Question

**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?**

Answer #1

**max.(Ke ^{-r}^{T} -S_{0} ,0)<p
<Ke^{-rT} **

**Lower bound:- 30*e- ^{0.05*(2/12)} - 27 =
$2.75**

**Upper bound: $29.75**

Since, **$1 < $2.925,**

An arbitrageur should borrow $28 at 5% for one month, buy the stock, and buy the put option. This generates a profit in all circumstances.

If the stock price is **above $30** in one month,
the option expires worthless, but the stock can be sold for at
least $30. A sum of $30 received in one month has a present value
of $29.75 today. The strategy, therefore, generates profit with a
present value of **at least $1.75**

If the stock price is **below $30** in one month
the put option is exercised and the stock owned is sold for exactly
$30 (or $29.75 in present value terms). The trading strategy,
therefore, generates a profit of exactly **$1.75 i**n
present value terms.

Calculate the upper and lower bounds respectively for a 9-month
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price is R120, the strike price is R125 and the risk-free rate of
interest is 8% per annum.

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) 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?

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...

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?

What is the price of a European put option on a
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price is $100, the risk-free interest rate is 8% per annum, the
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What is the price of a European put option on a
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A
European call option and put option on a stock both have a strike
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