Volatility

Putting the smile back on the face of derivatives

Cross-asset quadratic Gaussian models have been limited in the scale of their implementation by the difficulty in ensuring the correct drift conditions to omit arbitrage. Here, Paul McCloud shows how to exploit the symmetries of the functional form to…

Pricing with a smile

In the January 1994 issue of Risk, Bruno Dupire showed how the Black-Scholes model can be extended to make it compatible with observed market volatility smiles, allowing consistent pricing and hedging of exotic options

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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