Question

Question 1

A stock selling at $50 is expected to pay no dividend and has a
volatility of 40%. Consider put options with a 6-month maturity and
a $50 strike price. The risk-free rate is 10% per annum
continuously compounded.

Consider a three-step binomial tree.

(a) Use the binomial tree to price the put option if it is
American.

Answer #1

**Solution:**

The price of the option is **$4.982**

**Formula used:**

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A stock index is currently 1,500. Its volatility is 18%. The
risk-free rate is 4% per annum for all maturities and the dividend
yield on the index is 2.5% (both continuously compounded).
Calculate values for u, d, and p when a 6-month time step is used.
What is value of a 12-month European put option with a strike price
of 1,480 given by a two-step binomial tree?
In the question above, what is the value of a 12-month American
put...

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).

A stock index is currently 1,500. ITs volatility is 18% per
annum. The continuously compounded risk-free rate is 4% per annum
for all maturities.
(1) Calculate values for u,d, and p when a six-month time step
is used.
(2) Calculate the value a 12-month American put option with a
strike price of 1,480 given by a two-step binomial tree.

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

A 3-month American call option on a stock has a strike price of
$20. The stock price is $20, the risk-free rate is 3% per annum,
and the volatility is 25% per annum. A dividend of $1 per share is
expected at the end of the second month. Use a three-step binomial
tree to calculate the option price.

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 $40. Over
the next year it is expected to rise to $42 or fall to $37. An
investor buys put options with a strike price of $41 expiring in
one year. Please form a riskless portfolio and use no arbitrage
method to value this put option. Risk free rate is 3% per annum,
continuously compounded.

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?

Current price of a non-dividend paying stock is $50. Use a
two-step tree to value an AMERICAN PUT option on the stock with a
strike price of $52 that expires in 6 months. Each step is 3 months
and in each step the stock price either moves up by 10% or moves
down by 10%. Suppose that the risk-free rate is 7% per annum
continuous compounding. What should be this American put option
price?
$4.64
$6.10
$3.42
$7.43

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