Please Answer these Questions. Thank you!

$1.$ The current price of Estelle Corporation is $$25.$ In each of the next two years, this stock price will either go up by $20\%$ or go down by $20\%.$ The stock pays no dividends. The one$-$year risk free interest rate is $6\%$ and will remain constant. Using the Binomial model, calculate the price of a one year call option on Estelle stock with a strike price of $$25.$

$2.$ Using the information from problem $1,$ use the Binomial model to calculate the pri

$3.$ The current price if Natash Corporation stock is $$6.$ In each of the next two years, this stock price can either go up by $$2\mathrm{.}50$ or go down by $$2.$ The stock pays no dividends. The one year risk free interest rate is $3\%$ and will remain constant. Using the Binomial model, calculate the pri

$4.$ Roslin Robotics stock has a volatility of $30\%$ and a current stock price of $$60$ per share. Roslin pays no dividends. The risk free interest is $5\%.$ Determine the Black$-$Sholes value of one year, at the money call option on Roslin stock.

$5.$ Rebecca is interested in purchasing a Eurpoean call on hot new stock, Up$.$ Inc. The call has a strike price of $$100$ and expires in $90$ days. The current price of Up stock is $$120,$ and the stock has a standard deviation of $40\%$ per year. The risk free interest rate is $6\mathrm{.}18\%$ per year.

a$.$ Using the Black $-$ Sholes formula, compute the price of the call

b$.$ Use put call parity to compute the price of the put with the same strike and expiration date.

$6.$ Using the data in Table $21\mathrm{.}1,$ compare the price on July $24,2009,$ of the following options on JetBlue stock to the price predicted by the Black Sholes formula. Assume that the standard devistion of Jetblue stock is $65\%$ per year and that the short term risk free rate of interest is $1\%$ per year.

a$.$ December $2009$ call option with $$5$ strike price

b$.$ December $2009$ put option with $$5$ strike price

c$.$ March $2010$ put option with $$7$ strike price.