Problem:

Suppose XYZ stock is trading at $100, its annualized standard deviation is o=.25, and the continuous compounded risk-free rate is 6%.

Requirement:

Question 1: Determine the B-S equilibrium call prices for an XYZ European 100 call expiring in 90 days (T=.25) and for an XYZ European 105 call expiring in 90 days.

Question 2: Determine delta, theta, and gamma for the 100 call and the 105 call.

Question 3: How would you construct a neutral delta hedged portfolio? What is the value of the portfolio? What would be your position theta and gamma?

Question 4: Given your neutral-delta hedged portfolio, what would expect the change in the portfolio's value to be over a short period of time if there were no changed in the price of XYZ stock? What would you expect the change in value to be if there was a positive change or a negative change in the stock price?

Question 5: What would be the portfolio's profit or loss if the price of XYZ stock increased to $105 and the 100 call and 105 call traded at their B-S values of $8.9597 and $6.0162, respectively? What would be the portfolio's profit or loss if the price of the XYZ stock decreased to $95 and the 100 call and 105 call traded at their B-S values of $3.2890 and $1.8133, respectively? Are your results consistent with your answer to part (d)?

Note: Please explain comprehensively and give step by step solution.