Question

An options exchange has a number of European call and put
options listed for trading on ENCORE stock. You have been paying
close attention to two call options on ENCORE, one with an exercise
price of $52 and the other with an exercise price of $50. The
former is currently trading at $4.25 and the latter at $6.50. Both
options have a remaining life of six months. The current price of
ENCORE stock is $51 and the six-month risk free rate is 3% p.a.,
continuously compounded.

Required:

How would you exploit this situation to earn arbitrage
profits? You should assume the arbitrageur can borrow or lend at
the risk free rate, can short sell shares if necessary and does not
face any transaction costs.

Hint: For call options with different strike prices but the
same expiration date, the maximum difference between call prices is
C1 – C2 < (K2 – K1) e-rT where K2 > K1. You are expected to
employ the five-step proof method to demonstrate your arbitrage
strategies. When demonstrating the arbitrage opportunity, you will
need to consider different scenarios at time T, ie., if , ,
and.

Answer #1

An options exchange has a number of European call and put
options listed for trading on GEMCO stock. You have been paying
close attention to two put options on GEMCO, one with an exercise
price of $40 and the other with an exercise price of $42. The
former is currently trading at $2.20 and the latter at $4.50. Both
options have a remaining life of six months. The current price of
GEMCO stock is $41 and the risk-free rate is...

Seven months European call and put options on palladium
are trading at 9￥ and 13￥, respectively, with the same exercise
price of 190￥. The spot price is 179￥ and the interest rate is
7%.
Is there any arbitrage opportunity? Justify your
answer.
If yes, calculate the arbitrage profit in this
case.

1. Tucker Inc. common stock currently trades for $90/share.
6-month European put options on the stock have an exercise price
and premium of $93 and $4, respectively. The annual risk free rate
is 2%. What should be the value of a 6-month European call option
on the stock with an exercise price of $93 according to put-call
parity? Round intermediate steps to four decimals and your final
answer to two decimals.
a. 7.90
b. 0.065
c. 1.93
d. 2.84
e....

As a financial analyst at JPMorgan Chase investments, you are
evaluating European call options and put options using Black
Scholes model. Suppose BMI’s stock price is currently $75. The
stock’s standard deviation is 7.0% per month. The option with
exercise price of $75 matures in three months. The risk-free
interest rate is 0.8% per month. Please answer the following
questions.
Please choose all correct answers.
1.
The price of the European call option is
$13.14
2.
The price of the...

As a financial analyst at JPMorgan Chase investments, you are
evaluating European call options and put options using Black
Scholes model. Suppose BMI’s stock price is currently $75. The
stock’s standard deviation is 7.0% per month. The option with
exercise price of $75 matures in three months. The risk-free
interest rate is 0.8% per month. Please answer the following
questions.
which one is the correct answers
1.
The price of the European call option is $13.14
2.
The price of...

The prices of European call and put options on a
non-dividend-paying stock with 12 months to maturity, a strike
price of $120, and an expiration date in 12 months are $25 and $5,
respectively. The current stock price is $135. What is the implied
risk-free rate?
Draw a diagram showing the variation of an investor’s profit and
loss with the terminal stock price for a portfolio consisting
of
One share and a short position in one call option
Two shares...

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.

Problem 1: Properties of Options
The price of a European put that expires in six months and has a
strike price of $100 is $3.59. The underlying stock price is $102,
and a dividend of $1.50 is expected in four months. The term
structure is flat, with all risk-free interest rates being 8%
(cont. comp.).
a. What is the price of a European call option on the same stock
that expires in six months and has a strike price of...

Explain how you would exploit any arbitrage.
A stock which is currently trading at $14 has a 20% chance of
going up to $18 tomorrow and an
80% chance of dropping to $12 tomorrow. P is a binary put option on
the stock with an exercise
price of $14. In the market, the binary puts are selling for $0.50.
Call the portfolio set up to
eliminate risk. The risk-free rate of return is 0.8.

A call and a put are held in a portfolio, both have an exercise
price of $140
Premium for the call is $5.00
Spot price of the stock is $145, and the risk free rate is
4%.
A. Using continuous compounding, what is the Premium of the Put
if both options expire in 2.5 years?
B. Using monthly compounding, what is the Premium of the Put if
both options expire in 2.5years?
C. Does the Put-Call Parity equation work when...

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