Question

Use the Black-Scholes model to find the value for a European put
option that has an exercise price of $49.00 and 0.4167 years to
expiration. The underlying stock is selling for $40.00 currently
and pays an annual dividend yield of 0.01. The standard deviation
of the stock’s returns is 0.4400 and risk-free interest rate is
0.06. **(Round your final answer to 2 decimal places. Do not
round intermediate calculations.)**

Put value $ ?

Answer #1

d1 = [{ln(S0/X)} + {t(r - q + ^{2}/2)}]
/ [(t)^{1/2}]

= [{ln(40/49)} + {0.4167(0.06 - 0.01 +
0.44^{2}/2)}] / [0.44(0.4167)^{1/2}]

= -0.1418 / 0.2840 = -0.4991

d2 = d1 - [(t)^{1/2}]

= -0.4991 -
[0.44(0.4167)^{1/2}]

= -0.4991 - 0.2840 = -0.7832

P = [X x e^{-rt} x N(-d2)] - [S0 x e^{-qt} x
N(-d1)]

= [49 x e^{-0.06*0.4167}x N(0.7832)] -
[40 x e^{-0.01*0.4167} x N(0.4991)]

= [49e^{-0.06*0.4167} x 0.7832] - [40 x 0.6912]

= 37.43 - 27.65 = 9.78, or $9.78

Use Black-Scholes model to price a European call option
Use the Black-Scholes formula to find the value of a call option
based on the following inputs. [Hint: to find N(d1) and N(d2), use
Excel normsdist function.] (Round your final answer to 2
decimal places. Do not round intermediate
calculations.)
Stock price
$
57
Exercise price
$
61
Interest rate
0.08
Dividend yield
0.04
Time to expiration
0.50
Standard deviation of stock’s
returns
0.28
Call value
$

Use the Black-Scholes formula to find the value of a call option
based on the following inputs. (Round your final answer to
2 decimal places. Do not round intermediate
calculations.)
Stock price
$
12.00
Exercise price
$
5.00
Interest rate
5.00
%
Dividend yield
4.00
%
Time to expiration
0.4167
Standard deviation of stock’s
returns
31.00
%
Call value
$

Use the Black-Scholes formula to find the value of a call option
based on the following inputs. [Hint: to find N(d1) and N(d2), use
Excel normsdist function.] (Round your final answer to 2 decimal
places. Do not round intermediate calculations.) Stock price $ 57
Exercise price $ 61 Interest rate 0.08 Dividend yield 0.04 Time to
expiration 0.50 Standard deviation of stock’s returns 0.28

Calculate the price of a European call option using the Black
Scholes model and the following data: stock price = $56.80,
exercise price = $55, time to expiration = 15 days, risk-free rate
= 2.5%, standard deviation = 22%, dividend yield = 8%.

3.3 In the Black-Scholes option-pricing model, if volatility
increases, the value of a call option will increase but the value
of the put option will decrease. (True / False)
3.4 The Black-Scholes option pricing model assumes which of the
following?
Jumps in the underlying price
Constant volatility of the underlying
Possibility of negative underlying price
Interest rate increasing as option nears expiration

7. Use the Black -Scholes formula to find the value of a call
option on the following stock:
Time to expiration = 6 months
Standard deviation = 50% per year
Exercise price = $50 Stock price = $50
Interest rate = 3%
Dividend = 0
8. Find the Black -Scholes value of a put option on the stock in
the previous problem with the same exercise price and expiration as
the call option.
NEED HELP WITH NUMBER 8

Using the Black-Scholes option valuation, calculate the
value of a put option under the following parameters:
The underlying stock's current market price is $40; the
exercise price is $35; the time to expiry is 6 months; the standard
deviation is 0.31557; and the risk free rate of return is
8%.
A. $8.36
B. $1.04
C. $6.36
D. $2.20
The current market price of one share of ABC, Inc. stock
is $62. European style put and call options with a strike...

. Use the Black-Scholes model to find the price for a call
option with the following inputs: (1) current stock price is $45,
(2) exercise price is $50, (3) time to expiration is 3 months, (4)
annualized risk-free rate is 3%, and (5) variance of stock return
is 0.50.
. Using the information from question above, find the value of a
put with a $50 exercise price.

Which of the inputs in the Black-Scholes-Merton option pricing
model are directly observable?
The price of the underlying security
The risk-free rate of interest
The time to expiration
The variance of returns of the underlying asset return
The price of the underlying security, risk-free rate of
interest, and time to expiration

Black-Scholes Model Use the Black-Scholes Model to find the
price for a call option with the following inputs: (1) Current
stock price is $21. (2) Strike price is $24. (3) Time to expiration
is 5 months. (4) Annualized risk-free rate is 4%. (5) Variance of
stock return is 0.17. Round your answer to the nearest cent. In
your calculations round normal distribution values to 4 decimal
places.
Please show step by step calculations in excel. Thank you

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