2024/01/18 by Felix L. Wolf, Wolf, Felix L., Griselda Deelstra +3 · 1 citation
Economics, Econometrics and Finance · #91G20 91G30 #Complex Systems and Time Series Analysis #Computational Finance (q-fin.CP) #FOS: Economics and business #Pricing of Securities (q-fin.PR) #Risk Management (q-fin.RM) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2401.09955
openalex publication_date 2024/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.