Question

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?

Answer #1

Stock price S_{0} = $30

Exercise price K = $29

Interest rate r = .05

= 0.25

T = 4/12

Ex-dividend

The present value of the dividend must be substracted form the stock price

30-0.5e^{-0.125*0.05} = 29.5031

d_{1} =

=

=0.3068

d_{2 =}

= 0.1625

N(-d_{2}) = 0.3795, N(-d_{2})
=0.4355

We get 0.3795 by using NORMSDIST Function in Excel

=N(-3068) = 0.6205 Same method for N(-d_{2})

The Price of option when it is European Put is

29e^{-0.05*4/12} * 0.4355 - 29.5031 * .3795 = $1.22

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?

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.)

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).

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
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months?

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
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on Black-Scholes model? (Enter your answer in two decimals without
$ sign)

A non-dividend paying stock sells for $110. A call on the stock
has an exercise price of $105 and expires in 6 months. If the
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13.86
3.24
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Consider an option on a stock where the stock price is $30, the
strike price is $29, the continuously compounded risk-free rate of
return is 5% per year, the continuously compounded standard
deviation of its return is 25% per year and the time to maturity is
4 months. If this stock is due to go ex-dividend in 1.5 months and
paying a dividend of $0.50 then the Black-Scholes price of a
European call on the stock is closest to what...

A non-dividend paying stock sells for $110. A call on the stock
has an exercise price of $105 and expires in 6 months. If the
annual interest rate is 11% (0.11) and the annual standard
deviation of the stock’s returns is 25% (0.25), what is the price
of a European call option according to the Black-Scholes-Merton
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