Volatility

Smiling at convexity

The price of a constant maturity swap (CMS)-based derivative is largely determined by the value of swaption volatilities at extreme strikes. Fabio Mercurio and Andrea Pallavicini propose a simple procedure for stripping consistently implied volatilities…

Exotic spectra

Eigenfunction expansions can also be applied to finance. The method is particularly suited to barrier and Asian options, with convergence properties that compare favourably with Monte Carlo.

Pricing with a smile

Bruno Dupire shows how the Black-Scholes model can be extended tomake it compatible with observed market volatility smiles, allowingconsistent pricing and hedging of exotic options

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