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Are there any empirically-proven methods/formulas for weighting IV surfaces, pricing a discount/premium in an option, and/or adjusting any of the 1st- or 2nd-order Greeks for the magnitude (volume or dollar-volume basis traded) of activity in each option contract for a market?

The various debates that can be found amongst traders, quants and others regarding how to model volatility surfaces and price an option appear undecided...at the very least, the several methods for pricing an option not only assume some modest-to-minimal skew in the returns of an underlying market price, and each option seems to be priced 'in a bubble' i.e. not accounting for the activity in other strikes/expirations. These may be consistent with an oversimplified volatility smile, and the No-arbitrage Theory.

I'm approaching this line of inquiry and discussion from a hobbyist, amateur perspective, so my apology in advance if the basis explained below for the question is out of sorts...

I'm looking for a sound method to account for implied sentiment due to the quantity/distribution/moneyness/etc of option contracts traded across the strike range for the nearest several expirations along the forward curve, and model the aggregate impact of this activity for its underlying instrument (e.g. weekly and monthly options on AAPL, monthly options on natural gas futures, etc.)

A few papers are available online which discuss the notions of accounting for option open interest distributions for equities as an implied leading indicator as expiration approaches: Trading on the Information Content of Open Interest - McGill University and also "The Dynamic Relationship between Volatility, Volume and Open Interest in CSI 300 Futures Market"

Also, a more direct pricing approach which focuses less on the comprehensive distribution on the activity, and moreso on the specific contract at hand by a discrete method is discussed in this paper: Demand-Based Option Pricing

I understand that a closed-form solution cannot be found, and defining some method as 'correct' is partially a matter of probability and confidence intervals for such conclusions...appropriateness of a solution/model is largely a function of what market 'type' is declared. Like Emanuel Derman wrote:

“Years ago, when I first became aware of the smile, we hoped to find the 'right' model, and when I met people from other trading firms I used to ask them which model they thought was correct. But now there is such a profusion of models that I have begun to ask more practical questions...There isn’t a uniformly good model. Since Black-Scholes is the market’s language for quoting options prices, local volatility is a natural way to quote forward volatility in terms of the values of portfolios of options spreads, just as forward rates are a natural way to think about the future interest rates. Which model is right depends on your market.”

Any commentary on first steps to approach these aspects of modeling market more precisely, as a whole?

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