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 ten-month European put option on a dividend-paying stock is
currently selling for $4. The stock
price is $40, the strike price is $43, and the risk-free interest
rate is 6% per annum. The stock is expected
to pay a dividend of $2 two months later and another dividend of $2
eight months later. Explain the
arbitrage opportunities available to the arbitrageur by
demonstrating what would happen under
different scenarios.

A 1-month European put option on a non-dividend paying stock is
selling for P = $1: S0 = $45; K = $48: r = :06 annually. Assume
continuous discounting. Are there opportunities for arbitrage? If
so, explain in detail the arbitrage strategy that will be used.

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

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