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

  • $\begingroup$ Just to clarify, the example Natenberg gives is a calendar spread, but the answer you seek is for a non-calendar spread: all expiration dates are the same. Is that correct? Actually, the answer to this is quite simple if you accept Black-Scholes: compute the price of the spread as a function of volatility (using Black-Scholes) and then find the volatility(s) that mach the actual price. $\endgroup$ – user59 Dec 27 '16 at 16:39

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