Question

A stock has a price of $30 and an annual return volatility of 58 percent. The risk-free rate is 3.04 percent. Perform calculations in Excel. a. Calculate the call and put option prices with a strike price of $29.5 and a 90-day expiration. (Round your answers to 2 decimal places. Omit the "$" sign in your response.)

Call premium $

Put premium $

b. Calculate the deltas of the call and put. (Negative amounts should be indicated by a minus sign. Round your answers to 4 decimal places.)

Call delta

Put delta

Answer 1

S = Current Stock Price =	30
t = time until option expiration(years) = 90/360 =	0.2500
K = Option Strike Price =	29.5
r = risk free rate(annual) = 3.04% =	0.0304
s = standard deviation(annual) = 58% =	0.58
N = cumulative standard normal distribution
d1	= {ln (S/K) + (r +s^2/2)t}/s√t
	= {ln (30/29.5) + (0.0304 + 0.58^2/2)*0.25}/0.58*√0.25
	0.229200
d2	= d1 - s√t
	= 0.2292 - 0.58√0.25
	-0.0608
Using z tables,
N(d1) =	0.5906
N(d2) =	0.4758
C = Call Premium =	=SN(d1) - N(d2)Ke^(-rt)
	= 30*0.5906 - 0.4758*29.5e^(-0.0304*0.25)
	3.7882
N(-d1) =	0.4094
N(-d2) =	0.5242
P = Put Premium =	=N(-d2)Ke^(-rt) - SN(-d1)
	= 0.5242*29.5e^(-0.0304*0.25) - 30*0.4094
	3.0648

Hence,

Call Premium = 3.79
Put Premium = 3.06

Call Delta = d1 = 0.229
Put Delta = d2 = -0.061

Formula -