Question

You would like to be holding a covered call position on the stock XYZ. The stock XYZ is currently selling for $120. Over the next year, the stock price will either increase by 10% or decrease by 10%. The exercise price of the call option is $125. The risk free interest rate is 3% per year.

A. What is the price of the call option? (Use a one-period binomial model)

B. What is the cost of the covered call portfolio? What will be the payoff and profit on the covered call portfolio at a stock price of $140?

Answer #1

A.

If the stock price increases by 10%, stock price at maturity = (1+10%)*120 = $132

If the stock price decrease by 10%, stock price at maturity = (1-10%)*120 = $108

Call option payoff if the stock price increases by 10% = 132-125 = $7

Call option payoff if the stock price decreases by 10% = 0

Price of the call option is the discounted expected payoff

Price of the call option = 0.5*7*e^(-0.03*1) + 0.5*0

Price of the call option = $3.397

B.

Covered call consists of a long position in stock, and a short position in a call option

Covered call cost = $120- $3.397 = $116.603

Hence, the cost = $116.603

Payoff if the stock price of $140 = (140-120) - (140-125)

Payoff if the stock price of $140 = $5

Profit on the covered call = $(140-120-(140-125)+3.397)

Profit on the covered call = $8.397

Covered call: A \covered call" is a position whereby an investor
sells a call to their
broker, but also \covers" that option by placing the share with
the broker. If the call
option does not pay off, the broker returns the share to the
investor. The broker pay
for the cost of their option at maturity. Draw the payoff
diagram for the net covered
call position (that is, the value of one stock - a call option +
cash payment...

Binomial Model and Option Pricing
The shares of XYZ Inc. are currently selling for $120 per share.
The shares are expected to go up by 10 percent or down by 5 percent
in each of the following two months (Month 1 and Month 2). XYZ Inc.
is also expected to pay a dividend yield of 2 percent at the end of
Month 1. The risk-free rate is 0.5 percent per month.
a. What is the value of
an American call...

Call options with an exercise price of $125 and one year to
expiration are available. The market price of the underlying stock
is currently $120, but this market price is expected to either
decrease to $110 or increase to $130 in a year's time. Assume the
risk-free rate is 6%. What is the value of the option?

currently, a call option on Bayou stock is available with an
exercise price of $100 and an expiration date one year from now.
Assume that the price of Bayou corporation stock today is $100.
Furthermore, it is estimated that Bayou stock will be selling for
either $75 or $143 in one year. Also, assume that the annual
risk-free interest rate on a one year Treasury bill is 10 percent,
continuously compounded. Therefore, the T-bill will pay $100 x
e^(0.1), or...

Currently, a call option on Bayou stock is available with an
exercise price of $100 and an expiration date one year from now.
Assume that the price of Bayou Corporation stock today is $100.
Furthermore, it is estimated that Bayou stock will be selling for
either $62 or $152 in one year. Also, assume that the annual
risk-free interest rate on a one-year Treasury bill is 10 percent,
continuously compounded. Therefore, the T-bill will pay $100 ×
e^(0.1), or $110.25....

You are given the following information about a European call
option on Stock XYZ. Use the Black-Scholes model to determine the
price of the option:
Shares of Stock XYZ currently trade
for 90.00.
The stock pays dividends continuously
at a rate of 3% per year.
The call option has a strike price of
95.00 and one year to expiration.
The annual continuously compounded
risk-free rate is 6%.
It is known that d1 – d2 = .3000;
where d1 and d2...

10.Unlike a covered call writer, a naked call writer
will always lose if
a. the stock
price rises by more than the option premium
b. the stock
price declines by more than the option premium
c. a closing
transaction is executed
d. none of the
above
16.Which of the following is equivalent to a synthetic
call?
a. a long stock
and a short put position
b. a long put
and a long stock position
c. a long put
and a...

An investor creates a covered call position by purchasing 100
shares of the Tesla stock at a price of $840 per share and selling
100 call options on the Tesla stock with a strike price $840 per
share. The premium of the option is $35 per share. At which stock
price at the maturity of the option will the investor break even?
Please provide your answer in unit of dollars (without the dollar
sign), rounded to the nearest cent.

To protect an existing stock position, some traders like to use
a position known as a collar. When traders have a long position in
the stock, they create the collar by combining covered calls and
protective puts. Therefore the upside potential is limited beyond
the strike price of the short call while the downside is protected
by the long put. Suppose you purchased 100 shares of stock ABC at
$13 in May and would like a way to protect your...

The one year call option on Caddo Inc. stock has an exercise
price of 45. The current value of Caddo is 46. On the maturity
date, the value of Caddo will be either 51 or 43. The risk free
rate is 5%. Use the binomial option pricing model to find a fair
value for the call option.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 5 minutes ago

asked 11 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 4 hours ago

asked 4 hours ago

asked 5 hours ago