Extrapolating Bid Implied Volatility Beyond Observed Strikes

Summary

The document asks how to extend a concave shape in bid implied volatility data to strikes beyond those observed. It also asks whether bid volatility should approach zero as the strike approaches zero or infinity. These are posed as questions; the document gives no answer or supporting market data.

The author describes trying a polynomial surface with terms for strike, time, squared strike, and a strike-time interaction. They are unsure whether this approximation is accurate. No fitting procedure, extrapolation method, arbitrage constraints, or validation evidence is provided, so the proposed polynomial should be treated as an unvalidated idea rather than a recommendation. The note identifies a modeling problem but does not establish general boundary behavior for bid volatility.

Key ideas

• The note asks how to extrapolate a concave bid volatility shape beyond observed strikes.
• It questions whether implied volatility tends to zero at extremely low or high strikes.
• A polynomial involving strike and time is proposed, but its accuracy is not assessed.

Tags

# bid volatiliy interpolation


# bid volatiliy interpolation












I had a bid volatility data that had a concave shape. my question is how can I extrapolate for the the extreme strikes, and does the bid volatility goes to zero when strike->0 and strike-> infinity. I tried to approximate the smile by the following polynomial $(k,t)\rightarrow a_1+a_2k+a_3k^2+a_4t+a_5kt$ but I do not know if this approximation is accurate.

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.