I am running code that values vanilla options using the binomial model with discrete dividends. I am not sure how to decide how many time steps to use in the grid. Are there some guidelines for this?I'm thinking that one guideline would be to set the number of time steps based on the time to option expiration. For an option expiring in one week, I might set the number of time steps to 20, whereas for an option expiring in six months, I might set the number of time steps to 50.Another guideline would involve my desired accuracy. In my testing, I found that with an accuracy of three decimal places, my results start to converge when I set the time steps to about 15. With an accuracy of four decimal places, my results start to converge after about 50 - 75 time steps.In my code, I will have to calculate implied volatilities. I'm thinking that one way to solve for an implied volatility without requiring too many time steps in the algorithm would be to start with a low number of time steps when guessing at the implied volatility. As my guess gets closer, I'll increase the number of time steps. Would I run into any problems using this method?My last thought is that, if the underlying asset won't receive a dividend during the remaining life of the option, I'll skip the binomial model altogether and use the Black Scholes model with a dividend yield of zero.I ran some tests to check these, but I wanted to find out if anyone here has some rules of thumb that they follow.

Depends on how much precision you require.If you know your required precision, match it with the convergence rate.The convergence rate depends on the payoff function and can be anything between 1/n and 1/sqrt(n), see Heston & Zhou (2000): http://apps.olin.wustl.edu/faculty/zhou/HZ-MF00.pdf

Hello JRobinson. are you tackling a school exercise or do you intend to use the binomial method for real pricing of options?i mean authors point out the lack of accurateness of this method. see, for example Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach

i haven't use trees for discrete dividends but they can be highly accurate in the continuous case if done correctly.http://ssrn.com/abstract=1030143