Put-call symmetry: extensions and applications. (English) Zbl 1184.91198
Classic put-call symmetry relates the prices of puts and calls at strikes on opposite sides of the forward price. This paper extends put-call symmetry in several directions. Relaxing the assumptions, the authors generalize to unified local/stochastic volatility models and time-changed Lévy processes, under a symmetry condition. They establish necessary and sufficient conditions for symmetry to hold. When symmetry does not hold, they find techniques which map the pricing and hedging results for symmetric processes into the corresponding relationships for asymmetric processes. The authors view these results as part of a broad program which aims to use European options, whose values are determined by marginal distributions, to extract information about path-dependent risks (including barrier-contingent payoffs) and to hedge those risks robustly.
Reviewer: Nikolaos Halidias (Athens)
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 60H20 | Stochastic integral equations |
Keywords:
put-call symmetry; volatility smile; local volatility; stochastic volatility; time-changed Lévy process; barrier option; semistatic hedgingReferences:
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