Interpretation of Black Sholes Formula

Instructions: Use the following information in the Black Sholes
continuous dividend spreadsheet and answer the following problems.

Information provided for problem

SoftwareCo So=$30

R=4.0%

T=.75 years

Std deviation=40%

D=2.0%

1) What is the current price of the European call option?

The current price utilizing the above variables yields a call price of
$6.92. Although it wasn’t asked, the put price is $1.63.

2) What happens when the standard deviation is increased? Why?

The measurement of volatility is the standard deviation of the daily
price changes in the security. The more volatile the underlying
security, the greater the price of the option. Therefore, the call and
put prices also increase when the standard deviation is increased. The
d1, d2, N(d1), N(d2) prices decrease for the call outputs and increase
for the put outputs.

3)What happens when the time to maturity if increased? Why?

The call and put prices also increase when the time to maturity is
increased. The d1, d2, N(d1), N(d2) prices decrease for the call outputs
and increase for the put outputs. The value of an option will change
over time even if the stock price remains unchanged. This is because, as
the date of maturity comes close,r the expected change in the value of
the underlying asset reduces. When the time to maturity increases, the
opposite holds and the call and put prices also increase.

4)What happens when the exercise price is increased? Why?

The call price decreases and the put price increases. The outputs for
the call outputs decrease and the put outputs increase.

5)What happens when the riskfree rate is increased? Why?

The call price increase in value and the put price decrease. The outputs
for the call options increase and outputs for the put options decrease.
In practice, when interest rates go up usually stock

prices down, so a rate increase is bad for a call and good for a put.

6)What happens when the dividend yield is increased? Why?

The call price and the call outputs decrease while the put outputs and
put price increase.

7)What happens when the standard deviation is really close to zero? Why?


When the standard deviation is close to zero, there is low volatility
which lowers the call and put prices. The call outputs increase while
the put outputs decrease.

8)What happens when the time to maturity is really close to zero? Why?

The call and put prices decrease. An options price decays each day it is
in existence, and the closer the option gets to expiration the faster it
decays. Therefore, the call and put prices decrease.