

In this article, we propose a numerical algorithm for computing price of discrete single and double barrier option under the emph{Black-Scholes} model. In virtue of some general transformations, the partial differential equations of option pricing in different monitoring dates are converted into simple diffusion equations. The present method is fast compared to alterna...

A fast exponential time integration scheme is considered for pricing European and double barrier options in jump-diffusion models. After spatial discretization, the option pricing problem is transformed into the product of a matrix exponential and a vector, while the matrix bears a Toeplitz structure. The shift-and-invert Arnoldi method is then employed for fast approximations to such operation...

The payoff of a barrier option depends on whether or not a specified asset price, index, or rate reaches a specified level during the life of the option. Most models for pricing barrier options assume continuous monitoring of the barrier; under this assumption, the option can often be priced in closed form. Many (if not most) real contracts with barrier provisions specify discrete monitoring in...