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Why Equity Volatility Often Rises as Prices Fall

Article Quant Q&A · Author: Rounak gupta
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Summary

The answer explains the tendency for equity volatility to move inversely with stock prices by comparing equities with credit. For credit, falling prices can reflect growing concerns about whether borrowers can meet obligations; uncertainty can increase further around default and recovery values. For equities, the explanation focuses on their long-lived cash flows: bad news may reduce expected growth and raise the discount rate or risk premium, sharply lowering present value, while also increasing uncertainty.

A simplified dividend-growth example illustrates how a lower growth assumption and a higher discount rate can combine to reduce an asset’s value. The author presents this as an intuition for assets whose value depends heavily on distant growth expectations, rather than as a measured empirical result or a universal pricing law. The question also mentions the equity volatility smirk across strikes, but the answer chiefly addresses the relationship between share price and volatility; it does not derive the strike-price pattern or give a graph.

Key ideas

  • Credit prices can fall as perceived default risk and uncertainty about recovery values rise.
  • For equities, adverse news can lower expected growth while raising the discount rate or risk premium.
  • When much of an asset’s value depends on distant cash flows, changes in growth and discount assumptions can have large price effects.
  • The answer offers a qualitative explanation and illustrative valuation example, not a universal law or an empirical test.

Tags

EquitiesOptionsVolatility
Full text
# Why and how is Implied volatility directly related to stock price but inversely related to strike price?


# Why and how is Implied volatility directly related to stock price but inversely related to strike price?












I know that in equity markets there is a volatility smirk which results in higher IV for lower strike price options because of crashophobia and leverage related factors but I can't wrap my head around why there is a direct relationship between share price and IV... A graph to explain it all would be really helpful.

## Answer by demully (score 1)

https://quant.stackexchange.com/a/48654

One way to think about this is to forget about equities (for a moment), and think about credit.

90% of the time, credit just gets paid.

5% of the time, credit still gets paid; but a booming economy means that rates rise, so the increased certainty of getting paid is worth less than the decline to NPVs from the coupon becoming worth less.

3% of the time, there will be worries about the coupon becoming less affordable; but it still gets paid. A 1% probability of default becomes a perceived 2%, so bad things happen to credit prices.

1% of the time, there will be genuine worries about the coupon being affordable, but it is paid. The 10% odds of default on the subsequent ones will do bad things...

And 1% of the time, there will be an actual default. Which spurs a whole new round of speculation about default rates under liquidation and litigation. Is the bond worth 15, 25, 35 or 45 cents on the dollar? Volatility then would make stocks, even NatGas, look like a wimp’s game.

The point here is that the vol IS (negatively) correlated with price. With credit, this is for solvency reasons.

With equities, it is more to do with equities being perpetual assets. Let’s say, for simplicity’s sake, my stock is a 2% yield expected to grow by 4%.

Good news happens... new product is a huge success. Earnings and payouts jump 20%; but I assume is a sustainable gain in market share; don’t assume this acceleration persists. Price up 20%.

Bad news happens... new product is a total disaster. Earnings fall; but payouts can be maintained. I assume the ability to grow falls significantly (say 4% to 3%). Meanwhile, the negative newsflow causes me to raise my discount factor/risk premium from 6% to 7%.

Then d/(k-g) goes from 1/(6%-4%) = 50 to 1/(7%-3%) = 25. Down 50%.

This is obviously a figurative example; but hopefully the broad thrust is clear. For any asset driven by growth expectations, where the majority of the NPV will be delivered decades in the future, there is an intuitive fundamental tendency for price downside to coincide with volatility upside.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.