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.