I'm having a hard time in my financial risk management class as these quizzes and assignments are not based off of lectures or materials available in the book. I have several questions I need help working since the formulas are much more complex than what I am given. If you could show how each one is worked, that would be great!

#1. Compute

(delta) for the following call option. The stock is selling for $23.50. The strike price is $25.

The possible stock prices at the end of 6 months are $27.25 and $21.75.

#2. A stock is selling for $18.50. The strike price on a call, maturing in 6 months, is $20. The possible stock prices at the end of 6 months are $22.50 and $15.00. Continuous interest rate is 6.0%. How much money would you borrow to make a portfolio replicating the call payoffs?

#3. In the lecture example, a European call option on a with a $40 strike and 1 year to expiration. The stock pays no dividends, and its current

price is $41. The continuously compounded risk-free interest rate is 8%. The stock price in 1 year is either $60 or $30. Using the binomial model

we solve the call option price is $ 8.871. If the market price for the call is $8. You could set up the arbitrage portfoliop as follows, to _____ the

option, _____ the stock 2/3 of share and _____ $ 18.462 at 8%.

#4. Consider a European put option on the stock XYZ, with a $40 strike and 1 year to expiration. The stock does not pay dividends, and its current

rice is $41 The continuously compounded risk-free interest rate is 8%. The possible stock prices over 1 year is either $60 or $30. What are the payoffs

of the long put option when stock price is $60 or $30?

#5. Consider a European put option on the stock XYZ, with a $40 strike and 1 year to expiration. The stock does not pay dividends, and its current

rice is $41 The continuously compounded risk-free interest rate is 8%. The possible stock prices over 1 year is either $60 or $30. To find the replicating

portfolio, using

(delta) for the number of shares needed and y the amount of risk-free borrowing, we solve:

60

- y exp(0.08) = 0

30

- y exp(0.08) = 10

the solutions of

and y are:

#6. From the previous question, the signes of the solution for delta and y means the replicating portfolio of the put takes the ___ position of the stock and

____ positon of $18.462 risk-free asset.

#7. Consider a European put option on the stock XYZ, with a $40 strike and 1 year to expiration. The stock does not pay dividends, and its current

rice is $41 The continuously compounded risk-free interest rate is 8%. The possible stock prices over 1 year is either $60 or $30. What is the put

price using the binomial model?