Volatility's Past Trauma
How GARCH Adjusts for Environments and Extremes
Setting the Table:
Risk is back on in equity markets as a whiff of seasonality has combined with somewhat positive news out of the inflation/rates camp. There is concern about how quickly the rebound happened, as well as macro considerations of just what a falling rate environment would mean otherwise for the economy.
Liquidity in listed options has stayed sadly flat. While we’ve rebounded a bit with this rally, across the broad market we’re notably lower than we were the last time this big round number came around.
Seasonality and flow has a lot to do with short and medium term valuations in the market. We’ve seen large intraday hedging push the market one way or the other, and there are large mandates that can be relatively predictable. Ultimately this swirl of flows is difficult to predict, but here are two perspectives on what the end of the year might bring.
While not specifically options related, there have been a few comments on safe withdrawal rates for retirees.
As we discussed last week, one of the most important components of the pricing model is volatility. The expected variance, and how this variance is expected to change at different price levels (skew) are what determines the price of the probabilistic contract that you purchase.
It’s extremely important to understand that time and volatility are the same sides of a coin. Typically volatility figures are annualized, so that we can talk about them comparatively. If we want the answer in price terms, as in, “how much do we expect this to move before X date” then we look at the straddle pricing on that day.
A quick short hand for relating these two figures and grasping the inverse relationship between vol and time, is to take the annualized volatility, and divide it by the square root of 252. We divide by the square root of time, specifically the number of trading days in a calendar year, to get the expected daily move in % terms for a stock.
This can also be adjusted for different time frames, such that the 2 day expected move is found by dividing by the square root of (252/2). At the extreme (252/252) is just the annualized figure.
My experience is that this works well at both extremes, 1 day or 1 year. Once you start including days over weekends for this measure, it dislocates from market prices as sophisticated vol models account for the lack of expected variance when the market is closed.
Example: AAPL is currently trading at $190 and the implied volatility of the ATM option is roughly 17% for options expiring in the next 3 weeks. Take 17%/sqrt(252) and we get 1.07% daily moves (about $2.06).
The ATM $190 straddle in AAPL expiring at the close today is trading about $1.65 to start the session. Since there’s technically only 6.5 hours of trading left in that contract (albeit the most significant 6.5 hours) there’s some discount to a “daily” implied figure.
Today we will analyze how to take into account the variations in volatility over time with the GARCH model.
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