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In recent studies the truncated Levy process (TLP) has been shown to be verypromising for the modeling of financial dynamics. In contrast to the Levyprocess, the TLP has finite moments and can account for both the previouslyobserved excess kurtosis at short timescales, along with the slow convergenceto Gaussian at longer timescales. I further test the truncated Levy paradigmusing high frequency data from the Australian All Ordinaries share marketindex. I then consider, for the early Levy dominated regime, the issue ofoption hedging for two different hedging strategies that are in some senseoptimal. These are compared with the usual delta hedging approach and found todiffer significantly. I also derive the natural generalization of theBlack-Scholes option pricing formula when the underlying security is modeled bya geometric TLP. This generalization would not be possible without thetruncation.

Financial Modeling and Option Theory with the Truncated Levy Process