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I am aware of the reasoning of quoting vanilla options as implied volatilities rather than dollar values. However, I would like to have a literature reference where this is explained, to quote / cite in a thesis. I have gone through all books that I have and searched the internet for quite some time but I was unable to find a citable source - which surprises me, since this is such a fundamental consideration.

I would be grateful if somebody could point me to a good book or paper that includes at least a paragraph on this.

Best regards

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  • $\begingroup$ I think Talebs Dynamic Hedging has something about it, it might be that it cites another article but I'm not sure. $\endgroup$
    – Bob Jansen ♦
    Commented Aug 18, 2015 at 20:08
  • $\begingroup$ well my my books concepts etc discusses the practice $\endgroup$
    – Mark Joshi
    Commented Aug 22, 2015 at 7:06

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I don't believe you will necessarily find a cite-able source as, I believe, this comes from a practical rather than theoretical motivation.

As you know option prices are a function of: future prices, discount rates and implied volatility, volatility surface skew and other supple/demand factors. So when you are trading these instruments, you need to understand how all of these factors are moving over the course of pricing, the option, getting quotes and confirming the trades. (Note: for some OTC options this can take several hours).

By far the most volatile component driving an options price on given day (assuming the option isn't expiring soon) is the futures prices. Given that the option's delta can be hedged out for little transaction cost, dealers prefer to quote in implied volatility as that is the second biggest driver of prices; it will also be somewhat stable over the course of pricing and confirming the trade.

The pricing risk associated with other factors such as discount-rate risk and some local spot-vol correlation risk are usually incorporated into the vol quote you are given. However there these effects on the prices are usually minimal over the course of an hour.

Different markets will agree on different transformations between implied vols and spot dollar prices. Some markets use Black-Scholes Formula, in others more complex formulas can be used such as Stochastic-Local Volatility.

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