Again consider a one period binomial model with two assets $S^{\text{A}\text{A}\text{P}\text{L}}($for Apple$)$

and $S^{\frac{G}{O}OGL}($for Google$)$ as above. Let $u_1=1\mathrm{.}02,d_1=0\mathrm{.}95,d_2=0\mathrm{.}98,r=0,T=1.$

We leave $u_2$ to be determined later.

a$.$ The risk neutral probability is such that tilde$(E)(e^{-rT}{S}_T)=S_0$ where $S$ can be either

Apple or Google. What is the risk neutral probability here? $($Hint : You only need

to use the information on Apple stock here. $)$

b$.$ Assuming that that the risk neutral probability condition is satisfied in this

problem. That is tilde$(E)(e^{-rT}{S}_T^{\frac{G}{O}OGL})=S_0^{\frac{G}{O}OGL}.$ Find $u_2$ using this condition.

c$.$ Verify that the $u_2$ you found in part b is less than $u_1.$ Thus when the no

arbitrage condition is satisfied $($when the risk neutral probability exists$),$ it cannot

be the case that