I am using the explicit finite backward difference scheme to discretize and calculate the price of an European call option in a discretization stencil.

My goal is to find the error at a given time step (e.g. at the 200th time step in a 360 time step model) evaluated at each spatial step (which represents the underlying asset price in this case) for the numerical solution, as compared to the analytical Black Scholes solution.

However, I don't understand how to supply the 200th time step parameter to the Black Scholes equation to calculate the option value at that time step for different asset prices. As far as my understanding goes, the BS equation only takes in the size of the time step, which is calculated by dividing the option duration into equal sizes. It then gives the option value at t=0.

How can I use the BS model to find the option value at, say, t = 200/360?

  • $\begingroup$ Does the binomial model ring a bell? $\endgroup$
    – simsalabim
    Apr 4 at 7:01
  • $\begingroup$ That would not give me option prices at a certain time step evaluated for all asset prices. The goal here is to find the option price for every underlying asset price at a given time step. $\endgroup$
    – atastix
    Apr 4 at 7:11
  • $\begingroup$ Sure you can, if you know how the binomial model works you can apply that mechanism to BS as well? You just need a vector with the timesteps from t=1,...,TTM. I've done it myself. For every t in vT, you calculate the BS price. Fyi; it's a descending sequence. $\endgroup$
    – simsalabim
    Apr 4 at 8:23

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