2. CSR Limited (CSR) is an Australian company that primarily produces building products (e.g., concrete, bricks, etc.). It was initially founded as a company that milled and refined sugar, but sold all its sugar mills in 2010. CSR shares are currently (t = 0) trading at $3.72. An American and European put on CSR shares both have strike price $3.70, and the same expiry date. Consider a six-step binomial model, with (in crr notation) u = 1.37 and d = 1/u . The return over each time step is R = 1.02 .

(a) Construct a six-step binomial pricing tree for the European put and find the premium. (b) Construct a six-step binomial pricing tree for the American put and find the premium.

(c) Now say the European put is a down-and-out barrier option with barrier at the asset price $1.75. Construct a six-step binomial pricing tree for this barrier European put and find the premium.

(d) Now say the American put is a down-and-out barrier option with barrier at the asset price $1.75. Construct a six-step binomial pricing tree for this barrier American put and find the premium.

(e) Discuss the four premium values calculated in parts (a)-(d). In particular, discuss why some premiums are higher than others and why some are equal.