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Consistent asset modelling with random coefficients and switches between regimes

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  • Felix L. Wolf
  • Griselda Deelstra
  • Lech A. Grzelak

Abstract

We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for different behaviours across various times or regimes. To establish our framework, we initially construct a model with random parameters, where the switching between regimes can be dictated either by random variables or deterministically. Such a model is highly interpretable. We further ensure mathematical consistency by demonstrating that the framework can be elegantly expressed through local volatility models taking the form of standard jump diffusions. Additionally, we consider a Markov-modulated approach for the switching between regimes characterised by random parameters. For all considered models, we derive characteristic functions, providing a versatile tool with wide-ranging applications. In a numerical experiment, we apply the framework to the financial problem of option pricing. The impact of parameter uncertainty is analysed in a two-regime model, where the asset process switches between periods of high and low volatility imbued with high and low uncertainty, respectively.

Suggested Citation

  • Felix L. Wolf & Griselda Deelstra & Lech A. Grzelak, 2024. "Consistent asset modelling with random coefficients and switches between regimes," Papers 2401.09955, arXiv.org, revised Apr 2024.
  • Handle: RePEc:arx:papers:2401.09955
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    References listed on IDEAS

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    1. Lech A. Grzelak, 2022. "Randomization of Short-Rate Models, Analytic Pricing and Flexibility in Controlling Implied Volatilities," Papers 2211.05014, arXiv.org.
    2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
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