Question

3. A stock price follows geometric Brownian motion with an expected return of 16% and a volatility of 35%. The current price is $38. a) What is the probability that a European call option on the stock with an exercise price of $40 and a maturity date in six months will be exercised? b) What is the probability that a European put option on the stock with the same exercise price and maturity will be exercised?

Answer #1

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A spot price of an asset has an expected return of 16% and a
volatility of 35%. The current price is $38.
What is the probability that a European call option on the
asset with an exercise price of $40 and a maturity date in six
months will be exercised?
What is the probability that a European put option on the asset
with the same exercise price and maturity will be exercised?

Let s follow geometric Brownian motion with expected return µ
and volatility σ. Show the process followed by G(s, t) = s(a + bt),
where a and b are constants, also follows geometric Brownian
motion. Identify the drift and volatility terms. Please show all
work

If the value of a portfolio follows a geometric Brownian motion
with drift rate 6% and volatility
20%, then the log return of the portfolio from time ? to time ? is
normally distributed with
mean 6% − 0.5∗(20%)^2 (? – ?) and variance 0.04∗(? – ?).
What is the 10-day, 1% VaR of the portfolio? You should give your
answer in terms of log-returns.
You are also given the following number: For a standard normal
random variable with zero...

Consider an option on a non-dividend-paying stock when the
stock is $ 30, the exercise price is $29. The risk –free rate is 5%
per annum, the volatility is 25% per annum, and the time to
maturity is four months.
(a) What is the price of the option if it is European
call?
(b) What is the price of option if it is an American
call?
(c) What is the price of the option if it is a European
put?

Suppose a stock has an expected return of 10% per year and a
return volatility of 28% per year and equally likely transitions
(i.e. with probability 1/2). The risk-free rate is 4% per year. The
stock has a current price of $100 and has declared dividends of
$2.04 to be paid at the end of each six-month period.
Construct a binomial model for the stock price of ABC with 2
semi-annual periods.
Find the value of a European call option...

2.1 A stock price has an expected return of 15% and a volatility
of 25%. It is currently $56.
2.1.1 What is the probability that it will be greater than $85 in
two years? (4)
2
2.1.2 What is the stock price that has a 5% probability of being
exceeded in two years? (2)
2.2 A binary option pays off $150 if a stock price is greater than
$40 in three months. The
current stock price is $35 and its...

Consider an option on a non-dividend-paying stock when the stock
price is $52, the exercise price is $50, the risk-free interest
rate is 10% per annum, the volatility is 30% per annum, and time to
maturity is 3 months
What is the price of the option if it is a European
call?

The stock of Network Communication Corp. (NCC) is currently
traded at $50 on the market. Assume the stock price has a lognormal
distribution. The expected return from the stock is 15 percent per
annum and its volatility is 25 percent per annum. What is the
probability that a European call option on NCC
stock with a strike price of $52 and a maturity of 3 months will be
in-the-money at the maturity date?

A stock has a price of 100. It is expected to pay a dividend of
$3 per share at year-end. An at-the-money European put option with
1 year maturity sells for $8. If the annual interest rate is 4%,
what must be the price of an at-the-money European call option on
the stock with 1 year maturity.

Consider an option on a non-dividend-paying stock when the stock
price is $30, the exercise price is $29, the risk-free interest
rate is 5% per annum, the volatility is 25% per annum, and the time
to maturity is four months. Assume that the stock is due to go
ex-dividend in 1.5 months. The expected dividend is 50 cents. Using
the Black-Scholes-Merton model, what is the price of the option if
it is a European put?

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