Why Same-Expiry Option Spreads Lack a Single Implied Volatility

Summary

The document asks whether an equity option spread whose legs share an expiration can be represented by one exact volatility. It contrasts this with a calendar spread discussion in an options text, where a forward volatility is found by adjusting volatility until a model price matches the spread price. The source also presents a first-order approximation based on the spread's price and vega differences.

The question highlights a distinction between approximating volatility exposure and defining a spread-level implied volatility. It does not provide an answer, market data, or a proposed calculation for same-expiry spreads, so no exact method or conclusion can be drawn from the material itself. Any single volatility measure would need a specified pricing model, a target valuation convention, and a clear treatment of the individual legs. The described approximation is presented in the context of a calendar spread, and the document does not establish that it applies unchanged to spreads with a common expiry.

Key ideas

• The document asks how to summarize the volatility of a same-expiry equity option spread.
• It contrasts the question with a forward volatility calculation described for a calendar spread.
• A price-to-vega ratio is cited as an approximation in the calendar-spread discussion.
• No answer or exact method for same-expiry spreads is provided.

Tags

# How to calculate the volatility of a equity option spread


# How to calculate the volatility of a equity option spread












I would like to calculate the volatility of an equity option spread with all legs having the same expiration.

Reading Option Volatility and Pricing 2nd Edition by Natenberg, Chapter 20, section Forward Volatility he writes about calculating the volatility for a calendar spread:

> We need to reduce the volatility until we find the single volatility that will cause the spread to be worth 1.49. Using a computer, we find that the February/March calendar spread has an implied volatility of 25.94 percent.

He proceeds to give instructions for an approximation:

$ \frac{O_{2} - O_{1}}{V_{2} - V_{1}} $

with $O_{2} - O_{1}$ being the price of the spread and $V_{2} - V_{1}$ being the vega of the spread

How can one combine the volatilities of a spread, specifically a spread where all legs have the same expiration, into a single exact volatility quantity?

Many thanks

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