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Local Time Applications in Option Pricing and Replication

Article Quant Q&A · Author: TheBridge
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Summary

The document identifies two uses of local time in option theory. One is a concise route to deriving Dupire’s local volatility formula. The other is demonstrating a limitation of a naive replication strategy for a call payoff: placing conditional orders around the strike in a Black–Scholes setting does not achieve perfect replication. These examples connect a stochastic process concept to both volatility modeling and hedging behavior.

The author asks for further applications and references but supplies no derivations, proofs, or empirical evidence. The claims are presented as context for the question, not developed into a tutorial, and the document does not spell out the assumptions behind the replication result. Its scope is therefore an introduction to potential applications rather than a complete account of local time in finance. Any extension to other pricing or hedging settings would require checking the relevant model assumptions and cited sources.

Key ideas

  • Local time can provide a route to deriving Dupire’s local volatility formula.
  • A naive conditional-order strategy around the strike may fail to replicate a call payoff perfectly in a Black–Scholes setting.
  • The document asks for additional financial applications and references but provides no derivations.

Tags

OptionsDerivatives pricingVolatilityStatistics
Full text
# Use of Local Times in Option Pricing


# Use of Local Times in Option Pricing












I know two applications of local time in option pricing theory. First, it allows a derivation of Dupire's formula on local volatility in a neat way (i.e. without resorting to differential operator theory which I'm not really acquainted with).

Second, it can be used to show that you can't perfectly replicate (for example) a call option final payoff by the naive strategy of letting conditional orders on the market consistent with the strike in a Black-Scholes context.

Does anyone is aware of other applications of local times in finance, answers with references would be most appreciated ?

Best regards

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.