Chapter 9 Put Call Parity

Question 1

Formula for Put-Call Parity for European Option

Answer 1

C(K, T) - P(K, T) = PV(FV(0, T) - K) “Call minus Put equals the present value of the Future Value minus the Strike Price.”

Question 2

Formula for Put-Call Parity for American Options

Answer 2

Trick! Parity often fails for American Options

Question 3

Formula for Put-Call Parity with Stock as the underlying asset

Answer 3

C(K, T) - P(K, T) = S0 - PV(Div) - e^(-rt)

Question 4

Theory: why does the premium on puts and calls with the same strike and time to expiration vary?

Answer 4

Buying a call and selling put is the same as buying synthetic stock with a differing of payment, so the difference is the price of deferring payment until later i.e interest. Of course the opposite holds as well with selling a call and buying a put equal to selling synthetic stock, and receiving payment later, so the premium difference is to compensate you.

Question 5

Put-Call Parity Relationship to buy 1 Euro with American Dollars

Answer 5

C(K, T) - P(K, T) = e^(-rt)(X0*e^((r - rEURO)t) - K)
Where r is the interest rate in ‘Murica and rEuro is the interest rate in Europe and X0 is the starting currency exchange rate ($/Euros)

Question 6

Put-Call Parity Relationship to buy 1 Dollar with Euros

Answer 6

C(K, T) - P(K, T) = e(-rEUROS * t)(X0*e^((rEuros - r)t) - K) where X0 is the starting currency exchange rate (Euros/$)

Question 7

Put-Call Parity Relationship for a Bond

Answer 7

C(K, T) - P(K, T) = e^(-rt)(e^(rt)B0 - PV(Coupons) - K)

Question 8

General Put-Call Parity Relationship

Answer 8

Call - Put = Prepaid Forward Underlying - Prepaid forward for Strike

Question 9

Any Put is a Call if you…

Answer 9

switch the underlying and strike assets

Question 10

A Dollar Denominated Call is equal to a Euro Denominated Put times

Answer 10

strike * exchange rate

C(x, K, t) = K * X * P(1/x, 1/k, t)

Question 11

Premium bounds for a European Call

Answer 11

S>American Call>European Call>max [0, Put-Call Implied Rate] (or equal to)

Question 12

Premium bounds for a European Put

Answer 12

K > American Put > European Call > max[0, put-call implied rate] (or equal to)

Question 13

When should you exercise an American Call option on a non-dividend paying stock

Answer 13

Only at expiration, otherwise you make more by selling the option

Question 14

3 Effects of early exercise with an American Call

Answer 14

1. Pay Strike Price Early (T-V of Money)
2. Receive Dividends Early (if applicable)
3. Throw away implicit put protection

Question 15

When to rule out Early Excercise for an American Call Option.

Answer 15

If K - PV(K) > PV(Dividends) (I.e You lose K - PV(K) by exercising now interest on K must be greater than the gains you would get from dividends)

Question 16

When can’t we rule out Early Excercise for an American Put Option (No dividends)

Answer 16

if K - PV(K) < Call Premium

Question 17

American Options With more time to maturity have a price that is

Answer 17

higher

Question 18

European Options With more time to maturity have a price that is

Answer 18

higher if no dividends

idk otherwise

Question 19

If for some reason the strike price grew with time, puts and calls with longer time to expiration have a price that is

Answer 19

higher

Question 20

A call with a lower strike is ____ compared to a call with a higher strike.

Answer 20

worth more

Question 21

A put with a lower strike is ____ compared to a put with a higher strike.

Answer 21

worth less

Question 22

C(k1) - C(k2) <

Answer 22

k1 - k2

Question 23

P(k2) - P(k1) <

Answer 23

k2 - k1

Question 24

Premiums decrease at a _______ rate

Answer 24

decreasing