Consider the following information for a European call:

Strike price: $160.$

Current asset value: $150.$

Continuous compound annual risk$-$free rate: $6\%.$

The asset does not pay dividends.

The price is calculated using a two$-$period binomial model, each period being one half$-$year in length.

We also have the following price tree

$($a$)$ Find $u$ and $d$ for each period.

$($b$)$ Calculate the value of $p^{**}.$

$($c$)$ Obtain the value of the asset in each of $(V_0,V_1(H),V_1(T),V_2(HH),V_2(HT),V_2(TT)).$

$($d$)$ Calculate the value of the asset at time $0,$ using the binomial model.