Question

A non-dividend paying stock price is $100, the strike price is
$100, the risk-free rate is 6%, the volatility is 15% and the time
to maturity is 3 months which of the following is the price of an
** American Call** option on the stock. For
full credit I expect each step of the calculations tied to the
correct formulas.

Answer #1

d1 = [{ln(S0/X)} + {t(r - q + ^{2}/2)}]
/ [(t)^{1/2}]

= [{ln(100/100)} + {0.25(0.06 +
0.15^{2}/2)}] / [0.15(0.25)^{1/2}]

= 0.0178 / 0.075 = 0.2375

d2 = d1 - [(t)^{1/2}]

= 0.2375 -
[0.15(0.25)^{1/2}]

= 0.5235 - 0.075 = 0.1625

C = [S0 x e^{-qt} x N(d1)] - [X x e^{-rt} x
N(d2)

= [100 x e^{-0*0.25} x N(0.2375)] - [100 x
e^{-0.06*0.25} x N(0.1625)]

= [100 x 0.5939] - [100 x e^{-0.06*0.25} x 0.5645]

= 59.39 - 55.61 = 3.77, or $3.77

When the non-dividend paying stock price is $20, the strike
price is $20, the risk-free rate is 6%, the volatility is 20% and
the time to maturity is three months. Work the problem out how you
would do not use excel
(a) What is the price of a European put option on the stock using
BSM model?
(b) At what stock price the seller of the European put will
break even

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

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

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?

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...

The price of a European call option on a non-dividend-paying
stock with a strike price of $50 is $6. The stock price is $51, the
continuously compounded risk-free rate (all maturities) is 6% and
the time to maturity is one year. What is the price of a one-year
European put option on the stock with a strike price of $50?
a)$9.91
b)$7.00
c)$6.00
d)$2.09

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?

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?

The current price of a non-dividend paying stock is $50. Use a
two-step tree to value a American put option on
the stock with a strike price of $50 that expires in 12 months.
Each step is 6 months, the risk free rate is 5% per annum, and the
volatility is 50%. What is the value of the option according to the
two-step binomial model. Please enter your answer rounded to two
decimal places (and no dollar sign).

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.)

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