The vanna-volga method for implied volatilities

The vanna-volga method is a popular approach for constructing implied-volatility curves in the options market. In this article, Antonio Castagna and Fabio Mercurio give it both theoretical and practical support by showing its tractability and robustness

The vanna-volga (VV) method is an empirical procedure that can be used to infer an implied-volatility smile from three available quotes for a given maturity.1 It is based on the construction of locally replicating portfolios whose associated hedging costs are added to corresponding Black-Scholes (BS) prices to produce smile-consistent values. Besides being intuitive and easy to implement, this procedure has a clear financial interpretation, which further supports its use in practice.

The VV method is commonly used in foreign-exchange options markets, where three main volatility quotes are typically available for a given market maturity: the delta-neutral straddle, referred to as at-the-money (ATM); the risk reversal for 25D call and put; and the (vega-weighted) butterfly with 25D wings.2 The application of VV allows us to derive implied volatilities for any option's delta, in particular for those outside the basic range set by the 25D put and call quotes.

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