Question

The current spot price of a stock is $38.00, the expected rate of return (per annum) of the stock is 9.7%, and the weekly volatility of the stock is 3.4%. The risk-free rate (per annum) is 4.6%.

Assume there are 52 weeks in a year. Additionally, assume the
log-normal model for the stock. Let *X* be a random variable
denoting the natural log of the price of the stock in 12 months,
where *X* is normally distributed. Compute the mean μμ and
standard deviation σσ of *X* .

Answer #1

Current stock price is $150; volatility is 20% per annum. An
at-the-money European put option on the stock expires in 3 months.
Risk free rate is 5% per annum, continuously compounded. There is
no dividend expected over the next 3 months. Use a 3-step CRR model
to price this option.

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?

What is the price of a European call option on a
non-dividend-paying stock when
the stock price is $52, the strike price is $50, the risk-free
interest rate is 12% per annum, the
volatility is 30% per annum, and the time to maturity is three
months? (Hint: Remember Black-
Sholes-Merton Model. Please refer to the N(d) tables provided to
you to pick the N values you
need)

Assume risk-free rate is 5% per annum continuously compounded.
Use Black-Scholes formula to find the price the following
options:
European call with strike price of $72 and one year to maturity
on a non-dividend-paying stock trading at $65 with volatility of
40%.
European put with strike price of $65 and one year to maturity
on a non-dividend-paying stock trading at $72 with volatility of
40%

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?

The current price of a non-dividend paying stock is $50. Use a
two-step tree to value a European put option on
the stock with a strike price of $50 that expires in 12 months.
Each step is 6 months, the risk free rate is 5% per annum, and the
volatility is 50%. What is the value of the option according to the
two-step binomial mode

The value of the S&P500 stock index is 1,000. The risk-free
interest rate is 3% per annum with continuous compounding. The
dividend yield on the S&P 500 is 1%, and the volatility of the
index is 20% per annum. Find the delta on a 6 months put option
with strike price 950. Interpret your result.

The volatility of a non-dividend-paying stock whose price is
$40, is 35%. The risk-free rate is 6% per annum (continuously
compounded) for all maturities. Use a two-step tree to calculate
the value of a derivative that pays off [max(?!−52,0)]" where is
the stock price in six months?

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...

The volatility of a non-dividend-paying stock whose price is
$50, is 30%. The risk-free rate is 5% per annum (continuously
compounded) for all maturities. Use a two-step tree to calculate
the value of a derivative that pays off [max(?! − 63, 0)]" where ST
is the stock price in six months?

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