Question

Derive the upper and lower bound for a six-month call option with strike price K=$75 on stock XYZ. The spot price is $80. The risk-free interest rate (annually compounded) is 10%. If the option price is below the lower bound, describe the arbitrage strategy.

Answer #1

The lower bound can be calculated as:

= Spot Price – (Strike price * (e^(-Rf*Time)))

= 80 – (75 * (e^(-0.1*0.5))) = $8.67

Now, the present value of strike price is

= (75 * (e^(-0.1*0.5)) = 71.33

Now, if the option price is below the lower bound, say for eg. It is $4.

Now, the arbitrageur will buy the option and short the stock.

This will generate 80 – 4 = $76

Which he will invest at 10% for 6 month.

So, now if stock price goes below 75, the arbitrageur will lose the premium of $4 but he will gain on the short position, more than that.

For eg: stock price becomes 74. Then gain = (80-74) – 4 + ((1.1)^0.5 -1) * 80, which is greater than 0.

If stock price goes above 75, the arbitrageur will exercise the option and buy the shares at 75 and close the short position.

If price is say 78, gain = -4 + 80 – 78 + (0.1)^0.5 * 80, which is greater than zero

So, there will always be gain

a. What is a lower bound for the price of a five-month call
option on a non-dividend-paying stock when the stock price is $42,
the strike price is $38, and the continuously compounded risk-free
interest rate is 8% per annum?
b. What is a lower bound for the price of a four-month European
put option on a non-dividend- paying stock when the stock price is
$31, the strike price is $35, and the continuously compounded
risk-free interest rate is 7%...

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)...

(a) What is a lower bound for the price of a 6-month European
call option on a nondividend-paying stock when the stock price is
$50, the strike price is $48, and the risk-free interest rate is 5%
per annum? (b) What is a lower bound for the price of a 2-month
European put option on a nondividend-paying stock when the stock
price is $70, the strike price is $73, and the risk-free interest
rate is 8% per annum?

What are the upper and lower bounds for the price of a
two-month put option on a non-dividend-paying stock when the stock
price is $27, the strike price is $30, and the risk-free interest
rate is 5% per annum? What is the arbitrage opportunity if the
price of the option is $1? What are the net profits?

Suppose that a 6-month European call A option on a stock with a
strike price of $75 costs $5 and is held until maturity, and
6-month European call B option on a stock with a strike price of
$80 costs $3 and is held until maturity. The underlying stock price
is $73 with a volatility of 15%. Risk-free interest rates (all
maturities) are 10% per annum with continuous compounding.
Use put-call parity to explain how would you construct a
European...

There is a six month European call option available on XYZ stock
with a strike price of $90. Build a two step binomial tree to value
this option. The risk free rate is 2% (per period) and the current
stock price is $100. The stock can go up by 20% each period or down
by 20% each period.
Select one:
a. $14.53
b. $17.21
c. $18.56
d. $12.79
e. $19.20

Calculate the upper and lower bounds respectively for a 9-month
European call option on a non-dividend paying share when the share
price is R120, the strike price is R125 and the risk-free rate of
interest is 8% per annum.

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
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Kindly dont forget the second part of the question

Please show work.
The following are three-month call option prices: the call at
strike 100 is trading at $ 5 and the call at strike 102 is trading
at $ 2.5. The rate of interest (continuously compounded) is 3%. Is
there an arbitrage strategy is this market and how would you
implement it? Draw a cash flow table showing the outcome of your
strategy at maturity for every possible stock price level.

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.

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