Option Trading by Euan Sinclair

Author:Euan Sinclair [Sinclair, Euan]
Language: eng
Format: epub
ISBN: 9780470642528
Publisher: Wiley
Published: 2010-07-13T05:00:00+00:00

The Raw and Scaled Implied Volatilities of the QQQQ Options as a TABLE 8.1 Function of the Out-of-the-Money Delta from the Morning of September 13, 2007

We have to be a little careful here to use call delta or put delta across the entire curve. If we choose to use the out-of-the-money options we will get into trouble around the at-the-moneys because the 50-delta call will not have the same strike as the 50-delta put, so we will have two possible implied volatilites for this part of the delta curve.

We parameterize the smile by the delta of the option, and then divide all of the volatilities in a given month by the at-the-money volatility of that month. This gives a curve that is remarkably constant across expirations. This has long been a trick market makers have used to compare volatilities. This is quite possibly the only reason it has any validity: another self-fulfilling prophecy. Table 8.1 shows this method using the example of the QQQQ options.

Note than in delta terms the curves are relatively constant across time even though in strike terms the shorter expirations have much steeper curves.

We see in Chapter 3 that call spreads cannot have negative values. In the limit of small strike differences, this can be written as(8.2)

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