(a) -10. There are two traded options available: Delta Traded options 1 0.2 Traded options 2...

   

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(a) -10. There are two traded options available: Delta Traded options 1 0.2 Traded options 2 -0.1 0.3 What position in the traded option and/or underlying stock would make the portfolio Gamma and Vega neutral? (Required: Show your work step by step) Consider a portfolio with a Delta of 100, a Gamma of -20, and a Vega of Gamma 0.01 0.05 Vega 0.5 (b) 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 rate is 5%, the time to maturity is 1 year, and the sigma is 30%. Based on the BSM model, we can find the current delta, which is 0.6234. Fill in the information (i.e., shares purchased, cumulative shares purchased, cost ($), cumulative cost ($), and interest ($)) for months 0, 1, and 12 of the following table. Month Stock price Delta Shares purchased Cumulative shares purchased Cost ($) Cumulative cost ($) Interest ($) 0 0.6234 0.6845 1 ✰✰✰✰✰✰✰ 11 12 50 53 ******* 48 43 0.3555 0.0000 0 ********* 3,555 A ******. 0 ******* 212,000 ******* 883.33 (c) Is the following statement correct regarding the previous part of this question? Explain. "At maturity, the total cost of writing and hedging options is the cumulative cost minus the cash flow received from delivering stocks." (3+6+1 = 10 marks) DE (a) -10. There are two traded options available: Delta Traded options 1 0.2 Traded options 2 -0.1 0.3 What position in the traded option and/or underlying stock would make the portfolio Gamma and Vega neutral? (Required: Show your work step by step) Consider a portfolio with a Delta of 100, a Gamma of -20, and a Vega of Gamma 0.01 0.05 Vega 0.5 (b) 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 rate is 5%, the time to maturity is 1 year, and the sigma is 30%. Based on the BSM model, we can find the current delta, which is 0.6234. Fill in the information (i.e., shares purchased, cumulative shares purchased, cost ($), cumulative cost ($), and interest ($)) for months 0, 1, and 12 of the following table. Month Stock price Delta Shares purchased Cumulative shares purchased Cost ($) Cumulative cost ($) Interest ($) 0 0.6234 0.6845 1 ✰✰✰✰✰✰✰ 11 12 50 53 ******* 48 43 0.3555 0.0000 0 ********* 3,555 A ******. 0 ******* 212,000 ******* 883.33 (c) Is the following statement correct regarding the previous part of this question? Explain. "At maturity, the total cost of writing and hedging options is the cumulative cost minus the cash flow received from delivering stocks." (3+6+1 = 10 marks) DE

Answer rating: 100% (QA)

Gamma and Vega Neutral Portfolio To make the portfolio gamma and vega neutral you need to create a combination of Traded Option 1 and Traded Option 2 ... View the full answer