Let S(0) = 100 be the initial price of the risky asset. Consider a European call option with exercise price K and expiry time T = 1 (year). Consider several binomial models and investigate how does the rational price of the option ( ie C(0) ) depends on the choice of the parameters of the model and the strike price K.
I'm trying to answer this question but I'm unsure how to start it. I'm trying to do it on a 1-step, 2-step and a 3-step binomial model and maybe see if there is a pattern but I'm unsure how to start it for the 1-step other than probably having a strike price K = 100. Also I think the 2-step will take one step in 1/2 year and the 3-step model in 1/3 year etc.
What I mean is: when I have to assign random parameters U,D and R, do I just pick any numbers I want or is there a certain interval I should stick to? Like can I say that for 1-step U=1.1 and D=0.9 and then for 2-step something like U=1.2 and D=0.8? Does that work for the question or am I not getting it?