What would have been the dollar gain or loss to selling the options over the period.

VIX Futures data is attachedExcel file is requiredVolatility and OptionsWhen the bond-arbitrage strategy driedup, one of the strategies LTCM employed was volatility arbitrage. Let usexamine how profitable this is, with a twist. Calculate the GARCH (1,1)volatility of the S&P 500 from 2005 through 2021. Calculate the daily differencesbetween this series and the VIX index (VIX-GARCH) (make sure to divide VIX by100). Now calculate VIX front month futures overlapping returns (approx. 22- tradingday) for each day in the sample (Each day will have a return of (Dayt+22- Dayt)/Dayt).(Don’t worry abut the roll…you can thank me later)
Form5-volatility difference baskets (highest to lowest) and report the average returnand standard deviation for the VIX front month futures for each basket. Usethe first three years to establish the breakpoints for the baskets, then updatethem daily with each new observation. (6 points)Startingin 2008, assume you take a daily position and go 2x short the VIX futures inhighest basket, short the 2nd highest basket, cash the third basket, long the4th basket, and 2Xlong the lowest. Assume that there is an ETF built on thisproduct that is valued at 100 starting in 2008. What is the value today?HINT:To calculate this, start with 100, and then each day increased the value by thechange (not %) assuming you are holding (long or short depending on the basket)1 contract. (6 points)Nowassume LTCM sold monthly European straddles on this ETF product at the start ofeach month, from 2008 through 2021 (assume 1 straddle per month). What wouldhave been the dollar gain or loss to selling the options over the period. (6points)Explainhow LTCM could have hedged this exposure? (6 points)