The paper extends the Heston model to include regime switching volatility.
problem Real-world stock volatility is not constant.
method Integrates regime switching into a stochastic volatility model.
result Locally risk-minimizing option pricing is derived for the extended model.
Regime switching volatility models provide a tractable method of modelling stochastic volatility. Currently the most popular method of regime switching calibration is the Hamilton filter. We propose using the Baum-Welch algorithm, an established technique from Engineering, to calibrate regime switching models instead. …
The study extends asset pricing models to include time-dependent volatility and age-dependent regime switching.
problem Asset pricing in a market with time-varying interest rates and volatilities.
method Extension of Markov-modulated models to semi-Markov processes with age-dependent and time-dependent volatility.
result Option pricing in the extended model is equivalent to solving an integral equation.
In this paper, we consider the problem of pricing discretely-sampled variance swaps based on a hybrid model of stochastic volatility and stochastic interest rate with regime-switching. Our modelling framework extends the Heston stochastic volatility model by including the CIR stochastic interest rate and model paramete…
Study optimal asset liquidation under uncertain drift and volatility changes.
problem Optimal liquidation of assets with unknown drift and stochastic volatility.
method Modelled as a four-dimensional optimal stopping problem, solved using filtering theory and approximating sequences of three-dimensional problems.
result Determined optimal liquidation strategy and structural properties.
Study improves S&P 500 volatility forecasting through regime-switching methods.
problem Accurate prediction of S&P 500 volatility for risk management and investment.
method Regime-switching methods including soft Markov switching, spectral clustering, and coefficient-based clustering.
result Coefficient-based clustering algorithm outperformed other models during all time periods.
Optimizes dividend payouts with fixed costs and regime switching.
problem Maximizing dividends with fixed transaction costs and regime switching.
method Identifies optimal dividend strategy as a two-barrier impulsive strategy.
result Explicit determination of optimal strategy for various drift and volatility scenarios.
The paper optimizes portfolios using a new GARCH model with regime switching and tempered stable innovations.
problem Mitigating left tail risk in multi-asset portfolios.
method Proposes a Markov regime-switching GARCH model with multivariate normal tempered stable innovation (MRS-MNTS-GARCH) for portfolio optimization.
result Optimal portfolios with tail risk measures outperform standard deviation-based portfolios and equally weighted portfolios in various performance metrics.
This paper compares hedging strategies for pegged FX markets using a RS model.
problem Hedging performance in pegged foreign exchange markets.
method Regime switching model, Fourier approach for calibration, exact and approximated delta hedging.
result Approximated RS delta hedge is a viable alternative to the exact RS delta hedge and significantly faster.
Developed a method to detect jumps and estimate volatility in financial data.
problem Identifying jumps in financial time series data.
method Threshold method for jump detection and volatility estimation.
result Unprecedented accuracy in volatility estimation across various parameter values.
Volatility modelling has become a significant area of research within Financial Mathematics. Wiener process driven stochastic volatility models have become popular due their consistency with theoretical arguments and empirical observations. However such models lack the ability to take into account long term and fundame…
We pick up the regime switching model for asset returns introduced by Rogers and Zhang. The calibration involves various markets including implied volatility in order to gain additional predictive power. We focus on the calculation of risk measures by Fourier methods that have successfully been applied to option pricin…
The paper addresses numerical integration issues in SV models, proposing a fast regime switching algorithm.
problem Numerical integration challenges in SV models, especially with high precision and low computational time.
method Proposes a fast regime switching algorithm to determine when higher precision arithmetic is needed.
result Shows that numerical quadratures need to be carefully chosen based on model parameters and parameter values.
Quantum algorithms for financial derivatives and credit risk.
problem Estimating credit risk and option pricing in realistic financial models.
method Developed a regime switching volatility model for financial markets, using a Markov chain to determine volatility parameters.
result Quantum algorithms can be applied to realistic financial models, bringing quantum computing closer to practical applications.
The paper develops methods to price derivatives in a time-varying, age-dependent market.
problem Pricing derivatives in a market with time-inhomogeneous volatility and age-dependent processes.
method Geometric Brownian motion model with time-varying volatility and age-dependent semi-Markov processes. Solves a non-local PDE and integral equation.
result Explicit expressions for derivative prices and hedging strategies are derived.
