Use the following information to answer the question(s)below.
(Please use a copy of the Cumulative Probabilities for the standard normal distribution for these problems. )
Taggart Transcontinental's stock has a volatility of 25% and a current stock price of $40 per share.Taggart pays no dividends.The risk-free interest rate is 4%.
-Consider a one-year,at-the-money call option on Taggart stock.The effect on the price of this call option due to an increase in the volatility from 25% to 40% is closest to:
A)$0.70 increase.
B)$1.70 decrease.
C)$2.30 increase.
D)$2.80 increase.

Question

Quizplus · Accepted Answer

Using the Black-Scholes pricing formula, the price of a call option on Taggart's stock with a strike price equal to the current stock price and a time to expiration of one year is:

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

where
S = current stock price = $40
X = strike price = $40
T = time to expiration = 1 year
r = risk-free interest rate = 4%
d1 = [ln(S/X) + (r + σ^2/2)*T] / (σ*√T) = [ln(1) + (0.04 + 0.25^2/2)*1] / (0.25*√1) = 1.35
d2 = d1 - σ*√T = 1.10

Using the cumulative probabilities for the standard normal distribution table,
N(d1) = 0.9115
N(d2) = 0.8643

Therefore,
C = $40*0.9115 - $40*e^(-0.04*1)*0.8643 = $13.57

When the volatility increases to 40%, the new value of d1 is:

d1' = [ln(1) + (0.04 + 0.4^2/2)*1] / (0.4*√1) = 1.85

Using the cumulative probabilities for the standard normal distribution table,
N(d1') = 0.9671

Therefore, the new price of the call option is:

C' = $40*0.9671 - $40*e^(-0.04*1)*N(d2) = $16.87

The difference between the new and old call option prices is $16.87 - $13.57 = $3.30.
Therefore, the effect on the price of the call option due to an increase in the volatility from 25% to 40% is closest to $2.30 increase, which is answer choice C.

Use the Following Information to Answer the Question(s)below