Binomial Model

Question 1

An option can be replicated by buying ___ shares of the underlying stock and lending ___ at the risk free rate.

Answer 1

An option can be replicated by buying Δ shares of the underlying stock and lending B at the risk free rate.

Question 2

Replicating Portfolio

Δ =

Answer 2

Question 3

Replicating Portfolio

B = ?

Answer 3

Question 4

Replicating Portfolio

Option Price (V) = ?

Answer 4

Question 5

Replicating Portfolio

For Call Options, Δ is ( + / – ) and B is ( + / – )?

Answer 5

Replicating Portfolio

For Call Options, Δ is ( + ) and B is ( – )?

Question 6

Replicating Portfolio

For Put Options, Δ is ( + / – ) and B is ( + / – )?

Answer 6

Replicating Portfolio

For Put Options, Δ is ( – ) and B is ( + )?

Question 7

p^* = ?

Answer 7

Question 8

Option price (V) under risk neutral pricing

Answer 8

V = e^-rh[(p^*)V_u + (1-p^*)V_d]

Question 9

p = ?

Answer 9

Question 10

Option price (V) under true pricing

Answer 10

V = e^-γh[(p)V_u + (1-p)V_d]

Question 11

e^γh = ?

Answer 11

Question 12

Forward Tree

u = ?

d = ?

Answer 12

u = e^{( r - δ )h + σ√(h)}

d = e^{( r - δ )h - σ√(h)}

Question 13

Jarrow Rudd Tree

u = ?

d = ?

Answer 13

Question 14

Cox-Ross-Rubinstein Tree

u = ?

d = ?

Answer 14

u = e^σ√(h)

d = e^-σ√(h)

Question 15

How can you tell if arbitrage is available in the binomial model?

Answer 15

Arbitrage is available if the following inequality is not satisfied:

d < e^{( r - δ )h} < u

Question 16

What substitutions do you need to make for Options on Futures Contracts?

Answer 16

S_t →F_{t, T}

δ → r

Question 17

Options on Futures Contracts

p^* = ?

Answer 17

Question 18

Options on Futures Contracts

Δ = ?

Answer 18

Question 19

Options on Futures Contracts

B = ?

Answer 19

B = e^-rh[(p^*)V_u + (1 - p^*)V_d]