Exotic Options

Question 1

For arithmetic average options, how do you find S ?

Answer 1

Add up all the stock prices and divide by n

Question 2

For geometric average options, how do you find S ?

Answer 2

Multiply all the stock prices together and raise the product to the 1/n power

Question 3

The value of an Asain option is [≤, =, ≥] to the value of an otherwise equivalent ordinary option.

Answer 3

The value of an Asain option is ≤ to the value of an otherwise equivalent ordinary option.

Question 4

As N increases, the value of an average price options increases/decreases ?

Answer 4

As N increases, the value of an average price options decreases.

Question 5

As N increases, the value of an average strike options increases/decreases ?

Answer 5

As N increases, the value of an average strike options increases.

Question 6

What are the three types of barrier options?

Answer 6

1. Knock-In
2. Knock-Out
3. Rebate

Question 7

Knock-In Option + Knock-Out Option = ?

Answer 7

Knock-In Option + Knock-Out Option = Ordinary Option

Question 8

If barrier is less than or equal to the strike price, then

Answer 8

If barrier is less than or equal to the strike price, then

up-and-in call = ordinary call

Question 9

If barrier is greater than or equal to the strike price, then

Answer 9

If barrier is less than or equal to the strike price, then

down-and-in put = ordinary put

Question 10

Describe the mechanics of a compound option

Answer 10

At time 0, you purchase an option expiring at time t₁ that allows you to buy or sell another option that expires at time T for strike price x.

Question 11

Describe the payoff of a Compound Option

Answer 11

At time t₁, the payoff is the same as any other option, but you replace the stock price with the price of the underlying option.

Question 12

What are the two versions of PCP for compound options?

Answer 12

1. CallOnCall - PutOnCall = C_Eur - xe^-rt
2. CallOnPut - PutOnPut = P_Eur - xe^-rt

Above, t = t₁

Question 13

For Gap Options:

K₁ = ?

K₂ = ?

Answer 13

K₁ = Strike Price (determines the amount of payoff)

K₂ = Trigger Price (determines if there is a payoff)

Question 14

How do you find the price of Gap Options?

Answer 14

Use B-S equation.

K₁ gets used in the formula for the price of the option

K₂ gets used to calculate d₁ and d₂

Question 15

What is the PCP for Gap options?

Answer 15

GapCall - GapPut = S₀e^-δt - K₁e^-rt

Question 16

For an exchange option:

σ =

Answer 16

Question 17

What is the time t price of an Asset-or-Nothing Put?

Answer 17

AONP = S_te^-δ(T-t)N(-d₁)

Question 18

What is the time t price of an Asset-or-Nothing Call?

Answer 18

AONC = S_te^-δ(T-t)N(d₁)

Question 19

What is the time t price of an Cash-or-Nothing Put?

Answer 19

CONP = e^-r(T-t)N(-d₂)

Question 20

What is the time t price of an Cash-or-Nothing Call?

Answer 20

CONC = e^-r(T-t)N(d₂)

Question 21

Describe a Forward Start Option

Answer 21

A forward start option is an option expiring at time T whose strike price is set on future date t ≤ T to be x% of the time t stock price.

Question 22

What is the time 0 price of a forward start call option?

Answer 22

V₀ = F^P_0,t(S) • [e^-δ(T-t)N(d₁) - Xe^-r(T-t)N(d₂)]

Question 23

Max(A,B) =

Answer 23

Max(A,B) = Max(0,B-A) + A

or

Max(A,B) = Max(A-B,0) + B

Question 24

For c < 0, Max(cA,cB) =

Answer 24

For c < 0, Max(cA,cB) = c•Min(A,B)

Question 25

For c > 0, Max(cA,cB) =

Answer 25

For c > 0, Max(cA,cB) = c•Max(A,B)

Question 26

Max(A,B) + Min(A,B) =

Answer 26

Max(A,B) + Min(A,B) = A + B

Question 27

Min(A,B) =

Answer 27

Min(A,B) = -Max(A,B) + A + B