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Question: A bank holds a portfolio of options that are sensitive to an underlying stock portfolio. The delta of the portfolio is -30 and the gamma is -5.
i. Write down a quadratic approximation to the option portfolio price change as a function of delta, gamma, and the change in the stock portfolio S (i.e. you will have terms of dS and dS^2).
ii. What is the approximate change in the option portfolio value if the underlying stock portfolio value changes by 2?
iii. How would you make the portfolio delta and gamma neutral?
iv. Discuss how you could calculate the 99% 1-day VaR on the portfolio using the approximation in part i. and the historical simulation approach.
v. What other risk sensitivities could you consider?
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