INVESTING AND FINANCIAL MARKETS Surname 1
Capital Markets
Name
Institutional Affiliation
Course Code/ Name
Instructor
Due Date
, INVESTING AND FINANCIAL MARKETS Surname 2
1. A call option has a striking price of $8.10 and an expiry date of six months. The underlying
stock is currently trading at $7.60 and has historically exhibited a standard deviation of 10.6
percent. The standard deviation is not expected to change. The interest rate is 5.4 percent. Using
the black-Scholes equation, estimate the value of the call option described above. What are some
of the limitations of using black Scholes equation?
Solution
The following parameters are required in order to use the Black-Scholes equation to
estimate the call option's value;
Present value of the stock (S) = $7.60
Price at strike (K) = $8.10.
Expiration date (T) = six months (0.5 years)
Risk-free interest rate (r) = 5.4%, or 0.054
Volatility (σ) = 10.6% or 0.106
To price a European call option, we use the following Black-Scholes formula:
C=S0N(d1) − Ke^(9−rT) N(d2)
Where; C = call option price
S0= current stock price
N(d)= cumulative distribution
d1=
ln ( )(
S0
K
+ r+
σ2
2 )
T
σ √T
d2 = d1-σ √ T
Capital Markets
Name
Institutional Affiliation
Course Code/ Name
Instructor
Due Date
, INVESTING AND FINANCIAL MARKETS Surname 2
1. A call option has a striking price of $8.10 and an expiry date of six months. The underlying
stock is currently trading at $7.60 and has historically exhibited a standard deviation of 10.6
percent. The standard deviation is not expected to change. The interest rate is 5.4 percent. Using
the black-Scholes equation, estimate the value of the call option described above. What are some
of the limitations of using black Scholes equation?
Solution
The following parameters are required in order to use the Black-Scholes equation to
estimate the call option's value;
Present value of the stock (S) = $7.60
Price at strike (K) = $8.10.
Expiration date (T) = six months (0.5 years)
Risk-free interest rate (r) = 5.4%, or 0.054
Volatility (σ) = 10.6% or 0.106
To price a European call option, we use the following Black-Scholes formula:
C=S0N(d1) − Ke^(9−rT) N(d2)
Where; C = call option price
S0= current stock price
N(d)= cumulative distribution
d1=
ln ( )(
S0
K
+ r+
σ2
2 )
T
σ √T
d2 = d1-σ √ T
