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a. Use the result in the previous exercise to show that if the portfolio is both delta and gamma neutral, then it replicates the risk free asset, i.e. it has a risk free rate of return which is equal to the short rate r.
b. Show that for a European put option the delta and gamma are given by
c. Take as given the usual portfolio P, and investigate how you can hedge it in order to make it both delta and vega neutral.