Before I turn to the numerical implementation of a Crank-Nicolson scheme to solve this problem, let’s see already how the solution looks like in the video below. Your browser does not support the video tag. As you can see, the maximum of the function $u$ occurs at $t=0$, after which $u$ keeps decreasing.
2.2. Closed-form valuation. The closed-form solution for the vanilla options are known, but the closed-form prices for the barrier option and the rebate barrier option are valued using the extended Black-Scholes pricing formula, as given in Equation (2.7).Let ZRDO represent the value of the zero-rebate down-and-out call option, RDOE is the value of down-and-out call option that pays a rebate ...
To employ Crank-Nicolson for american options, linear systems in each layer can be solved using a numerical method called Projected SOR (Successive Overrelaxation). Using this method, for each time layer i, we have the iterative scheme: Pyhon implementation. Suppose we have an american put option:
The pseudo-code implementation of the Crank-Nicolson –nite di⁄erence method for pricing an American put option is given below. In our implementation, we have introduced a storage e¢ ciency improvement. The option value array C[i,j] only has two time indices, namely i=0,1. The time index i=1 is used to temporar-ily store the discounted ...
3.1 European Options 3.1.1 Methods Based on Reduction to the Heat Equation Recalling the transformation of Black-Scholes equation into the heat equation given in section
