A few years ago in a workshop in Asia on Volatility arbitrage two very high profile speakers enlightened its audience with how exotic and funky options can be used to create volatility 'invariant' (forgive the mathematical verbiage) structures. The essence of their talk was that one can use exploding options, barrier options to synthesize volatility invariant trades, arbitrage between equity and credit markets (via CDS) to synthesize trades that will be insensitive to volatility, and so on and so forth.

There was a wretched soul in that august gathering of delegates who had in his past life lost a huge amount of money on volatility trades. He was hunched, overweight and appeared disoriented, lonely and thoroughly disturbed. Why would someone with such disposition come to attend such a high profile and elite workshop was beyond anyone's imagination. He definitely seemed to be the one who might have paid from his own pocket to attend this workshop.

Half way through the post lunch session of the workshop the speaker, who was a training manager with a top tier investment bank (and who knew all about volatility trading because he had a Ph.D. in Economics from God's own University and sat amongst the traders on the trading floor) pointed to the Hunchback in the last row and said:"perhaps, Mr. R finds all this very trivial! K. and then:"or maybe the lunch too good"? All the bodies in the blue and grey pin striped suits laughed in unison.

The hunchback who was now roused from his state of half-sleep by this embarrassing laughter said:"no Mr. J, I am ok, Indians are used to good food and.."after fifteen seconds of silence:"and the only piece of trivia that I find disturbing is that by very definition of the Ito process volatility invariance should imply time invariance which means that by construction a volatility insensitive structure should (mathematically speaking) be duration insensitive; yet, we hardly use volatility hedging as a proxy for duration hedging. I don't understand why the theory breaks down in practice."

"Secondly, Mr. J, I am totally confused by the term Volatility Insensitivity. I mean, I have some idea about invariance transformations but in a trading context, what exactly is volatility insensitivity? And why would one need to trade in exotic options to create volatility insensitive structures, when vanilla options and derivatives can suffice for this purpose"

The hunchback, like hunchbacks of all epochs, believed in the simplicity of the universe and was therefore not to be taken seriously. No one ever recalls seeing the hunchback again in such workshops.

First piece of trivia:

By Ito process the value of any derivatives instrument is invariant to the

transformation of the nature

The symmetry however can break down in the presence of dividends and interest rates. If the dividend yield and/or the interest rates are high enough then the correction needs to be made by using strike price of options that are close the future value of the underlying. This has great implications in the fixed income markets.

Second piece of trivia

Volatility insensitivity is not a trivial concept. In fact, in our opinion, it is a very sophisticated and fundamental concept of derivatives pricing and trading. It does mean vega neutrality but over a range of volatility levels. Volatility sensitivity means that rather than looking at the vega (of a derivative product) at a specific volatility level, traders (buyers and sellers) use the price variation over a wide variation of volatility range (say, from 5% to 60%) to quantify vega.

To create volatility insensitive structures one needn't resort to exotic or funky products. Using vanilla options one can create volatility insensitive structures. Take the case of a simple call spread. If you sell a 110 call and buy a 100 call you create a call spread. Since both 110 call and the 100 call will have its own volatility dependent vega, if we multiply the long option position with its corresponding vega and add the short option position with its corresponding vega we will get the overall portfolio vega. And we want the overall portfolio vega to be zero then

Which implies that for the structure to be volatility insensitive we need to buy the options in a way such that:

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