(a) The gamma of a delta-neutral portfolio is 355. What is the impact on the portfolio value if the underlying asset price increases by $2.36? (Required: Show your work step by step)

(b) Consider a portfolio with a Delta of 90, a Gamma of -17, and a Vega of -10. A traded option is available with a Delta of 0.2, a Gamma 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)

(c) 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	50	0.6234
1	53	0.6111
.......	.......	.......	.......		.......	.......	.......
11	56	0.9800	0	9,800	0	212,000	883.33
12	59	1.0000

(d) 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.