Question

Consider an option on a non-dividend-paying stock when the
stock is $ 30, the exercise price is $29. The risk –free rate is 5%
per annum, the volatility is 25% per annum, and the time to
maturity is four months.

(a) What is the price of the option if it is European
call?

(b) What is the price of option if it is an American
call?

(c) What is the price of the option if it is a European
put?

Answer #1

Solution :

In the question, it is given that S=$30, Strike price = K = 29, Risk-free rate = 5% , Volatility = 25%

The Black-scholes formula and calculation is given in the below excel sheet

.a. The European call price is $2.52

b.The American call price is the same as the European call price. It is $2.52.

c.The European put price is $1.045

Consider an option on a non-dividend-paying stock when the stock
price is $30, the exercise price is $29, the risk-free interest
rate is 5% per annum, the volatility is 25% per annum, and the time
to maturity is four months. Assume that the stock is due to go
ex-dividend in 1.5 months. The expected dividend is 50 cents. Using
the Black-Scholes-Merton model, what is the price of the option if
it is a European put?

Consider an option on a non-dividend-paying stock when the stock
price is $52, the exercise price is $50, the risk-free interest
rate is 10% per annum, the volatility is 30% per annum, and time to
maturity is 3 months
What is the price of the option if it is a European
call?

What is the price of a European put option on a
non-dividend-paying stock when the stock price is $70, the strike
price is $75, the risk-free interest rate is 10% per annum, the
volatility is 25% per annum, and the time to maturity is six
months?

3) For a call option on a non dividend paying stock the stock
price is $30, the strike price is $20, the risk free rate is 6% per
annum, the volatility is 20% per annum and the time to
maturity is 3 months. Use the Binomial model to
find:
a) The price of the call option?
Please show work

What is the price of a European put option on a
non-dividend-paying stock when the stock price is $100, the strike
price is $100, the risk-free interest rate is 8% per annum, the
volatility is 25% per annum, and the time to maturity is 1 month?
(Use the Black-Scholes formula.)

3) For a call option on a non dividend paying stock the stock
price is $30, the strike price is $20, the risk free rate is 6% per
annum, the volatility is 20% per annum and the time to
maturity is 3 months. Use the Binomial model to
find:
a) The price of the call option?
Can you show the binomial model please

What is the price of a European call option on a
non-dividend-paying stock when
the stock price is $52, the strike price is $50, the risk-free
interest rate is 12% per annum, the
volatility is 30% per annum, and the time to maturity is three
months? (Hint: Remember Black-
Sholes-Merton Model. Please refer to the N(d) tables provided to
you to pick the N values you
need)

Consider a six-month European call option on a
non-dividend-paying stock. The stock price is $30, the strike price
is $29, and the continuously compounded risk-free interest rate is
6% per annum. The volatility of the stock price is 20% per annum.
What is price of the call option according to the
Black-Schole-Merton model? Please provide you answer in the unit of
dollar, to the nearest cent, but without the dollar sign (for
example, if your answer is $1.02, write 1.02).

Consider a European call option on a non-dividend-paying stock
where the stock price is
$40, the strike price is $40, the risk-free rate is 4% per annum,
the volatility is 30% per
annum, and the time to maturity is 6 months.
(a) Calculate u, d, and p for a two-step tree.
(b) Value the option using a two-step tree.
(c) Verify that DerivaGem gives the same answer.
(d) Use DerivaGem to value the option with 5, 50, 100, and 500...

q 19
A non-dividend paying stock is currently trading at $60 and its
volatility is 30% per annum. Risk free rate is 12% per annum.
Consider a European put option with a strike price of $59 that will
expire in three months. What is the price of this put option based
on Black-Scholes model? (Enter your answer in two decimals without
$ sign)

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