Question $3[15$ Points$]$

Assume that the present price of a stock is S$0=1.$ Every three months stock price

moves up by a factor u or moves down by a factor d$.$ The three month interest rate is r$.$

$1.$ Draw the binomial tree $[7\mathrm{.}5$ Points$]$

$2.$ Derive the price of an European call option where the strike price K satisfies following inequality: $[7\mathrm{.}5$ points$]$

u

$2$

d $>$ K