Local Variance Gamma - (EXTRA SEMINAR)
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Wed, 17/06/2009 12:00 |
Peter Carr (Bloomberg - Quantitative Financial Research) |
Nomura Seminar  |
Oxford-Man Institute |
| In some options markets (eg. commodities), options are listed with only a single maturity for each underlying. In others, (eg. equities, currencies), options are listed with multiple maturities. In this paper, we assume that the risk-neutral process for the underlying futures price is a pure jump Markov martingale and that European option prices are given at a continuum of strikes and at one or more maturities. We show how to construct a time-homogeneous process which meets a single smile and a piecewise time-homogeneous process, which can meet multiple smiles. We also show that our construction leads to partial differential difference equations (PDDE's), which permit both explicit calibration and fast numerical valuation | |||