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?**

Answer #1

**ANSWER DOWN BELOW. FEEL FREE TO ASK ANY DOUBTS. THUMBS
UP PLEASE.**

As per put-call parity

P+ S = present value of X + C

P= value of put option.

S= current price of the share

X= strike price

C= value of call option.

Present value of X = X/e^r

r = risk free rate.

Given:

P= value of put option = 2

S= current price of share= 45

X= strike price = 46

Present value of X = 46/e^(0.06*0.5)

r = risk free rate. 6%

2+45 =46/e^(0.06*0.5) +C

C= 2.36

Value/Price of call option =$2.36

b. If the value of the call option is $2.36, then put-call parity is violated as the actual call price is $1.

And there is an arbitrage opportunity.

Arbitrage Opportunity:

Now,

Buy Call

Buy Risk-Free Asset.

After 6 months.

Sell Put,

Sell Stock.

To utilise the opportunity.

Profit is equal to the difference between the call price. = Should be as per PCP-Actual

= 2.36-1

= $1.36 (Answer).

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.

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

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?

A 3-month European
put option on a non-dividend-paying stock is currently selling for
$3.50. The stock price is $47.0, the strike price is $51, and the
risk-free interest rate is 6% per annum (continuous compounding).
Analyze the situation to answer the following question:
If there is no
arbitrage opportunity in above case, what range of put option price
will trigger an arbitrage opportunity? If there is an arbitrage
opportunity in the above case, please provide one possible trading
strategy to...

A 3-month European
put option on a non-dividend-paying stock is currently selling for
$3.50. The stock price is $47.0, the strike price is $51, and the
risk-free interest rate is 6% per annum (continuous compounding).
Analyze the situation to answer the following question:
If there is no
arbitrage opportunity in above case, what range of put option price
will trigger an arbitrage opportunity? If there is an arbitrage
opportunity in the above case, please provide one possible trading
strategy to...

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).

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?

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?

What is the price of a European put option on a
non-dividend-paying stock when the stock price is $100, the strike
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volatility is 25% per annum, and the time to maturity is 1 month?
(Use the Black-Scholes formula.)

A six-month European call option's underlying stock price is
$86, while the strike price is $80 and a dividend of $5 is expected
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1) What should be the lowest bound price for a six-month
European call option on a dividend-paying stock for no
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2) If the call option is currently selling for $2, what
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1)...

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