Question

Consider a call and a put option, both with strike price of $30 and 3 months to expiration. The call trades at $4, the put price is $5, the interest rate is 0, and the price of the underlying stock is $29.

a.Suppose the stock does not pay dividends. Is there an arbitrage? If so, write down the sequence of trades and calculate the arbitrage profit you realize in 3 months. If not, explain why not.

b.Suppose the stock will pay a dividend of $2 in 2 months. Assume all other prices are as above. Is there an arbitrage? If so, write down the sequence of trades and calculate the arbitrage profit you realize in 3 months. If not, explain why not.

Answer #1

The strike price for a European call and put option is $56 and
the expiration date for the call and the put is in 9 months. Assume
the call sells for $6, while the put sells for $7. The price of the
stock underlying the call and the put is $55 and the risk free rate
is 3% per annum based on continuous compounding. Identify any
arbitrage opportunity and explain what the trader should do to
capitalize on that opportunity....

1. A European call option and put option on a stock both have a
strike price of $20 and an expiration date in three months. Both
sell for $3. The risk-free interest rate is 10% per annum, the
current stock price is $19, and a $1 dividend is expected in one
month. Is there an arbitrage opportunity? If there is an arbitrage
opportunity, clearly state what condition must be satisfied to
eliminate the arbitrage opportunity. What is the strategy
followed...

A
European call option and put option on a stock both have a strike
price of $20 and an expiration date in three months. Both sell for
$3. The risk-free interest rate is 10 % per aunum, the current
stock price is $19 , and a $1 dividend is expected in one month.
identify the arbitrage oppotunity to a trader.

A
European call option and put option on a stock both have a strike
price of $20 and an expiration date in three months. Both sell for
$2. The risk-free interest rate is 5% per annum, the current stock
price is $25, and a $1 dividend is expected in one month. Identify
the arbitrage opportunity open to a trader.

A European call option and put option on a stock both have a
strike price of $25 and an expiration date in four months. Both
sell for $4. The risk-free interest rate is 6% per annum, the
current stock price is $23, and a $1 dividend is expected in one
month. Identify the arbitrage opportunity open to a trader.

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.).
What is the price of a European call option on the same stock
that expires in six months and has a strike price of $100?
Explain in detail the arbitrage...

1. A put option has strike price $75 and 3 months to expiration.
The underlying stock price is currently $71. The option premium is
$10. "What is the time value of the put option?
Would this just be 0? Or: 71-75=-4 then 10-(-4)= 14?
2. The spot price of the market index is $900. After 3 months,
the market index is priced at $920. An investor had a long call
option on the index at a strike price of $930...

An investor purchases one call option (strike price $43 and
premium $1.20) and purchases 3 put options (strike price $43 and
premium $1.65) on the same underlying stock. What is the investor's
total profit or loss (enter profit as positive or a loss as a
negative value) per share if the stock price at expiration is
$21.15?

The price of a European call that expires in six months and has
a strike price of $28 is $2. The underlying stock price is $28, and
a dividend of $1 is expected in 4 months. The term structure is
flat, with all risk-free interest rates being 6%. If the price of a
European put option with the same maturity and strike price is $3,
what will be the arbitrage profit at the maturity?

A European call option on a stock with a strike price of $50 and
expiring in six months is trading at $14. A European put option on
the stock with the same strike price and expiration as the call
option is trading at $2. The current stock price is $60 and a $1
dividend is expected in three months. Zero coupon risk-free bonds
with face value of $100 and maturing after 3 months and 6 months
are trading at $99...

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