Option Markets And Contracts

Question 0

Can use put call parity to create _________

Answer 0

Synthetic instruments

Question 1

Put call parity

Answer 1

C0 + ( X ) = P0 + S0
———
(1+Rf)^T

Call+riskless bond = put + stock

Question 2

Synthetic call

Answer 2

Put + stock - riskless discount bond

Question 3

Synthetic put

Answer 3

= call - stock + riskless discount bond

Just rearrange put call parity

Question 4

Exploit violations of put call parity by buying ____ and shorting _____

Answer 4

Underpriced component

Overpriced component

Question 5

If fiduciary call > protective put,

Answer 5

Take advantage of arbitrage opp:

• sell fiduciary call
• buy protective put

Question 6

Calculate option value using binomial option pricing model

Answer 6

• calc payoff for up and down moves
• calc exp value of option in one year as prob weighted average
• discount exp value to present at risk free rate

Question 7

Given up movement, calculate down movement for stock option valuation (ie when 50% is not assumed)

Answer 7

D = 1/U

Question 8

Calc risk neutral probability of up and down movement

Answer 8

Pi U = 1+Rf-D
———
U - D

Pi D = 1 - Pi U

Question 9

If call option is in (out) of money, what is value?

Answer 9

In: tick price - t=0 price

Out: 0

Question 10

Steps to evaluate option on fixed income w/ binomial tree

Answer 10

1. Price bond at nodes w/projected int rate
2. Calc intrinsic option value at each node
3. Take PV of terminal option values

Assume 50% up/down

Question 11

Steps to value 2 year cap or floor

Answer 11

Calculate expiration value of caplet/floorlet at end of y2
Bring terminal caplet/floorlets to PV
Repeat for y1
Calc value as sum of individual caplets/floorlets

Question 12

Calc expiration value of caplet

Answer 12

1+1yr rate

Question 13

Expiration value of floorlet

Answer 13

1+1yr rate

Question 14

What are assumptions of Black-Scholes-Merton model (BSM)

Answer 14

• underlying asset price follows lognormal distribution
• continuous rf r constant, known
• constant known volatility of asset
• frictionless markets
• asset generates no cf
• European options

Question 15

When is BSM not appropriate?

Answer 15

Valuing int rate options/bond prices
Underlying asset volatility not constant, known
High taxes/transaction costs
Pricing American style options

Question 16

Name BSM sensitivity factors and inputs

Answer 16

Delta - asset price
Vega - volatility
Rho - risk free rate
Theta - time to expiration 
Exercise price

Question 17

Calculate delta

Answer 17

Delta = chg in call price
—————–
chg in stock price

For a call

Question 18

For small changes in stock price, calc change in call/put price

Answer 18

Chg call price ~= N(d1)* chg in stock

Chg put price ~= (N(d1)-1)* chg in stock

Question 19

Delta ranges from __ to __

Call is in the money at ___
Put is in the money at ___

Answer 19

-1 to 1

Close to 1
Close to -1

Question 20

What is Delta neutral portfolio

Answer 20

Combo of short call options w/underlying stock

Value of portfolio doesn’t change when value of stock changes

Requires readjusting to maintain hedge

Question 21

Calc num call options needed to delta hedge

Answer 21

Delta of call option

Question 22

What does gamma measure

Answer 22

Rate of change in delta as underlying stock price changes

Largest w/option at the money

Question 23

Put call parity for options on forwards and futures

Answer 23

C0 + X - Ft = P0
——-
(1+Rf)^T