Option pricing under risk-exogenous measures in a fractional jump diffusion market

risk-exogenous measure; fractional jump-diffusion model; fractional Girsanov theorem; option pricing

Authors

  • Ru Zhou Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, P R China
  • Jun Zhao Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, P R China
  • Peibiao Zhao Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, P R China
August 27, 2018

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In this paper we introduce the so-called risk-exogenous measure and study the price of exogenous risks based on a fractional jump-diffusion financial market model. The option price equation indicates that the evaluation of risk-exogenous is consistent with that of the classical neutral risk. An empirical example shows that the risk-exogenous valuation is more suitable for practical financial markets by comparing the error between actual price of stocks and the price computed from BS formula and the option price equation under risk-exogenous measures respectively.