Question

1. 1. You try to price the options on XYZ Corp. The current stock price of XYZ is $100/share. The risk-free rate is 5%. You project the stock price of XYZ will either be $90 or $120 in a year. Assume you can borrow or lend money at the risk-free rate. Use risk-neutral approach to price the 1-year call option on XYZ Corp with the strike price of $105. (Attention: using a wrong approach will cost you all the credits) (8 points)

2.2. You try to price the options on XYZ Corp. The current stock price of XYZ is $100/share. The risk-free rate is 5%. You project the stock price of XYZ will either be $90 or $120 in a year. Assume you can borrow or lend money at the risk-free rate. Use risk-free portfolio approach to price the 1-year put option on XYZ Corp with the strike price of $105. (Attention: using a wrong approach will cost you all the credits) (8 points)

3.3. Use put-call parity to verify the call and put option prices you just calculated in question #1 and question #2. (2 points)

4.4

Fisher Black and Myron Scholes receive the 1997 Nobel Prize in
Economic Science for their work on option pricing. Although the
model is theoretically elegant and beautiful, it was not widely
used to price options in real life because it calls for inherent
volatility which is unobservable. However, given the dependability
of risk-neutral approach, people today normally use risk-neutral
approach to price the options first, then they employ Black-Scholes
model to estimate the implied volatility. Based on the information
given in the previous questions (question #1 and #2) and the call
option price you just calculated, estimate **the implied
volatility** of XYZ Corp stock. (8 points)**(You will
receive zero credit if you only write down the final answer. I need
to know how exactly you reach the final answer. You can present the
detailed solutions. If you use excel, you need show me functions
you use and the parameters you enter. If you use online tools, you
need to write down the website and the parameters you
enter.)**

**They all together because they go one with another.
:)**

Answer #1

1:Consider a European call option on a stock with current price
$100 and volatility 25%. The stock pays a $1 dividend in 1 month.
Assume that the strike price is $100 and the time to expiration is
3 months. The risk free rate is 5%. Calculate the price of the the
call option.
2: Consider a European call option with strike price 100, time
to expiration of 3 months. Assume the risk free rate is 5%
compounded continuously. If the...

Current Price of Stock = 50
Divided Yield = 2%
Strike Price = 55
Time to Expiry = 6 months
Volatility = 35%
Risk-Free rate =4%
Using Black Scholes Model:
1. What is the Value of American Call option?
2. What is the Value of American Put Option?
solve it in excel.

stock price 42.27
strike 40
maturity 26 days
risk free 4.92%
volatility 45.75%
use black scholes in excel to comput the call and put option
value

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...

Assume that the current XYZ stock price is equal to $33, the
volatility of XYZ is 32%, and XYZ stock pays 1% dividends each
year. The risk free interest rate is 6% today. Consider an European
call option with a strike price of $35, and suppose that the option
will be expired after 68 days from today (1 year = 365 days). Then,
what is the value of the call option?

In this question, you need to price options with various
approaches. You will consider puts and calls on a share.
Based on this spot price (36) and this strike price (38) as well
as the fact that the risk-free interest rate is 6% per annum with
continuous compounding, please undertake option valuations and
answer related questions according to following instructions:
Binomial trees:
Additionally, assume that over each of the next two four-month
periods, the share price is expected to go...

XYZ Corp. will pay a $2 per share dividend in two months. Its
stock price currently is $74 per share. A call option on XYZ has an
exercise price of $66 and 3-month time to expiration. The risk-free
interest rate is 0.5% per month, and the stock’s volatility
(standard deviation) = 13% per month. Find the Black-Scholes value
of the American call option. (Hint: Try defining one “period” as a
month, rather than as a year, and think about the...

Problem 1: Properties of Options
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.).
a. What is the price of a European call option on the same stock
that expires in six months and has a strike price of...

A stock index currently stands at 300 and has a volatility of
20%. The risk-free interest rate is 8% and the dividend yield on
the index is 3%.
Use the Black-Scholes-Merton formula to calculate the price of
a European call option with strike price 325 and the price of a
European put option with strike price of 275. The options will
expire in six months.
What is the cost of the range forward created using options in
Part (a)?
Use...

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.)

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