arXiv
Open Access
2012
From characteristic functions to implied volatility expansions
Antoine Jacquier
Matthew Lorig
Abstrak
For any strictly positive martingale $S = \exp(X)$ for which $X$ has a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials in the log strike. We illustrate the versatility of our expansion by computing the approximate implied volatility smile in three well-known martingale models: one finite activity exponential Lévy model (Merton), one infinite activity exponential Lévy model (Variance Gamma), and one stochastic volatility model (Heston). Finally, we illustrate how our expansion can be used to perform a model-free calibration of the empirically observed implied volatility surface.
Penulis (2)
A
Antoine Jacquier
M
Matthew Lorig
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2012
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- arXiv
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- Open Access ✓