c$)$ Suppose the price of a stock today is $610.$ The strike prices of call

and put options trading on the stock are $590.$ These options mature in

$6$ months. The discount risk$-$free rate is $6\%$ per half annum. The riskneutral binomial analysis with a time step of $3$ months of a European put

option produces an option value of $18\mathrm{.}7.$ The downward factor for the

lattice model of the stock$-$price process is $0\mathrm{.}882.$ Identify $1)$ the riskneutral probabilities of the binomial tree, and $2)$ the quarterly variance

of stock returns. Show your calculations.