Consider a portfolio has a Delta of 90, a Gamma of -17, and a Vega of -10.

(a) 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 Gamma neutral? Show your work step by step.

(b) There are two traded options available: Delta of option Gamma of option Vega of option Traded options 1 0.2 0.01 0.02 Traded options 2 -0.1 0.05 0.02 What position in the traded option and/or underlying stock would make the portfolio Delta, Gamma, and Vega neutral? Show your work step by step.

(c) Explain why we need dynamic hedging for delta.