How Options Hedging Can Affect Underlying Stock Volatility

# Relationship between options open interest and spot price movement


# Relationship between options open interest and spot price movement












The hypothesis that I am mulling over (and more so, its effect on stock price movement) is the following.

Hypothesis: Buyers of options do not hedge (as they don't need to) while sellers usually hedge in some form or the other.

If that is true, what happens is that if buyers of stock keep buying, and spot price moves closer to a strike price, then the call sellers will buy more of the stocks to stay hedged based on the delta value of that particular call option. The put option sellers will reduce their short position as the stock price goes up as they do not need to short that many stocks when the spot price goes up. This creates additional buy pressure on the stock as if it got accelerated momentarily, which would have not existed had there been zero options open interest. In a similar way, the movement of the spot price gets accelerated when the spot starts to head downwards towards a strike price.

So in effect, these derivatives (I think futures has the same influence on the spot price) cause acceleration of the spot price in the direction of its movement as and when it moves closer to the strike levels. This will be more pronounced if the open interest is high around that strike price (and perhaps their neighbors too). I'd also wager that closer the option is to the expiry, the more is the acceleration near the strike prices as gamma is ultimately what dictates the rate at which the seller hedges.

Is my thought process above completely bullshit? Is any of it right? If there are (easy to understand) sources to learn more about these effects (assuming there is some truth to it), I'd appreciate it if you can share them with me.

## Answer by fes (score 5, accepted)

https://quant.stackexchange.com/a/76231

I think what you describe makes sense, at least loosely. This paper finds evidence of a mechanism that seems quite similar to what you describe. They write:

"The potential mechanism is that dynamic hedging of written option positions involves buying the underlying asset after its price has increased and selling it after its price has decreased. This pattern of buying and selling potentially causes the underlying asset to be more volatile than it otherwise would have been. Similarly, dynamic hedging of purchased option positions potentially causes volatility to be lower than it otherwise would have been. The magnitude of the buying and selling volume to rebalance hedges is determined by the option gamma of the net options position of delta hedgers, leading to the prediction that stock return volatility will be decreasing in the gamma of delta hedgers’ net options position."

Reference to published version:

Ni, S. X., Pearson, N. D., Poteshman, A. M., & White, J. (2021). Does option trading have a pervasive impact on underlying stock prices?. The Review of Financial Studies, 34(4), 1952-1986.

## Answer by lehalle (score 3)

https://quant.stackexchange.com/a/76278

This presentation by Robert Almgren cite most of the literature on this topic: Option Hedging with Market Impact. Olivier Guéant and Jiang Pu worked on the same topic (hedging taken market impact into account) with another philosophy in Option Pricing And Hedging With Execution Costs And Market Impact.

You intuition is correct: the pressure of hedging trades have an impact on the price formation process. It is nevertheless not as simple as being sure that open interest will provoke price moves, because intermediaries (investment banks or market makers on options) are netting their book before hedging. As a consequence the best situation for them is when they are selling opposite exposure to the same risk factors. In your case the risk factor is price moves, i.e. Delta, but it is true for the exposure to volatility (Vega), to maturities, etc.

Because of that, it is only the net exposure of each bank that is hedged, and it is only when the net exposure of all banks is not zero that it has an impact (otherwise they will simply simultaneously buy and sell; as a result their impacts would more or less cancel). It is something we explain in Financial Markets in Practice: From Post-Crisis Intermediation to FinTechs with Amine Raboun. The purpose of this book is exactly to explain financial intermediation, and what you mention is an example of intermediation: when I buy to an investment bank the option to buy a share in 3 months, the bank (while hedging) will slowly impact the price formation process with my desire to get this option. The more probably I will exercise this option, the more the hedge will impact the price as a buy.

## Answer by Newquant (score 2)

https://quant.stackexchange.com/a/76240

Empirically yes, it absolutely does, this paper from squeezemetrics started doing the rounds in 2020, though was released in 2017: https://squeezemetrics.com/monitor/download/pdf/white_paper.pdf

Note the chart above which is from page 6 of the paper. Squeezemetrics aims to estimate the gamma exposure of market makers, who are more likely to systematically hedge their deltas intraday. You can see a clear negative relationship relationship between the dispersion of returns, and the gamma exposure of market makers. Of course there is nuance in the calculations, but I believe this is sufficient evidence of an effect like your hypothesis would suggest.

If you can ignore the adverts and branding, this video from RealVision is quite good featuring Hari Krishnan (second leg down, market tremors author) : https://www.realvision.com/market-makers-and-coronavirus-the-mechanics-of-a-market-sell-off?utm_source=contributor&utm_medium=referral&utm_campaign=43900_HK_GH_CONT_W1_LINK

The materials on squeezemetrics are also quite good for wider reading: https://squeezemetrics.com/monitor