The gamma of a delta-neutral portfolio is 355. What is the impact on the portfolio value if
Question:
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."