**Please provide response in both excel and
word formats**

1.

A common stock will have a price of either $85 or $35 in 2 months.

A two month put option on the stock has a strike price of $40.

**Create a riskless portfolio. Buy one put option. How many shares
should you buy?**

*Make
sure that you show or explain all calculations.*

2.

Consider an option on a dividend-paying stock when the stock price

is $48, the strike price is $45, the risk-free interest rate is 6% per annum,

the volatility is 30% per annum, and the time to maturity is two months. The

dividend to be paid in 1 month is $2.

a. **What is the price of the
option if it is a European call?**

b. **What is the price of the
option if it is an American call?**

**Use the Black Scholes formula to answer the questions above.**

*Make
sure that you show or explain all calculations. Make sure you answer all
questions above.*

3.

Consider a European call option on a non-dividend-paying stock

where the stock price is $50, the strike price is $50, the risk-free rate is 5%

per annum, the volatility is 25% per annum, and the time to maturity is four

months.

c. **Calculate****u****,****d****,****a**** and****p**** for a two-step tree. [Use 4
decimal places in your calculations.]**

d. **Value the option using a
two-step tree. [Give your final answer to 2 decimal places.]**

*Make
sure that you show or explain all calculations. Make sure you answer both parts
a and b above. Make sure you complete the tree below.*

4.

Suppose that the premium on a European put option, p = $3. The

time to maturity, T = 1 year. The strike price is $20. The stock price of the

underlying common stock is $12 today. The risk-free interest rate is 8% per

annum. The stock does not pay dividends.

Observe that there is an arbitrage opportunity.

**Clearly state what the trader would do to make a profit.**

*Make sure that you demonstrate the relation that must be satisfied
to eliminate the arbitrage opportunity.*

5.

Consider the following portfolio: You __buy__ two July 2009

maturity call options on Dell with **exercise
price of 30**. You also

__sell__two July 2009 maturity put

options on Dell with an

**exercise**

price of 40. The Call premium is $3.30 and the Put premium is

price of 40

$2.50.

*Assume each option contract is for one share of stock.*

e. **What will be your profit/loss
on this position if Dell is selling at $42 on the option maturity date?**

f. **What will be your profit/loss
on this position if Dell is selling at $38 on the option maturity date?**

g. **At what stock price on the
option maturity date will you just break even on your investment?**

*Make
sure that you show or explain all calculations. Make sure you answer all
questions above.*

6.

Consider an option on a non-dividend-paying stock when the stock

price is $48, the strike price is $45, the risk-free interest rate is 6% per

annum, the volatility is 20% per annum, and the time to maturity is five

months. It can be shown that d_{1} = .7576 and d_{2} = .6285.

**Create a delta neutral portfolio of call options and stock. Short
10,000 call options (100 contracts). How many shares would you buy or sell?**

*Make sure that you show or explain all calculations. Make sure
that you state the number of shares. Make sure that you state whether you would
buy or sell the shares*