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Time-Changed Levy Processes and Option Pricing

Author

Listed:
  • Peter Carr

    (New York University)

  • Liuren Wu

    (Fordham University)

Abstract

As is well known, the classic Black­Scholes option pricing model assumes that returns follow Brownian motion. It is widely recognized that return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to non­normal return innovations. Second, return volatilities vary stochastically over time. Third, returns and their volatilities are correlated, often negatively for equities. We propose that time­changed Levy processes be used to simultaneously address these three facets of the underlying asset return process. We show that our framework encompasses almost all of the models proposed in the option pricing literature. Despite the generality of our approach, we show that it is straightforward to select and test a particular option pricing model through the use of characteristic function technology.

Suggested Citation

  • Peter Carr & Liuren Wu, 2002. "Time-Changed Levy Processes and Option Pricing," Finance 0207011, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpfi:0207011
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    References listed on IDEAS

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    More about this item

    Keywords

    random time change; Levy processes; characteristic functions; option pricing; exponen­tial martingales; measure change;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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