Question 5 (The Greeks) - (25 Marks) For this question please refer to the following call options: C4 C2 X = $100 c3 X = $110 X = $100 Call Options Strike Price Time to Maturity T = 180 days T = 180 days T = 90 days Option Price Delta Gamma Theta Vega Rho 10.3 0.6151 0.0181 -12.2607 26.8416 25.2515 6.06 0.4365 0.0187 -11.4208 27.6602 18.5394 6.91 0.582 0.0262 -15.8989 19.3905 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. Question 5 (The Greeks) - (25 Marks) For this question please refer to the following call options: C4 C2 X = $100 c3 X = $110 X = $100 Call Options Strike Price Time to Maturity T = 180 days T = 180 days T = 90 days Option Price Delta Gamma Theta Vega Rho 10.3 0.6151 0.0181 -12.2607 26.8416 25.2515 6.06 0.4365 0.0187 -11.4208 27.6602 18.5394 6.91 0.582 0.0262 -15.8989 19.3905 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