Question

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.

Answer #1

Prima facie there is a arbitrage opportunity as call option is at $3.5 and strike price is $95. So total cost is $98.5. The stock price is $100 so there is $(100-98.5) =$1.5 advantage. Int on $3.5 premium @6% p.a. at continuous compounding

Fv in continuous compounding =**PV x e (i x
t)**

**taking pv as 3.5 and e =2.7183, i=6/12=0.5 and
t=1**

**fv=5.77 so total cost would be 95+5.77 =100.77 which is
lesser than stock value of 100 so with continuous compounding @6
percent int rate there is no arbitrage opportunity**

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...

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?

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?

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

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
in two months. Assume that the risk-free interest rate is 5% per
annum with continuous compounding for all maturities.
1) What should be the lowest bound price for a six-month
European call option on a dividend-paying stock for no
arbitrage?
2) If the call option is currently selling for $2, what
arbitrage strategy should be implemented?
1)...

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 stock that does not pay dividend is trading at $20. A European
call option with strike price of $15 and maturing in one year is
trading at $6. An American call option with strike price of $15 and
maturing in one year is trading at $8. You can borrow or lend money
at any time at risk-free rate of 5% per annum with continuous
compounding. Devise an arbitrage strategy.

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?

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

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