Financial markets are complex adaptive systems characterized by collective behavior and abrupt regime shifts, particularly during crises. This paper studies time-varying dependencies in Nordic equity markets and examines whether correlation-eigenstructure dynamics can be exploited for regime-aware portfolio construction. Using two decades of daily data for the OMXS30, OMXC20, and OMXH25 universes, pronounced regime dependence in rolling correlation matrices is documented: crisis episodes are characterized by sharp increases in the leading eigenvalue and counter-cyclical behavior in the second eigenvalue. Eigenportfolio regressions further support a market-factor interpretation of the dominant eigenmode. Building on these findings, an adaptive portfolio allocation framework is proposed, combining correlation-matrix cleaning, an eigenvalue-ratio crisis indicator and long-only minimum-variance optimization with constraints that bound exposures to dominant eigenmodes. Backtesting results indicate improved downside protection and risk-adjusted performance during stress regimes, while remaining competitive with state-of-the-art benchmarks in tranquil periods.
This paper develops a model for option market making in which the hedging activity of the market maker generates price impact on the underlying asset. The option order flow is modeled by Cox processes, with intensities depending on the state of the underlying and on the market maker's quoted prices. The resulting dynamics combine stochastic option demand with both permanent and transient impact on the underlying, leading to a coupled evolution of inventory and price. We first study market manipulation and arbitrage phenomena that may arise from the feedback between option trading and underlying impact. We then establish the well-posedness of the mixed control problem, which involves continuous quoting decisions and impulsive hedging actions. Finally, we implement a numerical method based on policy optimization to approximate optimal strategies and illustrate the interplay between option market liquidity, inventory risk, and underlying impact.
We propose a numerical method for the valuation of European-style options under two-asset infinite-activity exponential Lévy models. Our method extends the effective approach developed by Wang, Wan Forsyth (2007) for the 1-dimensional case to the 2-dimensional setting and is applicable for general Lévy measures under mild assumptions. A tailored discretization of the non-local integral term is developed, which can be efficiently evaluated by means of the fast Fourier transform. For the temporal discretization, the semi-Lagrangian theta-method is employed in a convenient splitting fashion, where the diffusion term is treated implicitly and the integral term is handled explicitly by a fixed-point iteration. Numerical experiments for put-on-the-average options under Normal Tempered Stable dynamics reveal favourable second-order convergence of our method whenever the exponential Lévy process has finite-variation.
