On options pricing under a quadratic stochastic process modulated GBM model

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This paper deals with the European option-valuation problem under a prediction model for the underlying asset prices with an external impact. We suggest an alternative model for risky asset prices in which the parameters are dependent on a non-Markovian process. This generalizes the regime-switching models with continuous-time Markov-chain processes. A notable problem of this model is that the process embedded in the parameter of the stock price is non-Markovian; in addition, the market is incomplete. The change from the historical probability to a risk-neutral one is investigated, and the set of equivalent martingale measures is determined. In addition, an infinitesimal generator is obtained, which allows numerical simulations of the non-Markovian and the stock-price processes to be conducted. Several illustrations are provided.

Original languageEnglish
Pages (from-to)15-23
Number of pages9
JournalAdvances in the Theory of Nonlinear Analysis and its Applications
Issue number5
Publication statusPublished - 2023


  • Quadratic stochastic process Brownian motion Non-Markov Options pricing Regime switching models

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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