You estimate three year volatility at $25\mathrm{.}70\%$ and offer the option up three volatility points at $28\mathrm{.}7\%$ vol.Using your option calculator you calculate a value of $99\mathrm{.}66$ per share for the option.The client accepts your offer!$9/23/2024$MSFT$434\mathrm{.}12$MSFT $9/23/27434\mathrm{.}12$ Call $($OTC$)$FVZ$4$DescriptionOTC Option$5-$yr Note FutureStrike$434\mathrm{.}12$ExerciseEuropeanExpiration$9/23/2027$Rate$3\mathrm{.}230\%$Volatility$28\mathrm{.}70\%$Dividend$0\mathrm{.}79\%$ModelBlack$-$ScholesValue$99\mathrm{.}66$Delta$0\mathrm{.}658$Gamma $(1\%)0\mathrm{.}0070$Vega $(1$ vol point$)2\mathrm{.}870$Rho $($BPV $01)0\mathrm{.}05848\mathrm{.}96$Risk ReportShareSecurityPositionDelta$Delta$Gamma$Vega$Rho$0-500,000-329,000-142,825,480-1,519,420-1,435,000-29,000$MSFT$00000$FVZ$400000-329,000-142,825,480-1,519,420-1,435,000-29,000-5921)$ First, what do you need to do to implement a "Delta Neutral" hedge with stock?$2)$ If the stock rises $3\%$ tomorrow, estimate what will you need to do to remain "Delta Neutral"$3)$ If your Volatility estimate proves to be accurate for the period, what is your expected profit?$4)$ If interest rates rise $1\%($to $4\mathrm{.}23\%),$ what will be the effect on your P&L$?$ What could you do to minimize this risk?

Sheet $2$: Gamma and Vega Neutral

The Listed Option in Column C below looks like a good candidate to help reduce the Gamma and Vega risk in your portfolio.Use it to further reduce your risk$\mathrm{.}3/10/2021$MSFT$434\mathrm{.}120$MSFT $6/18/2026435$ Call $($Listed$)$FVZ$4$DescriptionOTC OptionListed Option$5-$yr Note FutureStrike$434\mathrm{.}12435$ExerciseEuropeanAmericanExpiration$9/23/276/18/26$Rate$3\mathrm{.}23\%3\mathrm{.}44\%$Volatility$28\mathrm{.}70\%26\mathrm{.}98\%$Dividend yield$0\mathrm{.}79\%0\mathrm{.}79\%$ModelBlack$-$ScholesBlack$-$ScholesValue$99\mathrm{.}6668\mathrm{.}65$Delta$0\mathrm{.}6580\mathrm{.}615$Gamma$0\mathrm{.}0070\mathrm{.}011$Vega $(1$ vol point$)2\mathrm{.}872\mathrm{.}16$Rho $($BPV $01)0\mathrm{.}0580\mathrm{.}03448\mathrm{.}96$Risk ReportShareSecurityPositionDelta$Delta$Gamma$Vega$Rho$0-500,000-329,000-142,825,480-1,519,420-1,435,000-29,000$MSFT $6/18/2026435$ Call $($Listed$)00000$MSFT$00000$FVZ$400000-329,000-142,825,480-1,519,420-1,435,000-29,000-5921)$ Construct a "Gamma Neutral" hedge with the listed option, stock and FVZ$3$ to minimize dynamic hedging.MSFT $6/18/2026435$ Call $($Listed$)$MSFTFVZ$42)$ Construct a "Vega Neutral" hedge with the listed option, stock and the FVZ$3$ to minimize volatility exposure.MSFT $6/18/2026435$ Call $($Listed$)$MSFTFVZ$43)$ Construct a blended hedge to get Vega above $-$$$250,000$ and Gamma positiveMSFT $6/18/2026435$ Call $($Listed$)$MSFTFVZ$4$