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Why Implied and Realized Spot-Volatility Beta Gaps Do Not Guarantee Arbitrage

Article Quant Q&A · Author: volquant
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Summary

The document considers whether a vanilla options-and-underlying position can profit when implied spot-volatility beta, inferred from risk reversals, disagrees with beta observed in recent market behavior. The example is a market with put volatility above call volatility even as at-the-money volatility rises with spot prices.

The response cautions that a return to historically typical behavior is not itself a source of positive expected returns: option prices already reflect the market's expectations for future behavior. It compares the idea with betting on realized volatility to revert to the level implied by option prices. As an alternative view, it suggests positioning for the unusual relationship to persist, using a risk reversal while rebalancing vega and spot exposure daily. The exchange gives no empirical test, payoff construction, or evidence that this continuation trade is profitable; it is a conceptual explanation, not a validated arbitrage strategy.

Key ideas

  • Implied spot-volatility beta is inferred from risk reversal prices, while realized beta is estimated from observed market behavior.
  • A recent mismatch between implied and realized beta does not by itself imply a profitable trade on reversion.
  • Option prices already incorporate expectations about future market behavior.
  • A risk reversal with daily vega and spot rebalancing is proposed as a way to bet on the unusual relationship continuing.

Tags

OptionsVolatilityArbitrageDerivatives pricing
Full text
# Arbitrage between implied and realised spot-vol beta


# Arbitrage between implied and realised spot-vol beta












Let's say there is a discrepancy is the market with respect to implied spot-vol beta (implied skew) and the actual beta of ATM vols with spot. Let's say Put vol > Call Vol but the atm vols are rising as spot goes up.

How to formulate a vanilla trade (combination of call,puts and underlying) that will have exposure on (implied beta - realized beta) using which I can take a bet on the arbitrage (statistical) of this pattern reverting to normal (same direction of implied and realized).

## Answer by dm63 (score 1)

https://quant.stackexchange.com/a/79805

To clarify terms , implied beta means the spot-vol correlation that is implied by the price of risk reversals. Realized beta means spot-vol correlation measured from recent market behavio.

I don’t believe a trade can be constructed with positive expectation if the market behavior returns to “normal”. The market is priced such that “normal” behavior is assumed already. The fact that recent behavior is different does not affect anything.

This is analogous to a simple vol trade where recent realized vol is 15% whereas options are priced at 12%. You cannot make money by betting that realized vol will return to 12%, because the market already assumes so.

However you can certainly bet that the abnormal behavior will continue, by trading a risk reversal and rebalancing Vega and spot exposure daily.

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.