S^a

Question 1

What is the expected value of S(T)^a ?

E[S(T)^a] =

Answer 1

E[S(T)^a​] = [S(t)^a]e^{a(α-δ) + 0.5a(a-1)σ^2}

Question 2

What is the forward price of [S(T)^a]?

F_t,T[S(T)^a] =

Answer 2

F_t,T[S(T)^a​] = [S(T)^a]e^{a(r-δ) + 0.5a(a-1)σ^2}

Question 3

What is the yield on the derivative of S(T)^a?

δ* =

Answer 3

δ* = r - a(r - δ) - 0.5a(a - 1)σ²

Question 4

What is the return on the option of S(T)^a?

γ =

Answer 4

γ = a(α - r) + r