embedding spot-vol correlation in option deltas
Friends,
Before we get to the heart of today’s education, this is a video follow up to yesterday’s HOOD: A Case Study in “Renting the Straddle”.
I talk about oil volatility as well and how it shows up in the Trade Ideas tool.
This concept of “spot-vol correlation” gets a lot of airtime from different angles even when it’s not explicit. The mass financial media doesn’t use the exact words but they know enough to call the VIX the “fear gauge”. VIX is a complicated formula that aggregates values representing annualized standard deviations from a strip of inverted Black-Scholes numerical searches with quadratic weights. But all of this gets translated to:
“when stock go down, that number go up”
That travels a lot faster. Even your cat knows that market volatility has an inverse relationship with stock returns.
The more your paycheck depends on option greeks, the more you will need to zoom in on this concept. Mostly because the relationship between vol and prices changes your actual risk. The Black-Scholes world assumes vol is constant, but we know better. The sensitivity of options to various market inputs (greeks are measures of risk) is naive without adjusting for behavior that is predictable enough for your cat make a better guess than random about what will happen to vol when stocks move.
How can use this cat knowledge to estimate better deltas so when our model says we are long $50mm worth of SPY, we aren’t suprised when it seems to act like we are only long $40mm worth?
There isn’t a single way to do this but I’m going to show you how I did it as a calculus-challenged orangutan.
Before we get to numbers and pictures, I want to mention one last thing.
There’s a riddle in the world’s best trading book Financial Hacking. An imaginary bank trader calls a meeting with management and says he’s found “greatest trade in the world”. He sits them down for a presentation and says he can buy calls for 20 vol and sell puts at 40 vol, delta hedge until expiry, and make a 20 point “arb”.
What’s the problem?
There are several, perhaps many, option traders reading this right now who have thought about the holy grail of long gamma, collecting theta. Look you can go do this right now.
Sell a strangle on 1-month oil futures and buy a ratio’d amount of 12-month CL straddles.
Buy a ratio time spread in a name that has a major event coming up
Trade SPY risk reversals
All of these trades will give you the “desired greeks”. But these are illusions. In order:
The lower vol on the deferred future makes the gamma of those options look higher than it is, but you need to weight the gamma by the lower beta those futures have to spot oil prices
The decay you think you collect on the near-dated short is unadjusted for the “shadow theta” or glide path of IV increasing as the upcoming event is a greater proportion of the variance remaining as each second elapses
Spot-vol correlation means that theta number is not just the cost of gamma but vanna. The owner of the put is getting more than gamma.
Ok, time for less words and more F9.
