Question

Please show work.

Consider a two-period binomial tree with the following parameters: S = 100, u = 1:20, d = 0:80, and R = 1:10. Suppose also that a dividend of $5 is expected after one period.

Find the tree of prices of a European Put option with a strike of 100 expiring in two periods.

Find the tree of prices of an American Put option with a strike of 100 expiring in two periods.

Is there a difference between the European and American Put price and why (if there is any)?

Answer 1

An european opton can be excercised only at the end of the period. While an American option can be excercised anytime. Hence the price of the options may differ.

European Put Option price = Binomial Value at all nodes

American Put option Price = Max ( Binomial Value, excercise price)

S0= 100

U taken as 1.2 (20% upward movement)

V taken as 20% downward movement

risk free rate taken as 1.1%

S0*U =120, S0*V =80

S0*U*U = 144, S0 *U*V =96, S0*V*V= 64

Calculating p

p= E^.01*1-.d/(u-d)

p=0.527, 1-p = 0.472

Vn= max {strike price-uS0,0} = 20,0 (for first level) and (44, 0,0) for second level

Price of European Put = 2.7^(-.011 *1) { p *20 +(1-p)*.

Similarly you can calculate the value of the option at each node.