Question

Consider an option on a non-dividend-paying stock when the stock price is $67, the exercise price is $61, the risk-free rate is 0.5%, the market volatility is 30% and the time to maturity is 6 months. Using the Black-Scholes Model when necessary:

Given: Two dividend payments $1.75 and $2.75, two months and five months from now.

(v) Compute the price of the option if it is an American Call (In Excel & show formulas).

Answer 1

In case of American Call option, valuation should be done by use of Binomial Option pricing model ,by by Cox, Ross and Rubinstein .

deo p-n P - und a

Pay off at last node for call option: Max [ (S_n− K), 0 ]

Value of option at previous node

= [p Option up + (1 -p) Option down] x exp (-r x At)

	Stock Price:	67.00
	Volatility (% per year):	30.00%
	Risk-Free Rate (% per year):	0.50%

Time to Expiration:	0.5000
Exercise Price:	61.00

Time	Dividend
0.1667	1.75
0.4167	2.75

Probability of up move, p = 0.4667
Up step size, u = 1.1618
Down step size, d = 0.8607

84.37587 23.37587 MAX(84.37587-61,0) 75.37069 14.37069 62.50718 71.507182 MAX(62.50718-61,0) 56.548141 0.702559 46.30646 OMAX(46.306-61,0) 7.072956 Node Time: 0.0000 0.2500 0.5000

Value of call option = $ 7.073