In this paper, we construct a numerical method to the solution of Black-Scholes partial differential equation modelling Barrier option pricing problem on a single asset. We use finite difference approximations for temporal derivative and then the option price is approximated with the redefined B-spline functions. Stability of this method has been discussed and shown that it is unconditionally s...

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...

How to price options efficiently and accurately is an important research problem. Options can be priced by the lattice model. Although the pricing results converge to the theoretical option value, the prices do not converge monotonically. Worse, for some options like barrier-options, the prices can oscillate significantly. Thus, large computational time may be required to achieve acceptable acc...

This paper presents a simple reduce-form approach to pricing credit derivatives. The definition of default is purely based on the market value of a risky bond and its potential recovery value. A risky bond is treated as a riskless bond with an embedded short position on a barrier option. The risky bond market implicitly prices this barrier option. The default implied volatility (DIV) curve for ...