Irony, according to the Oxford English Dictionary, is (a) a figure of speech in which the intended meaning is the opposite of that expressed by the words used (b) a condition of affairs or events of a character opposite to what was, or might naturally be, expected (In French, ironie du sort). In the following lines, I will propose a rereading of quantitative finance where irony, as opposed to theory, emerges as a leitmotiv, perhaps even a main guide. Variance swaps will provide me with a literal rehearsal of this ironic point, as I will show that the element of irony is inscribed in the movement motivating their existence, indeed in their very contractual terms.
The irony in quantitative finance, or specifically, in derivative pricing theory, is captured by the following observation. While the typical derivative paper is expressed in words and formulas aiming at the theoretical value of the derivative, it is really intended for derivative trading, which is the domain farthest away from theory. This is irony in the first sense. And while rational option pricing, as epitomized by the work of Black, Scholes and Merton, has triggered the explosion of options markets, the ensuing liquidity of option prices has turned volatility into a traded commodity thereby contradicting the crucial theoretical assumption of constant volatility. This is irony in the second sense.
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