I am currently working on the Tian4 trinomial model for vanilla American call/puts. The performance of price accuracy turns out to be quite good. However, I am wondering if there is any way to increase the computation accuracy of delta.

The traditional way of computing delta = (up price - down price)/(uS0 - dS0) performs quite poorly in terms of accuracy.

I believe there must be some ways of weighting up price and down price or middle price unevenly that can significantly increase the accuracy.

Also, since this way of computing delta happens at time dt, this method is inherently flawed. Is there any ways to avoid it or to offset the effects of dt.

Thanks a lot.