Question

Use the Black-Scholes formula to value the following options:

a. A Call option written on a stock selling for $100 per share with a $110 exercise price. The stock's standard deviation is 15% per quarter. The option matures in three months. The risk free interest is 3% per quarter.

b. A put option written on the same stock at the same time, with the same exercise price and expiration date.

Now for each of these options find the combination of stock and risk-free asset that would replicate the option.

Answer #1

So current stock price = 100

K strike price = 110

r risk free rate = 3% = 0.03

s: standard deviation = 15% per quarter

s: standard deviation per annum = 15%*(40.5) = 15%*2 = 30%

t: time to maturity = 3month = 0.25 year

d1 = -0.5104

d2 = -0.6604

N(d1) = normsdist(d1) = 0.3049

N(d2) = normsdist(d2) = 0.2545

C: value of call option

e: natural exponent

**c = 2.703**

p: price of put option

Using put call parity

c + K*exp^(-r*t) = p + So

**p = c + K*exp^(-r*t) - So = 11.881**

(a) Replicating portfolio call option

Buy N(d1) stocks = 0.3049

Value of stock = 100*0.3049 = 30.49

Sell bond worth = 30.49 - 2.703 = 27.787

(b) Replicating portfolio put option

Sell N(-d1) stocks = 1- 0.3049 = 0.6951

Value of stock = 100*0.6951 = 69.51

Buy bond worth = 69.51 + 11.881 = 81.391

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

1. What is the
value of the following call option according to the Black Scholes
Option Pricing Model? What is the value of the put options?
Stock Price = $55.00
Strike Price = $50.00
Time to Expiration = 3 Months = 0.25 years.
Risk-Free Rate = 3.0%.
Stock Return Standard Deviation = 0.65.
SHOW ALL WORK

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...

. Assume the following for a stock and a call option written on
the stock.
EXERCISE PRICE = $30
CURRENT STOCK PRICE = $30
Standard Deviation = .35 (square it to find variance)
TIME TO EXPIRATION = 3 MONTHS = .25
RISK FREE RATE = 4%
Use the Black Scholes procedure to determine the value of the
call option.
Use the Black Scholes procedure to determine the value of the
Put option

. 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.

Use the Black-Scholes formula to calculate the value of a
European call option on silver futures. The option matures in six
months. The current nine-month futures price is $10 per oz, the
strike price of the option is $8, the risk free interest rate is
12% per annum and the volatility of the futures price is 18% per
annum. Use the NORM.S.DIST(x) function in Excel. Round to two
decimals.
What is the delta of the call option on the futures...

An analyst is interested in using the Black-Scholes model to
value call options on the stock of Ledbetter Inc. The analyst has
accumulated the following information: The price of the stock is
$30. The strike price is $22. The option matures in 4 months. The
standard deviation of the stock’s returns is 0.40. The risk-free
rate is 4%. Using the Black-Scholes model, what is the value of the
call option?

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 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
$

1. Calculate the value of the D1 parameter for a call option in
the Black-Scholes model, given the following information: Current
stock price: $65.70 Option strike price: $74 Time to expiration: 7
months Continuously compounded annual risk-free rate: 3.79%
Standard deviation of stock return: 22%
2. Calculate the value of the D2 parameter for a call option in
the Black-Scholes model, given the following information: Current
stock price: $126.77 Option strike price: $132 Time to expiration:
6 months Continuously compounded...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 30 minutes ago

asked 41 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago