Consider a European call with an exercise priceof $50$ on a stock priced at $60.$ The stock can goup by $15$ percent or down by $20$ percent in eachof two binomial periods. The risk$-$free rate is $10$percent. Determine the price of the optiontoday. Then construct a risk$-$free hedge of longstockandshortoption.Ateachpointinthebinomial tree, show the composition and valueof the hedge portfolio and demonstrate that thereturn is the same as the risk$-$free rate. On anyrevisions to the hedge portfolio, make thetransactions $($buying or selling$)$ in stock andnot options. You can borrow any additionalfunds required at the risk$-$free rate, and anyexcess funds should be invested at the risk$-$freerate.