A SunSet Co. customer would like to obtain a 3-month option to purchase additional units of a product for $77 each. This product currently sells for $76 each. Assume u equals 1.1502 and d = .8694. Approximately what price per unit should SunSet charge for this option if the annual risk-free rate is 2.8 percent?

Question

A) $4.79
B) $5.98
C) $6.17
D) $6.02
E) $5.07

Answer 1

E) $5.07
Explanation: % increase = u ? 1
% increase = 1.1502 ? 1
% increase = .1502, or 15.02%
% decrease = d ? 1
% decrease = .8694 ? 1
% decrease = ?.1306, or ?13.06%
Price with increase = $76(1.1502)
Price with increase = $87.42
Price with decrease = $76(.8694)
Price with decrease = $66.07
rf = Probability of rise(Increase percent) + (1 ? Probability of rise)(Decrease percent)
.028(3/12) = Probability of rise(.1502) + (1 ? Probability of rise)(?.1306)
Probability of rise = .49, or 49%
Probability of fall = 1 ? .49
Probability of fall = .51, or 51%
Payoff if price increases = $87.42 ? 77
Payoff if price increases = $10.42
Payoff if price decreases = $0
Expected payoff = .49($10.42) + .51($0)
Expected payoff = $5.1058
Option value = $5.1058/{1 + [.028(3/12)]}
Option value = $5.07