Question

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?

Answer #1

Detailed solution is provided.

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 (St − 63, 0)]" where is the stock
price in six months?

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?

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 current price of a non-dividend paying stock is $50. Use a
two-step tree to value a American 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 model. Please enter your answer rounded to two
decimal places (and no dollar sign).

Price a European call option on non-dividend paying stock by
using a binomial tree. Stock price is €50, volatility is 26%
(p.a.), the risk-free interest rate is 5% (p.a. continuously
compounded), strike is € 55, and time to expiry is 6 months. How
large is the difference between the Black-Scholes price and the
price given by the binomial tree?

Price a European call option on non-dividend paying stock by
using a binomial tree. Stock price is €50, volatility is 26%
(p.a.), the risk-free interest rate is 5% (p.a. continuously
compounded), strike is € 55, and time to expiry is 6 months. How
large is the difference between the Black-Scholes price and the
price given by the binomial tree?

Consider a European call option on a non-dividend-paying stock
where the stock price is
$40, the strike price is $40, the risk-free rate is 4% per annum,
the volatility is 30% per
annum, and the time to maturity is 6 months.
(a) Calculate u, d, and p for a two-step tree.
(b) Value the option using a two-step tree.
(c) Verify that DerivaGem gives the same answer.
(d) Use DerivaGem to value the option with 5, 50, 100, and 500...

The current price of a non-dividend paying stock is $50 and the
continuously compounded risk free interest rate 8%. Using options,
you would like to just expose yourself to the risk and returns of
the stock over a period of 6 months without actually buying the
stock. Though you don’t have to pay the price of the stock for
this, there is still a cost involved now. How much is it?

Consider a six-month European call option on a
non-dividend-paying stock. The stock price is $30, the strike price
is $29, and the continuously compounded risk-free interest rate is
6% per annum. The volatility of the stock price is 20% per annum.
What is price of the call option according to the
Black-Schole-Merton model? Please provide you answer in the unit of
dollar, to the nearest cent, but without the dollar sign (for
example, if your answer is $1.02, write 1.02).

A non-dividend paying stock price is $100, the strike price is
$100, the risk-free rate is 6%, the volatility is 15% and the time
to maturity is 3 months which of the following is the price of an
American Call option on the stock. For
full credit I expect each step of the calculations tied to the
correct formulas.

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