Question

A stock is currently at $50. Over each of the next two 6-month periods, the stock may move up to a factor 1.2 or down by a factor of 0.8 in each period. A European put option with strike price of $48 and maturity of one year is available. The current risk-free rate is 4.0% per year (20 points). a. Is the put option in the money or out the money

Answer 1

Step-by-step explanation:

Solution:

Parameters are u = 0.1, d = −0.1, 1 + r = e

0.5×0.08. So the risk-neutral probability is

p

∗ = 0.7. After evaluation of the options at the terminal nodes we use the risk-neutral

valuation to get (i)

πC(0) = e

−2(0.5×0.08) £

0.7

2 × 21 + 2 × 0.7(1 − 0.7) × 0 + (1 − 0.7)2 × 0

¤

= 9.61

and (ii)

πP (0) = e

−2(0.5×0.08) £

0.7

2 × 0 + 2 × 0.7(1 − 0.7) × 1 + (1 − 0.7)2 × 19¤

= 1.92

(iii) For put-call parity one has to verify S − πC + πP = Ke−r

, here :

100 − 9.61 + 1.92 = 100e

−0.08

.