I've been curious why vanilla options are quoted (and traded) in terms of volatility. Considering that every financial institution has its own options pricing model, volatility as an input would cause different prices for the same option. It would be obvious if the contracts were standardized and the models were explicitly specified. This, however, is not the case because the FX products are quoted in the same way, and the FX markets are OTCs.

Could someone shed some light on this?



You kind of answered the question yourself. Precisely because different market participants use different inputs to their pricing models, it is much easier to quote one single input (implied vols) than the output of 5 different inputs (BS option price). What is important is that you clearly differentiate between quoting and agreeing on the trade vs. the final settlement price. The process generally goes like this:

  • You ask interdealer-brokers (if you are a market maker) or sell-side desks (in case you are a price taker such as prop side) for a quote, you generally are given an implied vol quote.

  • You then compare those and settle on who you want to deal with.

  • Only then when you agreed on the trade with the counter party both of you then look at the "fine print", meaning you settle on the precise price of the option. Not seldom it happens that the counter party sends you a confirmation and you figure out that the stated price is not what you see in your system, so you call back and figure out what caused the discrepancy. Sometimes it is different dividend curves (in the case of single stock options), sometimes different settlement days possibly due to bank holidays or misunderstanding of settlement conventions, or anything else, but the implied vol quote is agreed and I have hardly ever heard that the vol quote is later on adjusted. Sometimes when an implied vol quote sounds and looks too "juicy" then it probably was an honest mistake by the counter party and if you intend to deal with the same party in the future then you would "let them out" as a courtesy. But in border line cases, I sometimes insisted on the trade, pointing to the fact that generally the "done" point in time when implied vols are agreed then that is the equivalent of the handshake or signature on a contract.

Here couple additional thoughts:

  • Most OTC options, not all but most are quoted in implied volatility terms. I can say so with confidence about single stock options, equity index options, caps, floors, swaptions. I am still flabbergasted about why some seasoned quants disagree with this fact. Now, again the final price is in currency terms (unless you create a new coin called "implied vol") but I find this just a trivial distraction from the actual fact that what matters when you trade options is the implied volatility at which those options are quoted.

  • Make sure you understand the local market habits and terms. Often single stock options and even index options are understood to be traded with the delta, meaning, as part of the deal you exchange the delta in order to have the option initially delta hedged. That is why aside the implied vol quote agreement often the delta level is agreed on as well at the time of agreeing on the quote. In that way both counter parties know exactly at which spot level they are delta hedged, even though the deal is not yet settled.

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    $\begingroup$ Fascinating insight into options trading. Presumably if you calculate a price using your favoured model, you could work out what implied vol was needed in the common market's model to get you the same price and quote that? $\endgroup$ – Phil H Feb 21 '13 at 8:14
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    $\begingroup$ For quoting purposes, pretty much everyone is using the same model, thus, as long as you input identical parameters everyone should arrive at an identical price. But I cannot stress enough of how little importance the price is. Its just the currency which you use to pay for the volatility you buy and sell in the market, never the other way around. $\endgroup$ – Matthias Wolf Feb 21 '13 at 8:32
  • $\begingroup$ glad it helped ;-) $\endgroup$ – Matthias Wolf Feb 22 '13 at 13:19
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    $\begingroup$ In addition to OTC options, there exist a few other markets where quoting conventions are in terms of a (standard) model rather than on true price. High-grade corporate CDS and bonds are quoted in spread terms, CDX are quoted in bond-like price terms, tranche protection in implied correlation terms, and convertible bonds in price/delta/underlying terms. And for exchange-traded contracts, we have eurodollar futures which are quoted as an affine transformation of LIBOR. $\endgroup$ – Brian B Feb 24 '13 at 16:59
  • $\begingroup$ Good points. It highlights the distinction between quoting assets and the settlement of a trade in such asset. $\endgroup$ – Matthias Wolf Feb 25 '13 at 0:07

You are referring to implied volatility, more specifically, Black-Scholes implied volatility.

The Black-Scholes framework is, even though its extremely simplifying, common knowledge and does not depend on any other than generally known assumptions. Therefore option prices can be quoted in terms of their BS-IV, which is sometimes more convenient. So to answer your question, the model is actually specified to be BS. For other products, this would be to complicated, so it is rarely used.

Furthermore, many interpolation procedures are performed on BS-IV surfaces due to numerical biases.

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  • $\begingroup$ I really doubt that market participants use the BS model only because of its unrealistic assumptions. $\endgroup$ – ryzhiy Feb 22 '13 at 12:58
  • $\begingroup$ Sorry, that was not my point. Freddy gave a much better explanation, its about simplifying the set of parameters you are agreeing upon which reduces complexity. The BS-Model is common knowledge, and everybody knows how it works. You can simply translate back and forth between prices and BS-IVs and if you want to use your own model, just use that. Your specific assumptions you mention (proprietary valuation models) do not matter here. $\endgroup$ – zuiqo Feb 22 '13 at 15:05

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