Regime-switching models, in particular Hidden Markov Models (HMMs) where the switching is driven by an unobservable Markov chain, are widely-used in financial applications, due to their tractability and good econometric properties. In this work we consider HMMs in continuous time with both constant and switching volati…
Efficient method for lookback option pricing under Markov models.
problem Pricing lookback options under Markov models.
method Model-free representations combined with numerical quadrature and Markov chain approximation.
result Efficient method applicable to various Markov models.
The Financial Chaos Index models stock market volatility across three regimes based on mutual price fluctuations.
problem Capturing regime-dependent volatility in stock markets.
method Developed a regime-switching framework using the Financial Chaos Index (FCIX) and elastic net regression.
result Identified three market regimes: low-chaos, intermediate-chaos, and high-chaos, each with distinct volatility characteristics.
For nearly every major stock market there exist equity and implied volatility indices. These play important roles within finance: be it as a benchmark, a measure of general uncertainty or a way of investing or hedging. It is well known in the academic literature, that correlations and higher moments between different i…
The article detects market regimes from covariance matrices using VLSTAR and clustering models.
problem Market regime switching is hard to detect due to time-varying correlation coefficients.
method The article applies VLSTAR and unsupervised hierarchical clustering on monthly realized covariance matrices.
result VLSTAR outperforms clustering in detecting market regimes.
This paper studies the pricing of European-style Asian options when the price dynamics of the underlying risky asset are assumed to follow a Markov- modulated geometric Brownian motion; that is, the appreciation rate and the volatility of the underlying risky asset depend on unobservable states of the economy described…
A hybrid framework for American option pricing under time-varying rough volatility.
problem Pricing American options under time-varying rough volatility.
method Signature method combined with gradient-boosted ensemble for Hurst parameter estimation, regime switch, and Random Fourier Features for acceleration.
result The proposed hybrid framework improves performance over fixed-roughness baselines and reduces duality gaps in some regimes.
In order to obtain a reasonable and reliable forecast method for crude oil price volatility, this paper evaluates the forecast performance of single-regime GARCH models (including the standard linear GARCH model and the nonlinear GJR-GARCH and EGARCH models) and the two-regime Markov Regime Switching GARCH (MRS-GARCH) …
Paper extends Lévy models with memory to better price FX double barrier options.
problem Efficiently pricing double barrier options in complex FX models.
method Introduces regime-switching Lévy models with memory and a modified numerical method.
result New models and method improve accuracy of option pricing.
This paper investigates the pricing of European-style lookback options when the price dynamics of the underlying risky asset are assumed to follow a Markov-modulated Geo-metric Brownian motion; that is, the appreciation rate and the volatility of the underlying risky asset depend on unobservable states of the economy d…
Novel method recovers market regime changes from option prices.
problem Recovering market regime changes from option prices.
method Assumed Markov regime switching, computed implied volatility, validated recovery of regime changes.
result Implied volatility time series can recover market regime changes.
Investigates optimal portfolio selection with regime-switching-induced stock price shocks.
problem Mean-variance portfolio selection with regime-switching and stock price jumps.
method Modeling regime-switching and stock price jumps, deriving optimal portfolio strategy and efficient frontier using ODEs.
result Added complexity due to regime-switching-induced stock price shocks, leading to nonlinear ODEs.
Model predicts risk-adjusted returns across various financial markets.
problem Stationary models fail in predicting risk-adjusted returns due to market regime changes.
method Asset-independent regime-switching model using hidden Markov models.
result Accurately detects bull, bear, and high volatility periods for improved risk-adjusted returns.
Optimized portfolio management with dynamic market regimes using RL and OC learning.
problem Mean-Variance portfolio optimization in a regime-switching market.
method Reinforcement learning (RL) with Orthogonality Condition (OC) learning for regime-switching market dynamics.
result OC learning outperforms TD learning in simulated and real market scenarios, leading to better portfolio performance.
By Gyongy's theorem, a local and stochastic volatility (LSV) model is calibrated to the market prices of all European call options with positive maturities and strikes if its local volatility function is equal to the ratio of the Dupire local volatility function over the root conditional mean square of the stochastic v…
Model captures external influences through random parameters and regime switching.
problem Capturing external influences in asset dynamics with uncertainty and regime changes.
method Developed a stochastic model with random parameters and regime switching, mathematically consistent and interpretable.
result Demonstrated the model's versatility through local volatility models and characteristic functions.
Proves existence and uniqueness of calibrated LSV model.
problem Calibrating a local stochastic volatility model to market data.
method Proves strong existence and uniqueness of solution to a McKean-Vlasov SDE.
result Establishes well-posedness of a calibrated two-factor LSV model.
