Find the value of the option

For this assignment, you must keep at least 6 decimal digits for all calculations (in fact, please, do not round at all since, given that this is a computational assignment, rough rounding will lead to mark reduction) and must submit 2 files:

1) A PDF file with your solutions and answers and

2) An Excel file with your computations

In PDF file, make sure to reference the portions of the Excel file where you did the computations for each question. In Excel file, use different colors to highlight your answers (and make a small note that it is the answer).

Problem 1: Consider a stock with current price S=100 and standard deviation of annual returns =30%. Stock does not pay any dividends. Consider a 1-year European call option on this stock with strike price of $95. The risk-free interest rate is 8%.

a) Find the value of this option using Cox-Ross-Rubenstein 2-step binomial option pricing model.

b) Using Excel, find the value of this option using Cox-Ross-Rubenstein 5-step binomial option pricing model.

c) Using Excel, find the value of this option using Cox-Ross-Rubenstein 10-step binomial option pricing model.

d) Using Excel or any other methods (except option price calculators), find the value of this option using Black-Scholes model.

Problem 2 :Consider a 6-month European put option with strike price of $2050 on a stock index if the current index value is $2000. The dividends paid by the stock included in the index can be approximated by a continuously compounded dividend yield of 10%. The risk-free interest rate is 8%. The standard deviation of the index price appreciation is =30%.

a) Find the value of this option using Cox-Ross-Rubenstein 2-step binomial option pricing model.

b) Using Excel, find the value of this option using Cox-Ross-Rubenstein 10-step binomial option pricing model.

c) Using Excel or any other methods (except option price calculators), find the value of this option using Black-Scholes model

Problem 3 :

A 7-month forward price on a stock is $100. The price of a 3-months European call option with strike price of $98 on this forward contract is $5. Using Black’s model, find the price of a 4-months European put option with strike price of $101 on the same forward contract if the risk-free interest rate is 8%. You may want to use Excel for this question.