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Probability and Math Finance Seminar
Uwe Wystup, Frankfurt School of Finance and Management, Frankfurt, GermanyPricing of First Generation Exotics with the Vanna-Volga Method, pros and cons AbstractThe vanna-volga method, also called the "traders' rule of thumb" is an empirical procedure that can be used to infer an implied-volatility smile from three available quotes for a given maturity. It is based on the construction of locally replicating portfolios whose associated hedging costs are added to corresponding Black-Scholes 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. In fact, SuperDerivatives has implemented a type of this method in their pricing platform as one can read in the patent that SuperDerivatives has filed. 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 25 delta call and put; and the (vega-weighted) butterfly with 25 delta wings. The application of vanna-volga pricing allows us to derive implied volatilities for any option's delta, in particular for those outside the basic range set by the 25 delta put and call quotes. In the financial literature, the vanna-volga approach was introduced by Lipton and McGhee (2002) who compare different approaches to the pricing of double-no-touch options, and by Wystup (2003), who describes its application to the valuation of one-touch options. The vanna-volga procedure is reviewed in more detail and some important results concerning the tractability of the method and its robustness are derived by Castagna and Mercurio (2007) MONDAY, November 10, 2008 |