Question

The price of a stock is $40. The price of a one-year European put option on the stock with a strike price of $30 is quoted as $7 and the price of a one-year European call option on the stock with a strike price of $50 is quoted as $5. Suppose that an investor buys 100 shares, shorts 100 call options, and buys 100 put options. Draw a diagram illustrating how the investor’s profit or loss varies with the stock price over the next year. How does your answer change if the investor buys 100 shares, shorts 200 call options, and buys 200 put options?

Suppose that you are the manager and sole owner of a highly
leveraged company. All the debt will mature in one year. If at that
time the value of the company is greater than the face value of the
debt, you will pay off the debt. If the value of the company is
less than the face value of the debt, you will declare bankruptcy
and the debt holders will own the company.

Express your position as an option on the value of the company.

Express the position of the debt holders in terms of options on the value of the company.

What can you do to increase the value of your position?

Answer #1

ANSWER.

**The investor’s profit varies
with the stock price in the first case.**

**Loss $ 1,200 will get if stock
price is less than $30.**

**As the stock price increases
from $30 to $50 the profit increases from –$1,200 to
$800.**

**Above $50, the profit is
$800.**

**call which is $10 out of the
money is less expensive than a put which is $10 out of the
money.**

**The profit varies with stock
price in the second case.**

**In this case the profit pattern
has a zigzag shape.**

**many different patterns can be
obtained by including calls, puts, and the underlying asset in a
portfolio.**

The price of a stock is $40. The price of a one-year European
put option on the stock with a strike price of $30 is quoted as $7
and the price of a one-year European call option on the stock with
a strike price of $50 is quoted as $5. Suppose that an investor
buys 100 shares, shorts 100 call options, and buys 100 put
options.
a) Construct a payoff and profit/loss table
b) Draw a diagram illustrating how the...

The current price of a stock is $40. The price of a one-year
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quoted at $2 and the price of a one-year European call option on
the stock with a strike price of $50 is quoted at $3.
a) Investor A is bullish on the stock and buys 100 shares.
Compute his dollar profit and return if the share price is $25,
$42, or $56 in one...

Q4. A trader longs a European call and shorts a European put
option. The options have the same underlying asset, strike price
and maturity. Please depict the trader’s position. Under what
conditions is the value of position equal to zero? (Hint: compare
the payoff pattern of the option position with that of a forward
contract.)

Consider a European call option and a European put option on a
non dividend-paying stock. The price of the stock is $100 and the
strike price of both the call and the put is $104, set to expire in
1 year. Given that the price of the European call option is $9.47
and the risk-free rate is 5%, what is the price of the European put
option via put-call parity?

For a European call option and a European put option on the same
stock, with the same strike price and time to maturity, which of
the following is true?
A) When the call option is in-the-money and the put option is
out-of-the-money, the stock price must be lower than the strike
price.
B) The buyer of the call option receives the same premium as the
writer of the put option.
C) Since both the call and the put are risky...

For a European call option and a European put option on the same
stock, with the same strike price and time to maturity, which of
the following is true?
A) Before expiration, only in-the-money options can have
positive time premium.
B) If you have a portfolio of protected put, you can replicate
that portfolio by long a call and hold certain amount of risk-free
bond.
C) Since both the call and the put are risky assets, the
risk-free interest rate...

The price of a European put option on a stock with a strike
price of $30.00 is $6.80. The stock price is $28.00, the
continuously compounded risk-free rate (all maturities) is 4% and
the time to maturity is one year. A dividend of $2.00 is expected
in three months. What is the price of a one-year European call
option on the stock with a strike price of $30.00?
Select one:
a. $7.22
b. $4.00
c. $6.98
d. $4.74

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A trader is purchasing three European call options with a strike
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price of $50. Both options have the same maturity date. The price
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Use put-call parity to explain how would you construct a
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