Question

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% per annum?

Answer #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?

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.

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).

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?

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.

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 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

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
non-dividend-paying stock when the stock price is $100, the strike
price is $100, the risk-free interest rate is 8% per annum, the
volatility is 25% per annum, and the time to maturity is 1 month?
(Use the Black-Scholes formula.)

What is the price of a European put option on a
non-dividend-paying stock when the stock price is $70, the strike
price is $75, the risk-free interest rate is 10% per annum, the
volatility is 25% per annum, and the time to maturity is six
months?

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