Question

Suppose that you are holding a European call option on General Motors stock that expires in 5 years. The option is currently at-the-money. GM's current stock price is $42.50 and the current yield on a 5-year Treasury bond is 2%. The standard deviation of returns on GM stock is 25%. For the purposes of this series of questions, you should assume that GM does not pay dividends.

You may assume that all of the information above applies.

What is the Black-Scholes value of the European call? (Hint: you may use the spreadsheet that we considered in Week 6 to help you answer this question. Please express your answer to the nearest cent.)

Given your answer to the previous question, what is the value of a European put option on GM stock that expires in 5 years and is also currently at-the-money? (Please express your answer to the nearest cent.)

Suppose that the current price of GM stock were $50 instead of $42.50, but the strike price of the options, the time to expiration, the risk-free rate, and the volatility of returns on GM stock were all the same. How would the values of the put and call option change? Provide a clear explanation for why the values move in the direction that you propose. (No additional calculations are necessary for this problem.)

Answer #1

Black Scholes Formula For finding out option pricings:

Excel working

b) For Put Formula is :

excel working:

c) When stock price change to $ 50

you just have to change the Stock price and calculation will be as follows:

as you can see the call option price has increased and put one has decreased due to stock price upward movement.

Thanks Please rate the answer and give feedback

like my work it gives me confidence thaks

1. A call option with a strike price of $35 on ABC stock expires
today. The current price of ABC stock is $30. The call is:
2. A put option with a strike price of $35 on ABC stock expires
today. The current price of ABC stock is $30. The put is:
a. at the money
b. out of the money
c. in the money
d. none of the above

The price of a European call on a stock that expires in one year
and has a strike of $60 is $6. The price of a European put option
on the same stock that also expires in one year and has the same
strike of $60 is $4. The stock does not pay any dividend and the
one- year risk-free rate of interest is 5%. Derive the stock price
today. Show your work.

The price of a European call on a stock that expires in one year
and has a strike of $60 is $6. The price of a European put option
on the same stock that also expires in one year and has the same
strike of $60 is $4. The stock does not pay any dividend and the
oneyear risk-free rate of interest is 5%. Derive the stock price
today. Show your work.

For a European call option and a European put option on the same
stock, with the same strike price and time to maturity, which of
the following is true?
A) Before expiration, only in-the-money options can have
positive time premium.
B) If you have a portfolio of protected put, you can replicate
that portfolio by long a call and hold certain amount of risk-free
bond.
C) Since both the call and the put are risky assets, the
risk-free interest rate...

For a European call option and a European put option on the same
stock, with the same strike price and time to maturity, which of
the following is true?
A) When the call option is in-the-money and the put option is
out-of-the-money, the stock price must be lower than the strike
price.
B) The buyer of the call option receives the same premium as the
writer of the put option.
C) Since both the call and the put are risky...

Consider a European call option and a European put option on a
non dividend-paying stock. The price of the stock is $100 and the
strike price of both the call and the put is $104, set to expire in
1 year. Given that the price of the European call option is $9.47
and the risk-free rate is 5%, what is the price of the European put
option via put-call parity?

Suppose that a 6-month European call A option on a stock with a
strike price of $75 costs $5 and is held until maturity, and
6-month European call B option on a stock with a strike price of
$80 costs $3 and is held until maturity. The underlying stock price
is $73 with a volatility of 15%. Risk-free interest rates (all
maturities) are 10% per annum with continuous compounding.
Use put-call parity to explain how would you construct a
European...

Consider a European call option and a European put option, both
of which have a strike price of $70, and expire in 4 years. The
current price of the stock is $60. If the call option currently
sells for $0.15 more than the put option, the continuously
compounded interest rate is
3.9%
4.9%
5.9%
2.9%

Find the current fair values of a D1 month European call and a
D2 month European put option, using a current stock price of D3,
strike price of D4, volatility of D5, interest rate of D6 percent
per year, continuously, compounded. Obtain the current fair values
of the following:
1.European call by simulation.
2.European put by simulation.
3.European call by Black-Scholes model.
4.European put by Black-Scholes model.
D1
D2
D3
D4
D5 D6
11.2
10.9
31.7
32.6
0.65 9.5

You are given the following information about a European call
option on Stock XYZ. Use the Black-Scholes model to determine the
price of the option:
Shares of Stock XYZ currently trade
for 90.00.
The stock pays dividends continuously
at a rate of 3% per year.
The call option has a strike price of
95.00 and one year to expiration.
The annual continuously compounded
risk-free rate is 6%.
It is known that d1 – d2 = .3000;
where d1 and d2...

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