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

VIX Futures data is attached
Excel file is required
Volatility and Options
When the bond-arbitrage strategy dried
up, one of the strategies LTCM employed was volatility arbitrage. Let us
examine 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 differences
between this series and the VIX index (VIX-GARCH) (make sure to divide VIX by
100). Now calculate VIX front month futures overlapping returns (approx. 22- trading
day) 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)

Form
5-volatility difference baskets (highest to lowest) and report the average return
and standard deviation for the VIX front month futures for each basket. Use
the first three years to establish the breakpoints for the baskets, then update
them daily with each new observation. (6 points)
Starting
in 2008, assume you take a daily position and go 2x short the VIX futures in
highest basket, short the 2nd highest basket, cash the third basket, long the
4th basket, and 2Xlong the lowest. Assume that there is an ETF built on this
product 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 the
change (not %) assuming you are holding (long or short depending on the basket)
1 contract. (6 points)
Now
assume LTCM sold monthly European straddles on this ETF product at the start of
each month, from 2008 through 2021 (assume 1 straddle per month). What would
have been the dollar gain or loss to selling the options over the period. (6
points)
Explain
how LTCM could have hedged this exposure? (6 points)

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