Study Session17 - Option Markets and Contracta

Question 0

Protective put

Answer 0

Long position in a Euro put option with an excercise price of X that matures in T years

+

Long position in the underlying stock

Question 1

Fiduciary call composition

Answer 1

Long position in a Euro call option with an exercice price of X maturing in T years on a stock

+

Long position in a pure discount riskless bond that pays X in T years

Question 2

Put-Call parity for euro options

Answer 2

C_0 + [X/(1+Rf)^T] = P_0 + S_0

Question 3

Synthetic euro call option

Answer 3

Buy a Euro put option on the same stock with the same exercice price X and same maturity T

+

Buy the stock

+

Short the PV of X worth of a pure discount riskless bond

Question 4

Synthetic Euro put option

Answer 4

Buying a Euro call option

+

Short the stock

+

Buying the discount bond

Question 5

Synthetic stock position

Answer 5

Buying a euro call option

+

Short a euro put option

+

Buy the discount bond

Question 6

Synthetic pure discount riskless bond

Answer 6

Buy a euro put option

+

Buy the stock

+

short a euro call option

Question 7

probabilities of an up-move and a down-move

Answer 7

πU = risk-neutral probability of an up-move = (1+Rf-D)/(U-D)

πD = 1 - πU

Question 8

Obtenir la valeur d’une option sur actuon sans dividende/intérêt avec arbre binomial

exemple avec période 0—-1—–2

Answer 8

calculer prix de l’action à la dernière période (down/up-move)

calculer la valeur de l’option (max(0, S-c) si c’est un call)

calculer πU et πD

faire la moyenne de la valeur de l’option pondéré par πU et πD

actualiser la valeur avec le risk-free rate

réactualisé jusqu’à T=0 en n’oubliant pas de tenir compte de πU et πD

Question 9

calculer la valeur d’une option sur un actif à revenu-fixe avec arbre binomial

Answer 9

1) calculer le prix de l’obligation à chaque noeud. on peut soit les calculer chacun séparément à la calcu ou calculer à la calcu juste ceux de la dernière période (exemple: T=3) et trouver le prix de l’obligation à la période précédente (T=2) en actualisant au taux d’intérêt de la période précédente (T=2) en faisant la moyenne 50/50 des prix obtenus selon le up/down-move
2) calculer la valeur de l’option à la dernière période et ramener la valeur à aujourd’hui de la même façon qu’expliqué en 1 pour le prix de l’obligation

voir page 71 volume 5

Question 10

expiration value of caplet

Answer 10

max{0,[(final year rate - cap rate)*notional principal)]} / 1+final year rate

floor rate - final year rate in the case of a floorlet

voir page 75 volume 5

Question 11

valuing an interest rate cap

Answer 11

calculate the cap value at final year and actualize it the way we actualize options on bonds

Question 12

Black-Scholes-Merton model assumptions

Answer 12

lognormal distribution

the continous risk-free rate and the volatility of the underlying asset are constant and known

markets are frictionless

the underlying asset has no cash flow

the option valued are euro option

Question 13

Delta describes…

Call option delta are +, - or neutral?
put “””””””””””?

Answer 13

the relationship between asset price and option price

call: positive
put: negative

Question 14

Vega measures…

Answer 14

the sensitivity of the option price to changes in the volatility of returns on the underlying asset

both call and put options are more valuable, all else equal, the higher the volatility

Question 15

Rho measures…

Answer 15

the sensitivity of the option price to changes in the risk-free rate

Call options increase in value as the RF rate increases

Put options decrease in value as the RF rate increases

Question 16

Theta measures…

Answer 16

the sensitivity of the option price to the passage of time

value of call options decline as most put options do as time passes

Question 17

Delta calculation

Answer 17

Delta_call = (C_1 - C_2)/(S_1 - S_2)

= delta C / Delta S