Question

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?

Answer #1

**Calculation of European put option via put-call
parity:**

Formula for put call parity :

**C + PV (S) = P + MP**

where, C = price of call option

PV(S) = present value of strike price

P = price of put option

MP = market price of stock

Given,

price of call option = $9.47

Strike price = $104

Risk free rate = 5%

Present value of strike price(PV) = $104/1.05

= $99.047

Market price = $100

substituting above values in formula

**C + PV (S) = P + MP**

$9.47+$99.047 = P + $100

$108.517 = P + $100

P = $108.517 - $100

P = $8.517

Therefore, price of European put option = $8.517

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 $100, the strike
price is $100, the risk-free interest rate is 8% per annum, the
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(Use the Black-Scholes formula.)

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...

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non-dividend-paying stock when the stock price is $70, the strike
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months?

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).

Price a European call option on non-dividend paying stock by
using a binomial tree. Stock price is €50, volatility is 26%
(p.a.), the risk-free interest rate is 5% (p.a. continuously
compounded), strike is € 55, and time to expiry is 6 months. How
large is the difference between the Black-Scholes price and the
price given by the binomial tree?

Price a European call option on non-dividend paying stock by
using a binomial tree. Stock price is €50, volatility is 26%
(p.a.), the risk-free interest rate is 5% (p.a. continuously
compounded), strike is € 55, and time to expiry is 6 months. How
large is the difference between the Black-Scholes price and the
price given by the binomial tree?

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
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The price of a non-dividend paying stock is $45 and the
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What is the net profit in six months?

A
one-month European call option on a non-dividend-paying stock is
currently selling for$2.50. The stock price is $47, the strike
price is $50, and the risk-free interest rate is 6% per annum. What
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