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A decomposition formula for fractional Heston jump diffusion models

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  • Marc Lagunas-Merino
  • Salvador Ortiz-Latorre

Abstract

We present an option pricing formula for European options in a stochastic volatility model. In particular, the volatility process is defined using a fractional integral of a diffusion process and both the stock price and the volatility processes have jumps in order to capture the market effect known as leverage effect. We show how to compute a martingale representation for the volatility process. Finally, using It\^o calculus for processes with discontinuous trajectories, we develop a first order approximation formula for option prices. There are two main advantages in the usage of such approximating formulas to traditional pricing methods. First, to improve computational effciency, and second, to have a deeper understanding of the option price changes in terms of changes in the model parameters.

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  • Marc Lagunas-Merino & Salvador Ortiz-Latorre, 2020. "A decomposition formula for fractional Heston jump diffusion models," Papers 2007.14328, arXiv.org.
    • Handle: RePEc:arx:papers:2007.14328
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    References listed on IDEAS

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