(a) Explain why the following positions could NOT be a delta-neutral portfolio: a long position in calls plus a long position in the underlying stock (b) The gamma of a delta neutral portfolio is 255. What is the impact on the value of the portfolio if the price of the underlying asset increases by $2.367 (Required: Show your work step by step) (c) Consider a portfolio that has a Delta of 90, a Game of -17and a Vega of -10. A traded option is available with a Delta ot 02, a Game of 0.01, and a Vega of 0.02. What position in the traded option and/or underlying stock would make the portfolio both Delta neutral and Vega neutral (Required: Show your work step by step) (d) Suppose you need to hedge a short call option on 10.000 shares and plan to perform a delta hedge that is rebalanced monthly. The current stock price is 50, the strike price is 50, the risk-free tate is 5, time to maturity is 1 year, sigma is 30%. Based on the BSM model, we can find the current delta, which is 0.6243. Fil in the information (ie, shares purchased, cumulative shares purchased, cost (S), curulative cost (S), and interest (sy) for months 0.1, and 12 of the following table. Cumulative shares Cost Cumulative Monthstock price Dota Share purchased purchased (8) Cot($) Interest ($ 50 0.6234 53 0.6711 0 1 11 56 12 59 09800 0 9,800 0 212.000 883 33 1.0000 (c) ts me following statement correct regarding the previous part of this question? Explain "At matiwity, the total cost of writing and hedging options in the cumulare cost" (a) Explain why the following positions could NOT be a delta-neutral portfolio: a long position in calls plus a long position in the underlying stock (b) The gamma of a delta neutral portfolio is 255. What is the impact on the value of the portfolio if the price of the underlying asset increases by $2.367 (Required: Show your work step by step) (c) Consider a portfolio that has a Delta of 90, a Game of -17and a Vega of -10. A traded option is available with a Delta ot 02, a Game of 0.01, and a Vega of 0.02. What position in the traded option and/or underlying stock would make the portfolio both Delta neutral and Vega neutral (Required: Show your work step by step) (d) Suppose you need to hedge a short call option on 10.000 shares and plan to perform a delta hedge that is rebalanced monthly. The current stock price is 50, the strike price is 50, the risk-free tate is 5, time to maturity is 1 year, sigma is 30%. Based on the BSM model, we can find the current delta, which is 0.6243. Fil in the information (ie, shares purchased, cumulative shares purchased, cost (S), curulative cost (S), and interest (sy) for months 0.1, and 12 of the following table. Cumulative shares Cost Cumulative Monthstock price Dota Share purchased purchased (8) Cot($) Interest ($ 50 0.6234 53 0.6711 0 1 11 56 12 59 09800 0 9,800 0 212.000 883 33 1.0000 (c) ts me following statement correct regarding the previous part of this question? Explain "At matiwity, the total cost of writing and hedging options in the cumulare cost
