A Modified Black-Scholes-Merton Model for Option Pricing

Numerical Solutions for Fractional Black-Scholes Option Pricing Equation

In this article we have applied a numerical finite difference method to solve the Black-Scholes European and American option pricing both presented by fractional differential equations in time and asset.

Numerical algorithm for discrete barrier option pricing in a Black-Scholes model with stationary process

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...

How Close Are the Option Pricing Formulas of Bachelier and Black-merton-scholes?

We compare the option pricing formulas of Louis Bachelier and Black-Merton-Scholes and observe – theoretically and by typical data – that the prices coincide very well. We illustrate Louis Bachelier’s efforts to obtain applicable formulas for option pricing in pre-computer time. Furthermore we explain – by simple methods from chaos expansion – why Bachelier’s model yields good short-time approx...

Notes : Black - Scholes - Merton Model ( IEOR 4707 ,

denote an increment of the BM (with ds > 0). We also use N(μ, σ2) to denote a normal distribution with mean μ and variance σ2. Recall some of the key properties of BM: (i) B0 = 0; (ii) independent increments, i.e., dBs and dBt are independent, for any s + ds ≤ t; (iii) stationary increments, i.e., dBs follows a normal distribution N(0, ds). Note this last distribution depends only on the length...

The Black-Scholes-Merton Approach to Pricing Options