Question 5 (The Greeks) - (25 Marks) For this question please refer to the following call options: Call Options C2 C3 C4 Strike Price X = $100 X = $110 X = $100 Time to Maturity T = 180 days T = 180 days T =90 days Option Price 10.3 6.06 6.91 Delta 0.6151 0.4365 0.582 Gamma 0.0181 0.0187 0.0262 Theta -12.2607 11.4208 15.8989 Vega 26.8416 27.6602 19.3905 Rho 25.2515 18.5394 12.6464 Part A (15 Marks) A trader can create a delta neutral portfolio from a stock and a call option written on that stock or from a stock and a put option written on that stock. In general, a stock plus one option can be made neutral to one of the Greek parameters. a) A portfolio composed of a stock and a single option written on that stock can only be made both delta and gamma neutral if what special condition is true? (5 Marks) b) Create a portfolio that is both Delta and Gamma neutral using stock, call C2 and call C3. Also calculate and comment on this portfolio's theta, vega and rho. (10 Marks) Part B (10 Marks) Consider a calendar spread formed of call C2 and call C4. What is the cost of establishing this position now? Calculate the Greek sensitivities for this option position now. Comment on these values