Regime-Switching Models

Optimal mean-variance portfolio selection under regime-switching-induced stock price shocks ArXiv ID: 2507.19824 “View on arXiv” Authors: Xiaomin Shi, Zuo Quan Xu Abstract In this paper, we investigate mean-variance (MV) portfolio selection problems with jumps in a regime-switching financial model. The novelty of our approach lies in allowing not only the market parameters – such as the interest rate, appreciation rate, volatility, and jump intensity – to depend on the market regime, but also in permitting stock prices to experience jumps when the market regime switches, in addition to the usual micro-level jumps. This modeling choice is motivated by empirical observations that stock prices often exhibit sharp declines when the market shifts from a bullish'' to a bearish’’ regime, and vice versa. By employing the completion-of-squares technique, we derive the optimal portfolio strategy and the efficient frontier, both of which are characterized by three systems of multi-dimensional ordinary differential equations (ODEs). Among these, two systems are linear, while the first one is an $\ell$-dimensional, fully coupled, and highly nonlinear Riccati equation. In the absence of regime-switching-induced stock price shocks, these systems reduce to simple linear ODEs. Thus, the introduction of regime-switching-induced stock price shocks adds significant complexity and challenges to our model. Additionally, we explore the MV problem under a no-shorting constraint. In this case, the corresponding Riccati equation becomes a $2\ell$-dimensional, fully coupled, nonlinear ODE, for which we establish solvability. The solution is then used to explicitly express the optimal portfolio and the efficient frontier. ...

European Option Pricing in Regime Switching Framework via Physics-Informed Residual Learning ArXiv ID: 2410.10474 “View on arXiv” Authors: Unknown Abstract In this article, we employ physics-informed residual learning (PIRL) and propose a pricing method for European options under a regime-switching framework, where closed-form solutions are not available. We demonstrate that the proposed approach serves an efficient alternative to competing pricing techniques for regime-switching models in the literature. Specifically, we demonstrate that PIRLs eliminate the need for retraining and become nearly instantaneous once trained, thus, offering an efficient and flexible tool for pricing options across a broad range of specifications and parameters. ...

Estimation of domain truncation error for a system of PDEs arising in option pricing ArXiv ID: 2401.15570 “View on arXiv” Authors: Unknown Abstract In this paper, a multidimensional system of parabolic partial differential equations arising in European option pricing under a regime-switching market model is studied in details. For solving that numerically, one must truncate the domain and impose an artificial boundary data. By deriving an estimate of the domain truncation error at all the points in the truncated domain, we extend some results in the literature those deal with option pricing equation under constant regime case only. We differ from the existing approach to obtain the error estimate that is sharper in certain region of the domain. Hence, the minimum of proposed and existing gives a strictly sharper estimate. A comprehensive comparison with the existing literature is carried out by considering some numerical examples. Those examples confirm that the improvement in the error estimates is significant. ...

Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in Lévy models ArXiv ID: 2312.03915 “View on arXiv” Authors: Unknown Abstract We analyze the qualitative differences between prices of double barrier no-touch options in the Heston model and pure jump KoBoL model calibrated to the same set of the empirical data, and discuss the potential for arbitrage opportunities if the correct model is a pure jump model. We explain and demonstrate with numerical examples that accurate and fast calculations of prices of double barrier options in jump models are extremely difficult using the numerical methods available in the literature. We develop a new efficient method (GWR-SINH method) based of the Gaver-Wynn-Rho acceleration applied to the Bromwich integral; the SINH-acceleration and simplified trapezoid rule are used to evaluate perpetual double barrier options for each value of the spectral parameter in GWR-algorithm. The program in Matlab running on a Mac with moderate characteristics achieves the precision of the order of E-5 and better in several several dozen of milliseconds; the precision E-07 is achievable in about 0.1 sec. We outline the extension of GWR-SINH method to regime-switching models and models with stochastic parameters and stochastic interest rates. ...