The stocks price S is $100. After three months, it either goes up and gets multiplied by the factor U = 1.13847256, or it goes down and gets multiplied by the factor D = 0.88664332. Options mature after T = 0.5 year and have a strike price of K = $105. The continuously compounded risk-free interest rate r is 5 percent per year. Todays European call price is c and the put price is p. Call prices after one period are denoted by cU in the up node and cD in the down node. Call prices after two periods are denoted by cUD in the up, and then down node and so on. Put prices are similarly defined. Call prices (in dollars) are given by:

Group of answer choices

c = 6.00, cU = 12.16, cUU = 24.61, and zero at other nodes

c = 4.78, cU = 9.69, cUU = 19.61, and zero at other nodes

c = 7.68, cU = 15.09, cD = 0.47, cUU = 29.61, cUD = 0.94, cDD = 0

c = 8.81, cU = 17.84, cUU = 36.11, and zero at other nodes

please provide explanation