Lognormal Model

Question 1

What is the mean of the lognormal distribution, E[Y]?

Answer 1

E[Y] = e^{m+0.5(v^2)}

Question 2

What is the Variance of the Lognormal Distribution, Var[Y]?

Answer 2

(E[Y])²[e^{v^2}-1]

Question 3

Answer 3

Question 4

E[S_T|S_t] = ?

Answer 4

E[S_T|S_t] = S_te^(α-δ)(T-t)

Question 5

Var[S_T|S_t] = ?

Answer 5

Var[S_T|S_t​] = (E[S_T|S_t)²(e^{v^2}-1)

Question 6

S_T = ?

Answer 6

Question 7

Median =

Answer 7

Median = S_te^{(α-δ-0.5σ^2)(T-t)}

Question 8

Cov(S_t, S_T) =

Answer 8

Question 9

Pr[S_T < K] = ?

Answer 9

Question 10

Pr[S_T > K] = ?

Answer 10

Question 11

Answer 11

Question 12

Answer 12

Question 13

Answer 13

Question 14

Answer 14

Question 15

Express z^U in terms of z^L

Answer 15

z^U = -z^L

Question 16

E[S_T|S_T < K] = ?

Answer 16

Question 17

E[S_T|S_T > K] = ?

Answer 17

Question 18

E[Call Payoff] = ?

Answer 18

Question 19

E[Put Payoff] = ?

Answer 19