If you are analyzing options on a stock that pays dividends, which of the following cases can the binomial tree handle:

I. Fixed dividend $($i$.$e$.$ $$2$ dividend in $6$ months$)$

II$.$ Percentage dividend $($i$.$e$.4\%$ of the share price in $6$ months$)$

III. Conditional dividend $($i$.$e$.$ $$4$ dividend if share is up$,$ $$1$ if share is down$)$

IV$.$ Random dividend $($i$.$e$.$ dividend is randomly determined by coin flip in $6$ months$)$

None of the choices are correct

I, II and III only

I and II only

I only

I, II$,$ III and IV