Question

1. Consider a stock which trades for $50 (S_{0} = 50).
Consider also a European **call** option with an
exercise price of $50 which expires in one year. The risk free rate
is 5% cc. Suppose that you calculate the risk-neutral probability
of an upward move to be 0.5064. What is the fair
price of the option, based on a two-period binomial
model? Choose the closest answer.

A)5.28

B)5.84

C)6.45

D)13.05

2. Consider a stock which trades for $50 (S_{0} = 50).
Consider also a European **put** option with an
exercise price of $50 which expires in one year. The risk free rate
is 5% cc. Suppose that you calculate the risk-neutral probability
of an upward move to be 0.5064. What is the fair price of the
option, based on a two-period binomial model? Choose
the closest answer.

A)4.01

B)4.60

C)5.28

D)5.84

Answer #1

Current price S | 50 | ||||

European call option | |||||

Exercise price | 50 | ||||

Time | 1year | ||||

Probablity of upward movement u= | 0.5064 | ||||

Find fair price of the option
- Exercise price - X - 50 |
|||||

pi | 0.5064 | ||||

two period binomial -
1/2 |
0.5 |
years |
|||

1.5064 | |||||

S= | 50 | ||||

At the end of 2 years | 12.82205 | ||||

C | 6.493085 | 6.183891 | |||

1.05 | |||||

P | 6.328963 | 6.027584 | |||

1.05 |

You want to price a European call option on stock X, which
currently trades at $40 per share (this stock does not currently
pay dividends). Suppose there are two possible outcomes for share
prices of stock X next period: It can go up by 15%, or it can drop
by 10%.
The option expires in one period, and has a strike price of $41.
The risk-free rate over the next period is 5% (you can lend and
borrow at the...

Consider a European call with an exercise price of $50 on a
stock priced at $60. The stock price can go up by 15 percent or
down by 20 percent in each of two binomial periods. The risk free
rate is 10 percent. (Show ALL your workings.)
(a) Calculate the stock price sequence.
(b) Determine the possible prices of the call at expiration.
(c) Find the possible prices of the call at the end of the first
period.
(d) What...

Problem 43.1 Consider a chooser option on a stock. The stock
currently trades for $50 and pays dividend at the continuously
compounded yield of 8%. The choice date is two years from now. The
underlying European options expire in four years from now and have
a strike price of $45. The continuously compounded risk- free rate
is 5% and the volatility of the prepaid forward price of the stock
is 30%. Find the delta of the European call with strike...

Peter has just sold a European call option on 10,000 shares of a
stock. The exercise price is $50; the stock price is $50; the
continuously compounded interest rate is 5% per annum; the
volatility is 20% per annum; and the time to maturity is 3 months.
(a) Use the Black-Scholes-Merton model to compute the price of the
European call option. (b) Find the value of a European
put option with the same exercise price and expiration as the call...

Calculate the American call price using the two-period binomial
model. The current stock price is 50 and the exercise price is 55.
The option expires in 25 days and volatility is 75%. Would the
European call have a different price? If so, would it be higher or
lower? Using the information from the problem show how to create a
riskless portfolio. Proves that it is riskless after 1 period.
(You do not have to draw the stock price path and...

Consider a one step binomial model. The initial stock price is
S0 = $80. There is a 60% chance the stock price will rise to $90,
and a 40% chance it will fall to $75. The risk-free interest rate
is 5%.
• Identify u and d
• What would the option prices be if the probabilities changed
to 70% chance the stock price rises and 30% chance it falls?

Consider a European-style call option on a stock that is
currently trading at £100. The strike price of the call is £90.
Assume that, in the next 12 months, the stock price can either go
up to £120 or go down to £80. Using risk-neutral valuation,
calculate the current value of the option if the risk-free rate is
5 percent per annum. Use discrete compounding. Which of the
following is correct?
A. £18
B. £18.5
C. £18.75
D. £19

You observe a 50 stock price for a non-dividend paying stock.
The call has two years to mature, the periodically compounded
risk-free interest rate is 5%, the exercise price is 50, u = 1.356,
d = 0.744. Assume the call option is European-style.
The current value of the call option is closest to:
a) 9.53
b) 9.71
c) 9.87

Multi Step Binomial Tree: Consider again the at-the-money
European call option with one year left to maturity written on a
non-dividend paying stock. As in exercise 2, let today’s stock
price be 80 kr, the stock volatility be 30% and the risk free
interest rate be 6%.
(a) Construct a one-year, five-step Binomial tree for the stock
and calculate today’s price of the European at-the-money call.
(c) The option can be replicated by a portfolio consisting of
the stock and...

1. Tucker Inc. common stock currently trades for $90/share.
6-month European put options on the stock have an exercise price
and premium of $93 and $4, respectively. The annual risk free rate
is 2%. What should be the value of a 6-month European call option
on the stock with an exercise price of $93 according to put-call
parity? Round intermediate steps to four decimals and your final
answer to two decimals.
a. 7.90
b. 0.065
c. 1.93
d. 2.84
e....

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 6 minutes ago

asked 8 minutes ago

asked 9 minutes ago

asked 9 minutes ago

asked 12 minutes ago

asked 12 minutes ago

asked 12 minutes ago

asked 12 minutes ago

asked 12 minutes ago

asked 13 minutes ago

asked 14 minutes ago