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Multiscale exponential L�vy-type models

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  • Matthew Lorig
  • Oriol Lozano-Carbass�

Abstract

We consider the problem of valuing a European option written on an asset whose dynamics are described by an exponential L�vy-type model. In our framework, both the volatility and jump-intensity are allowed to vary stochastically in time through common driving factors-one fast-varying and one slow-varying. Using Fourier analysis we derive an explicit formula for the approximate price of any European-style derivative whose payoff has a generalized Fourier transform; in particular, this includes European calls and puts. From a theoretical perspective, our results extend the class of multiscale stochastic volatility models of Fouque et al. [ Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives , 2011] to models of the exponential L�vy type. From a financial perspective, the inclusion of jumps and stochastic volatility allow us to capture the term-structure of implied volatility, as demonstrated in a calibration to S&P500 options data.

Suggested Citation

  • Matthew Lorig & Oriol Lozano-Carbass�, 2015. "Multiscale exponential L�vy-type models," Quantitative Finance, Taylor & Francis Journals, vol. 15(1), pages 91-100, January.
    • Handle: RePEc:taf:quantf:v:15:y:2015:i:1:p:91-100
    DOI: 10.1080/14697688.2014.934712
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