Question

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.

Answer #1

The binomial tree is given in the diagram above with the working. T1 is the first month, T2 second month and T3 third month.

As this is a call option .. the price of option will be Spot price -(minus) Strike price. For e.g at the end of First month (T1) month the Price increase at $25 will have the call option price to be $25 (spot price)-$20(stike price)= $5. so on for each time frame.

If at end of any time frame the spot price is lesser than the strike price the option price will be zero.

3) For a call option on a non dividend paying stock the stock
price is $30, the strike price is $20, the risk free rate is 6% per
annum, the volatility is 20% per annum and the time to
maturity is 3 months. Use the Binomial model to
find:
a) The price of the call option?
Can you show the binomial model please

3) For a call option on a non dividend paying stock the stock
price is $30, the strike price is $20, the risk free rate is 6% per
annum, the volatility is 20% per annum and the time to
maturity is 3 months. Use the Binomial model to
find:
a) The price of the call option?
Please show work

Consider a call option on a stock, the stock price is $29, the
strike price is $30, the continuously risk-free interest rate is 5%
per annum, the volatility is 20% per annum and the time to maturity
is 0.25.
(i) What is the price of the option? (6 points)
(ii) What is the price of the option if it is a put? (6
points)
(iii) What is the price of the call option if a dividend of $2
is expected...

A
European call option and put option on a stock both have a strike
price of $20 and an expiration date in three months. Both sell for
$2. The risk-free interest rate is 5% per annum, the current stock
price is $25, and a $1 dividend is expected in one month. Identify
the arbitrage opportunity open to a trader.

A bank has written a call option on one stock and a put option
on another stock. For the first option the stock price is 50, the
strike price is 51, the volatility is 28% per annum, and the time
to maturity is nine months. For the second option the stock price
is 20, the strike price is 19, the volatility is 25% per annum, and
the time to maturity is one year. Neither stock pays a dividend,
the risk-free...

A bank has written a call option on one stock and a put option
on another stock. For the first option the stock price is 50, the
strike price is 51, the volatility is 28% per annum, and the time
to maturity is nine months. For the second option the stock price
is 20, the strike price is 19, the volatility is 25% per annum, and
the time to maturity is one year. Neither stock pays a dividend,
the risk-free...

Suppose that a 6-month European call A option on a stock with a
strike price of $75 costs $5 and is held until maturity, and
6-month European call B option on a stock with a strike price of
$80 costs $3 and is held until maturity. The underlying stock price
is $73 with a volatility of 15%. Risk-free interest rates (all
maturities) are 10% per annum with continuous compounding.
Use put-call parity to explain how would you construct a
European...

There is a six month European call option available on XYZ stock
with a strike price of $90. Build a two step binomial tree to value
this option. The risk free rate is 2% (per period) and the current
stock price is $100. The stock can go up by 20% each period or down
by 20% each period.
Select one:
a. $14.53
b. $17.21
c. $18.56
d. $12.79
e. $19.20

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.

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...

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