Question

Suppose S = $100, r = 8% per annum (continuously compounded), t = 1 year, σ = 30% per annum, and δ = 5% per annum. Construct an eight-period binomial tree for the underlying stock using each of the following models

1. Forward binomial tree

2. Cox-Ross-Rubinstein binomial tree

3. Lognormal tree

Using the binomial trees you constructed, please compute the prices an American put struck at K=$95 and has 1 year to expiration. Please highlight early exercise locations on your trees.

Answer 1

Binomial tree by Cox-Ross-Rubinstein

b. 8 period Cox-Ross- Rubistein model. The parametee values are. A = I , ltr = ero= e 0.08 x 33 : 20.01 - 1.0102 tu=erra e 3578 = 1.1119 td = eo - 0.8994 for the risk neutral probability, we get P= rd -d u-d = 1.0102 -0.8994 l'llig - 0.8994 - 0.1108 0.2125 -0.5214

210:11 188.98 189.97 169.95 169.95 152.85 12.85 15285 137-46 137.46 13746 12363 12363 123.63 123.63 100 160 S = loo 89.44 89.94 $9.99 89,94 8099 80-89 8089 80-89 42.752 4245 235 5.43 45-43 5293 52-43 47.6K *-4 42.82 t: t=2 t=3 tus