On options pricing under a quadratic stochastic process modulated GBM model

On options pricing under a quadratic stochastic process modulated GBM model


  • Taimun Qaisar, Youssef El-Khatib, Farrukh Mukhamedov, Qasem Al-Mdallal


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


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 in nitesimal generator is obtained, which allows numerical simulations of the non-Markovian and the stock-price processes to be conducted. Several illustrations are provided.


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How to Cite

On options pricing under a quadratic stochastic process modulated GBM model. (2023). Advances in the Theory of Nonlinear Analysis and Its Application, 7(5), 15-23. https://doi.org/10.17762/atnaa.v7.i5.322