Question

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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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?

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.)

You are evaluating a European call option on a no-dividend
paying stock that is currently priced $42.05. The strike price for
the option is $45, the risk-free rate is3% per year, the volatility
is 18% per year, and the time to maturity is eleven months. Use the
Black-Scholes model to determine the price of the option.

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).

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?

A stock index level is currently 2,000. Its volatility is 25%.
The risk-free rate is 4% per annum (continuously compounded) for
all maturities and the dividend yield on the index is 2%. Using the
Black-Scholes model:
a) Derive the value a 6-month European put option with a strike
price of 2020.
b) Derive the position in the index that is needed today to
hedge a long position in the put option. Assume that the option is
written on 250 times...

Consider an option on a non-dividend-paying stock when the
stock is $ 30, the exercise price is $29. The risk â€“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?

The price of a non-dividend paying stock is $19 and the price of
a three-month European put option on the stock with a strike price
of $20 is $1.80. The risk-free rate is 4% per annum. What is the
price of a three-month European call option with a strike price of
$20? Is the call option in the money or out of the money? Explain
Is the put option in the money or out the money? Explain

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)

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

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