It is a valuable collection of key ideas concerning the FX smile surface and hedging of first generation exotics. I am very please Antonio took time to share his intuitive insights. Strongly recommended. Attention is given to a wide range of topics, ranging a wide spectrum between theory and practice, from market quoting conventions to volatility surfaces, change of measure techniques, dynamic arbitrage-free models, hedging and risk analysis. Among the several techniques presented to deal with volatility smile consistent pricing, I am glad room has been given to the mixture dynamics, one of the few tractable approaches where the Markovian projection is explicit and realized in the mixture diffusion and the uncertain volatility models, with striking results in the correlation between volatility and underlying in the projected diffusion version.
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The Volatility Surface 4. This is a fundamental building block of market-making activity and risk management, so we devote an in-depth analysis to the building of a consistent volatility surface. Volatility surface. The volatility surface, or matrix we will use the two terms without any distinction , is the map of the implied volatilities quoted by the market for plain vanilla options struck at different levels and expiring at different dates.
The volatility smile refers to a single expiry, whereas the volatility surface refers to a set of maturities. In practice, the matrix is built according to three main conventions, each prevailing as a standard in the market according to the traded underlying: the sticky strike, the sticky Delta, and finally the sticky absolute. These are simple rules used to conveniently quote and trade options written on different assets and, as such, are not intended to model the evolution of the volatility surface.
Definition 4. Sticky strike rule. When the sticky strike rule is effective, implied volatilities are mapped, for each expiry, with respect to the strike prices; this is the rule usually adopted in official markets e.
FX Options and Smile Risk (eBook, PDF)
FX Options and Smile Risk by Antonio Castagna
FX Options and Smile Risk