2016/02/17 by Vikram Krishnamurthy, Krishnamurthy, Vikram, Elisabeth Leoff +4
Economics, Econometrics and Finance · #91B55 #91G70 #93E11 #Complex Systems and Time Series Analysis #Economic Policies and Impacts #FOS: Economics and business #Financial Risk and Volatility Modeling #Statistical Finance (q-fin.ST) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1602.05323
openalex publication_date 2016/02/17 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
Regime-switching models, in particular Hidden Markov Models (HMMs) where the\nswitching is driven by an unobservable Markov chain, are widely-used in\nfinancial applications, due to their tractability and good econometric\nproperties. In this work we consider HMMs in continuous time with both constant\nand switching volatility. In the continuous-time model with switching\nvolatility the underlying Markov chain could be observed due to this stochastic\nvolatility, and no estimation (filtering) of it is needed (in theory), while in\nthe discretized model or the model with constant volatility one has to filter\nfor the underlying Markov chain. The motivations for continuous-time models are\nexplicit computations in finance. To have a realistic model with unobservable\nMarkov chain in continuous time and good econometric properties we introduce a\nregime-switching model where the volatility depends on the filter for the\nunderlying chain and state the filtering equations. We prove an approximation\nresult for a fixed information filtration and further motivate the model by\nconsidering social learning arguments. We analyze its relation to the switching\nvolatility model and present a convergence result for the discretized model. We\nthen illustrate its econometric properties by considering numerical\nsimulations.\n