The latest generation of volatility derivatives goes beyond variance and volatility swaps and probes our ability to price realized variance and sojourn times along bridges for the underlying stock price process. In this paper, we give an operator algebraic treatment of this problem based on Dyson expansions and moment …
Develops a new model to better predict corporate bond yields.
problem Persistent shifts in interest rates undermine single-regime models.
method Regime-switching generalized CIR model with two-state short-rate process and credit factors.
result The model improves joint curve fit and delivers interpretable probabilities.
Hybrid model improves synthetic equity data generation.
problem Generating realistic synthetic financial time series.
method Discretized excess growth rates into states with Poisson jumps, estimating parameters directly.
result Framework achieved high pass rates for distributional and volatility clustering tests.
Investigates JM for reducing downside risk in market regimes.
problem Mitigating downside risk during market downturns.
method Statistical jump model for identifying market regimes, optimizing penalty for state transitions.
result JM-guided strategies outperform traditional models in reducing risk and enhancing returns.
This study develops a multi-factor framework where not only market risk is considered but also potential changes in the investment opportunity set. Although previous studies find no clear evidence about a positive and significant relation between return and risk, favourable evidence can be obtained if a non-linear rela…
Unified model explains volatility memory in stocks and forex.
problem Understanding the components of volatility memory in financial markets.
method Developed a three-dimensional decomposition of volatility memory into level, shape, and tempo.
result Unified model shows that volatility memory is state-dependent, with different gates prevailing in equities and forex.
New method samples from piecewise smooth distributions using Hamiltonian Monte Carlo.
problem Sampling from distributions with discontinuous gradients.
method Generalized Randomized Hamiltonian Monte Carlo (GRHMC) for piecewise smooth targets.
result GRHMC processes sample from piecewise smooth target distributions with the desired distribution as the invariant distribution.
Optimal dividends strategy in a two-state regime-switching environment.
problem Maximizing profits from dividends until bankruptcy in a company with fluctuating cash surplus and regime changes in drift, volatility, and bankruptcy levels.
method Analyzes the optimal dividend payout strategy considering four factors: Brownian fluctuations in cash surplus, regime changes in drift, volatility, and bankruptcy levels.
result Rich structure of the optimal strategy, which can be either barrier-type or liquidation-barrier type, depending on model parameters.
Two new models for volatility in Markov-switching environments capture financial time-series properties.
problem Modeling volatility in environments with regime switches and exogenous jumps.
method Generalizations of COGARCH and Barndorff-Nielsen-Shephard models using Markov-modulated generalized Ornstein-Uhlenbeck processes.
result Models inherit properties of original models and capture stylized facts of financial time-series.
In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes we firstly outline the Fourier transform method both in log-price and log-strik…
The paper prices European options in a model with changing regimes and jumps.
problem Pricing European options in a model with changing regimes and jumps.
method A regime-switching jump diffusion model with semi-Markov process.
result The locally risk minimizing price of European options is found.
This study compares VaR-based portfolio insurance with CPPI in a regime-switching market.
problem Designing dynamic portfolio insurance strategies in a market with multiple regimes.
method Extends VaR-based portfolio insurance to a Markov-modulated regime-switching market, comparing it to CPPI.
result CPPI strategy generally offers better risk-return tradeoff and stability.
Study new Hawkes processes to model price changes in limit order books.
problem Model price volatility in limit order books.
method Prove LLN and FCLTs for general compound and regime-switching general compound Hawkes processes.
result Volatilities of price changes are expressed in terms of parameters describing arrival rates and price changes.
New method clusters financial time series into volatility regimes.
problem Finding the number of volatility regimes in nonstationary financial time series.
method Change point detection and clustering of segment distributions.
result Optimized trading strategy based on learned volatility regimes.
Paper introduces new Hawkes processes to model price changes in limit order books.
problem Modeling price volatility and order flow in limit order books.
method Introduces compound and regime-switching compound Hawkes processes, proving Law of Large Numbers and FCLTs.
result Volatilities of price changes are linked to parameters of arrival rates and price changes.
Leveraged ETFs can outperform their targets in certain market conditions, contrary to the volatility drag hypothesis.
problem The long-term performance decay of leveraged ETFs due to volatility drag.
method Unified framework incorporating AR(1) and AR-GARCH models, continuous-time regime switching, and flexible rebalancing frequencies.
result Return dynamics, including return autocorrelation, volatility clustering, and regime persistence, determine LETF performance.