Question

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

Answer #1

Using put-call parity,

cash + call = Stock + put

20 / (1+4% x 3/12) + call = 19 + 1.80

Therefore, call = $ 1.00

Price of a three-month European call option with a strike price of $20 = $ 1.00

Option is said to be in the money, if it has positive value, had it been exercised now.

Strike price of call option is $20

Current spot price is $19

Therefore, call is out of the money

Strike price of put option is $20

Current spot price is $19

Therefore, put option is in the money

Since put option is option to sell the asset at strike price. Therefore if put option is exercised now, it has positive value $1

the price of a non-dividend-paying stock is $19 and the price of
a 3-month European call option on the stock with a strike price of
$20 is $1, while the 3-month European put with a strike price of
$20 is sold for $3. the risk-free rate is 4% (compounded
quarterly). Describe the arbitrage strategy and calculate the
profit.
Kindly dont forget the second part of the question

The price of a non-dividend paying stock is $45 and the
price of a six-month European call option on the stock with a
strike price of $46 is $1. The risk-free interest rate is 6% per
annum. The price of a six-month European put option is $2. Both put
and call have the same strike price. Is there an arbitrage
opportunity? If yes, what are your actions now and in six months?
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
opportunities are there for an arbitrageur?

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.)

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?

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?

A 1-month European call option on a non-dividend-paying-stock is
currently
selling for $3.50. The stock price is $100, the strike price is
$95, and the risk-free interest
rate is 6% per annum with continuous compounding.
Is there any arbitrage opportunity? If "Yes", describe your
arbitrage strategy using a table of cash flows. If "No or
uncertain", motivate your answer.

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)

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)

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