Question

A stock’s current price S is $100. Its return has a volatility of s = 25 percent per year. European call and put options trading on the stock have a strike price of K = $105 and mature after T = 0.5 years. The continuously compounded risk-free interest rate r is 5 percent per year. The Black-Scholes-Merton model gives the price of the European put as:

please provide explanation

Answer #1

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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 the following data for a two-period binomial model.
The stock’s price S is $100. After three months, it either goes
up and gets multiplied by the factor U = 1.138473, or it goes down
and gets multiplied by the factor D = 0.886643.
Options mature after T = 0.5 year and have a strike price of K =
$110.
The continuously compounded risk-free interest rate r is 5
percent per year.
Today’s European call price is c and the...

— The stock’s price S is $100. After three months, it either
goes up and gets multiplied by the factor U = 1.13847256, or it
goes down and gets multiplied by the factor D = 0.88664332. —
Options mature after T = 0.5 year and have a strike price of K =
$105. — The continuously compounded risk-free interest rate r is 5
percent per year. — Today’s European call price is c and the put
price is p. Call...

A 3-month European call on a futures has a strike price of $100.
The futures price is $100 and the volatility is 20%. The risk-free
rate is 2% per annum with continuous compounding. What is the value
of the call option? (Use Black-Scholes-Merton valuation for futures
options)

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...

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...

A stock is currently traded for $135. The risk-free rate
is 0.5% per year (continuously compounded APR) and the stock’s
returns have an annual standard deviation (volatility) of 56%.
Using the Black-Scholes model, we can find prices for a call and a
put, both expiring 60 days from today and having strike prices
equal to $140.
(a) What values should you use for S, K, T−t, r, and σ
in the Black-Scholes formula?
S =
K =
T - t...

Find the current fair values of a D1 month European call and a
D2 month European put option, using a current stock price of D3,
strike price of D4, volatility of D5, interest rate of D6 percent
per year, continuously, compounded. Obtain the current fair values
of the following:
1.European call by simulation.
2.European put by simulation.
3.European call by Black-Scholes model.
4.European put by Black-Scholes model.
D1
D2
D3
D4
D5 D6
11.2
10.9
31.7
32.6
0.65 9.5

TSLA stock price is currently at $800. The stock return has an
annualized volatility (sigma) of 70%. The stock does not pay
dividend and assume zero interest rate. Compute the
Black-Merton-Scholes delta on a 6-month European call option on
TSLA with a strike of $1000.

TSLA stock price is currently at $800. The stock return has an
annualized volatility (sigma) of 70%. The stock does not pay
dividend and assume zero interest rate. Compute the
Black-Merton-Scholes delta on a 6-month European call option on
TSLA with a strike of $1000.

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