Question

Today’s price of Microsoft (MSFT) is $100 per share. MSFT does not pay dividends. The c.c. risk-free interest rate is zero percent. Assume there is no arbitrage and the Black-Scholes model assumptions hold.

The market price of a European call option on MSFT with a strike of $100 and a maturity of one year is $1.99. What is the implied volatility of the call option?

Answer #1

Implied volatility of call option is 4.98872389668773%

Today’s price of Microsoft (MSFT) is $100 per share. MSFT does
not pay dividends. The c.c. risk-free interest rate is zero
percent. Assume there is no arbitrage and the Black-Scholes model
assumptions hold. The market price of a European call option on
MSFT with a strike of $100 and a maturity of one year is $1.99.
What is the implied volatility of the call option?

Today’s price of Apple (AAPL) is $200 per share. AAPL does not
pay dividends. The annualized volatility of AAPL is 15 percent. The
c.c. risk-free interest rate is one percent. Assume there is no
arbitrage and the Black-Scholes model assumptions hold.
What is the price of a European call option on AAPL with a
strike of $200 and a maturity of two months?

Today’s price of Chipotle (CMG) is S0. CMG does not pay
dividends. A one-year European call option on CMG has a strike of
$450 and a premium of $104.52. A one-year European put option on
CMG has a strike of $450 and a premium of $7.57. The c.c. risk-free
interest rate is five percent. Assume there is no arbitrage. What
is today’s stock price S0?

Today’s price of Marriot (MAR) is $75. MAR does not pay
dividends. Each year, the
stock price of MAR can either go up or down. If the stock price
goes up, the gross rate
of return is u = 2. If the stock price goes down, the gross rate of
return is d = 0.5.
The c.c. risk-free interest rate is zero percent. You are
interested in a European put
option on MAR with a strike of $80 and a...

Imagine that both Microsoft stock (MSFT) and Facebook stock (FB)
are currently trading at 20 USD/share. The price volatility of MSFT
is significantly lower than that of FB. A call option on MSFT with
a strike price of 20 USD and a time to maturity of 3 months is
trading at a premium of 1.5 USD. Which of the following call
options on FB could possibly be trading at the same price as the
option on MSFT?
A. Call option...

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...

You are evaluating a European call option on a no-dividend
paying stock that is currently priced $42.05. The strike price for
the option is $45, the risk-free rate is3% per year, the volatility
is 18% per year, and the time to maturity is eleven months. Use the
Black-Scholes model to determine the price of the option.

Spot price of the stock=26.64
Strike price=26.64
Monthly stock volatility=10.681%
No dividends
Maturity=3 years
Risk-free rate=2.28%
Solve the European call option price using BSM model. More
specifically, how do you get the annualised stock volatility?

Question 6 - Chapter 7 Textbook:
The current share price of Elica plc is £2.26 per share. It
offers a continuously compounded dividend yield of 2.00% per year.
The volatility of its stock returns is 50% and risk free rate is
5%, both per annum with continuous compounding.
Using Black-Scholes-Merton (B-S-M) model, find the values of
N(d1) and N(d2) for an option with a strike price of £2.00 and
maturity in six months. (show all step-by-step calculations)
Determine the price...

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