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
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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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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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Consider a six-month European call option on a
non-dividend-paying stock. The stock price is $30, the strike price
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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).

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large is the difference between the Black-Scholes price and the
price given by the binomial tree?

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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
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The price of a non-dividend paying stock is $19 and the price of
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(a) What is the price of the option if it is European
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(b) What is the price of option if it is an American
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(c) What is the price of the option if it is a European
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