11) American Options and Replicating Portfolios

Question 1

What is an American Option

Answer 1

An option that may be exercised at any time prior to expiry

Question 2

What is the lower bound of an American Put Option

Answer 2

Question 3

Describe the proof of the lower bound of an American Put Option

Answer 3

Question 4

How is the value of an American put option calculated at each node in a binomial tree

Answer 4

Question 5

What are the possible payoffs of an American put option

Answer 5

Question 6

Prove that an American call option and a European call option (with the same share, the same exercise price, and the same expiry date) have equal price

Answer 6

Question 7

How is a European call option replicated using a portfolio

Answer 7

Question 8

What is a trading stratgery

Answer 8

The pair (∆, N)
In general the values of ∆ and N may be different for every value of S and t

Question 9

What is a self financing portfolio

Answer 9

The portfolio Π is called self-financing if any change in ∆ (buying/selling shares) is offset by a change in N (selling/buying bonds)