Question

4. The spot price of Apple (AAPL) is $200. The risk-free rate is 0%. Assume that over the next 26 weeks (1/2 year), in the risk-neutral world, every week, AAPL will go up by $4 with 50% chance or down by $4 with 50% chance. (a) (6 points) Let X, denote the (absolute, not percentage) change in the price of AAPL during week i: Compute, in the risk-neutral world, the expectation E(Xi) and variance V(x).

Answer 1

X	p
4	0.5
-4	0.5

E(Xi) = 4 * 0.5 -4*0.5 = 0

Var(Xi) = E(X^2) -E(X)^2

E(X^2) = 16

hence

var(X) = 16