An Efficient Numerical Method for Pricing Double-Barrier Options on an Underlying Stock Governed by a Fractal Stochastic Process

After the discovery of fractal structures financial markets, enormous effort has been dedicated to finding accurate and stable numerical schemes solve fractional Black-Scholes partial differential equations. This work, therefore, proposes a scheme for pricing double-barrier options, written on an underlying stock whose dynamics are governed by non-standard stochastic process. The resultant model is time-fractional herein referred as model. presence derivative helps capture time-decaying effects while capturing globalized change in prices barriers. In this paper, we present construction proposed scheme, analyse it terms its stability convergence, two examples double knock-in barrier-option problems. results suggest that unconditionally convergent with order O(h2+k2).