This question asks you to price and describe the replicating portfolio for options on a non-dividend-paying stock whose price is currently $16. The price evolves on a binomial tree as follows:

The time interval between each stage is h = 6 months (ie, six months from today the price will be either 24 or 12; six months later, it will be either 36, 18, or 9). The discretely compounded six-month rate is 5.127%.

(b) Find the price of the following options:

i. An at-the-money European call expiring in 6 months.

ii. A European call with strike 17, expiring in 1 year.

iii. An American call with strike 17, expiring in 1 year.

iv. A European put with strike 17, expiring in 1 year.

v. An American put with strike 17, expiring in 1 year.

Bok or sta as k