Question

A stock is currently priced at $75.00. The risk free rate is 4.5% per annum with continuous compounding. Use a one-time step Cox-Ross-Rubenstein model for the price of the stock in 13 months assuming the stock has annual volatility of 24.9%. Compute the price of a 13 month call option on the stock with strike $80.00.

Answer 1

und dze-ovim

the value of call option at previous node ;

Binomial Value = [p x Option up + (1 - p) x Option down] x exp(-- * At)

option value on Up or Down in case of call : Max (S_n-K,0)

from given data :

Stock Price	75
Strike Price	80
Volatility	24.90%
Risk free Rate	4.50%
time	13 month	1.083(year)
U	1.296011	2.72^(24.9%*((1.083)^0.5))
d	0.771598	2.72^-(24.9%*((1.083)^0.5))
P	0.530834	(2.72^(0.045*1.083)-0.771598)/(1.296011-0.771598)
1-P	0.469166	1-0.530834
			call value
option up	97.20084	75*1.296011	17.20084386	MAX(97.20084-80,0)
option down	57.86987	75*0.771598	0	MAX(57.86987-80,0)
binomial value of call option	8.696202	(0.530834*17.20+0.469166*0)/(2.72^(0.045*1.083))