Question

Suppose you have a call option on a stock with a strike price of $2 2. A) Fill in the stock price and strike price in the table and calculate the exercise value ( B) Plot the Stock price on the x-axis and the Exercise value on the y-axis. Be sure to label both axes with titles and include a chart title. Now assume you have the following data for a call option: Current stock price Strike price Time to expiration Risk - free rate Stock return standard deviation $65.00 $70.00 1.0 4 . 0 % 35 .00% C) Fill in the components of the Black -Scholes model and calculate d 1 and d 2 D) Calculate the value of N(d 1 ) and N(d 2 ) using the Excel function and find the value of V C Now use the binomial option pricing model in conjunction with the following data to value a call option: Current stock price, P = $27.00 Risk - free rate, r RF = 5 % Strike price, X = $25.00 Up factor for stock price, u = 1.41 Down factor for stock price, d = 0.71 Years to expiration, t = 0.50 E) Calculate the stock price using the binomial model and find the option payoff in each case, in addition to the value of N S F) Calculate the portfolio payoff in each case and find the present value of the payoff, in addition to the value of the call option

Answer 1

Soln : A) Please refer the table here, we are assuming the stock price and prepare the table :

Stock Price	Strike price	Exercis value
19	22	0
20	22	0
21	22	0
22	22	0
23	22	1
24	22	2
25	22	3

B) Please refer the graph here :

C) Given Data:

Current Stock Price, S	Strike price, K	Time to expiration,t	Risk free rate, r	Std. deviation,s
65	70	1	4%	35%

Now , Let C be the call option value, as per black scholes option formula,

C = S*N(d1) -X*e^-rt *N(d2)

d1=( ln(S/K) + (r+s²/2)*t)/s*t^0.5, on putting the values, we will get the value of d1 = 0.0775

and d2 = d1 - s*t^0.5, = 0.0775 - 0.35*1^0.5 = -0.2725

D) Using excel formula normsdist(d1) &d2 we will get N(d1) = 0.5309 and N(d2) = 0.3926

We can calculate C = 65*0.5309 - 70*0.3926 *e^-0.04 = 8.10

Value of call option = 8.10

E) Given , u = 1.41 and d = 0.71 , t = 0.50

Lets calculate the probability,p of going up of pricing and 1-p is for price go down

p = (e^rt-d) /(u-d) = (e^0.5*0.05 - 0.71)/(1.41-0.71) = 0.45 and 1-p = 0.55

Up price = current price *u = 27*1.41 = $38 and down price = 27*0.71 = 19.17

Strike price = 25 , So , the value of the call option = (38-25) *e^-0.5*0.05 * 0.45- 0 *0.55 = $5.74

Pay off in this case is either 0 or 13