Narrow Results

Inspired by the negative price of WTI crude oil observed during the COVID-19 pandemic, we develop a new model for commodity pricing which allows structural change between price normality and lognormality under a Markov regime-switching (RS) framework. We augment the Extended Kalman Filter to calibrate the structural changing model. The model performance in calibration is compared to that of the common RS model with historical WTI spots, various futures and hypothetical scenarios. We conclude that our model is superior in capturing price dynamics especially in the oil market downturns. Encouragingly, the regime probabilities estimated with the new model indicate that during severe events including the 2008–2010 financial crisis, 2014–2016 oil crash and the outbreak of COVID-19 in 2020, WTI spot itself follows normal rather than the widely assumed lognormal process. This finding is consistent with our empirical studies. In addition, we assess the probability density of spot prices with the new model. Finally, we present the PDE finite difference and Monte Carlo approaches to price commodity options under the new model.

This paper examines the extent to which the Indonesia's currency crisis can be accounted for by macro and micro economic fundamentals by employing Markov-switching approach under cross-generation crisis models. In order to represent the speculative attack in the economy, the study utilized one of the measures that is most widely adopted to signal the breakup of a crisis, the Exchange Market Pressure Index (EMPI). This paper found the following. First, liquidity (DC), real exchange rate (RER2) and ratio of banking credit to GDP (BCred) were found to significantly influence the EMPI, indicating that the behavior of EMPI has the characteristic that is predicted by the first, second, and third generation of crisis model found to significantly influence the EMPI, indicating that the behavior of EMPI has the characteristic that is predicted by the first, second and third generation of crisis models. Second, the LR test showed that regime switching dynamic model is more robust than ordinary dynamic model in explaining the EMPI, suggesting that speculative attacks tend to have the characteristics of multiple equilibria. Third, the transition probability matrix results showed that the tranquility regime was more persistent than the volatile regime.

In this article, the dependence structure of the asset classes stocks, government bonds, and corporate bonds in different market environments and its implications on asset management are investigated for the US, European, and Asian market. Asset returns are modelled by a Markov-switching model which allows for two market regimes with completely different risk-return structures. Using major stock indices from all three regions, calm and turbulent market periods are identified for the time period between 1987 and 2009 and the correlation structures in the respective periods are compared. It turns out that the correlations between as well as within the asset classes under investigation are far from being stable and vary significantly between calm and turbulent market periods as well as in time. It also turns out that the US and European markets are much more integrated than the Asian and US/European ones. Moreover, the Asian market features more and longer turbulence phases. Finally, the impact of these findings is examined in a portfolio optimization context. To accomplish this, a case study using the mean-variance and the mean-conditional-value-at-risk framework as well as two levels of risk aversion is conducted. The results show that an explicit consideration of different market conditions in the modelling framework yields better portfolio performance as well as lower portfolio risk compared to standard approaches. These findings hold true for all investigated optimization frameworks and risk-aversion levels.

We present a mathematical model for stock market volatility flocking. Our proposed model consists of geometric Brownian motions with time-varying volatilities coupled with Cucker–Smale (C–S) flocking and regime switching mechanisms. For all-to-all interactions, we assume that all assets' volatilities are coupled to each other with a constant interaction weight, and we show that the common volatility emerges asymptotically and discuss its financial applications. We also provide several numerical simulations and compare them to existing analytical results.

A large body of empirical work is clear-cut in suggesting that the international post-war inflation experience may be described in terms of switches among multiple regimes. A definite explanation of this stylized fact, however, is still under debate. In this paper, we model an economy composed of a large number of interacting price-setting firms which can replicate the evidence at hand. Interactions emerge as a by-product of consumers' uncertainty on the prices charged by different firms. The underlying Markovian structure possesses a stationary distribution with multiple modes, so that its associated dynamics is characterized by multiple regimes and sudden transitions among them. In particular, for any (almost-fully accommodating) monetary policy reaction function, the existence of a multiplicity of inflation regimes is associated to the information acquisition technology consumers have in searching for the lowest price.

We investigate the optimal investment timing strategy in a real option framework. Depending on the state of the economy, whose changes are modeled by a Markov chain, the investment cost can take one of two values. The optimal investment timing decision is determined by finding the free boundary of a perpetual American option. Three investment timing policies, based on different assumptions of investors' information sets, are determined and compared. In the full information case, a significantly earlier optimal exercising time is indicated. We show that an optimal-timing policy suggested by the conventional real option model might ruin the investment opportunities.

We present a very fast and accurate algorithm for calculating prices of finite lived double barrier options with arbitrary terminal payoff functions under regime-switching hyper-exponential jump-diffusion (HEJD) models, which generalize the double-exponential jump-diffusion model pioneered by Kou and Lipton. Numerical tests demonstrate an excellent agreement of our results with those obtained using other methods, as well as a significant increase in computation speed (sometimes by a factor of 5). The first step of our approach is Carr's randomization, whose convergence we prove for barrier and double barrier options under strong Markov processes of a wide class. The resulting sequence of perpetual option pricing problems is solved using an efficient iteration algorithm and the Wiener-Hopf factorization.

The paper discusses the pricing of derivatives using a stochastic discount factor modeled as a regime switching geometric Brownian motion. The regime switching is driven by a continuous time hidden Markov chain representing changes in the economy. The stochastic discount factor enables to define a risk neutral measure. We model the stock price as discounted future dividends driven by the same continuous time Markov chain. The stochastic discount factor is used to price European style options under the historical probability measure. The introduction of occupation times of the Markov chain and the corresponding conditional characteristic function allows the evaluation of the expected value of European type claims. The option price is given as a semi-analytical form using the Fourier transform.

Recent empirical studies have demonstrated the informative nature of the equity returns in explaining the variation of the underlying firm's credit default swap (CDS) spreads. Motivated by these findings, we propose a unified credit-equity model by extending the latent structural model in Kijima et al. (2009). As in the original latent model, we treat the actual status of the firm to be unobservable and one can extract information from the marker process that is observable to the investors. Default occurs when the actual firm value drops below a default threshold for the first time. Different from the model in Kijima et al. (2009), however, we define the marker process to be the firm's equity process. Choosing firm's equity process to be a marker process subsequently relaxes the restrictions imposed in Kijima et al. (2009), enabling us to price firm-related securities.

Additionally, we enrich the original latent structural model with jump and regime-switching dynamics. The purpose of the extensions is to capture more realistic credit spreads and implied volatility skews under different economic environments. The proposed model maintains analytical tractability even under such complex dynamics, for the prices of CDSs and equity options admit semi-closed-form solutions. In sum, our model can evaluate corporate securities and their derivatives in a unified framework.

We investigate asset management in a regime switching framework when the fund manager aims to beat a certain target for the assets under management over an infinite horizon or over a finite horizon. We consider both a full information and a partial information setting. In a full information setting, the asset manager tends to take more risk in the good state and less risk in the bad state with respect to the constant parameter environment. Confidence risk induces the agent to increase his risk exposure.

We develop a pricing model for Sovereign Contingent Convertible bonds (S-CoCo) with payment standstills triggered by a sovereign’s Credit Default Swap (CDS) spread. We model CDS spread regime switching, which is prevalent during crises, as a hidden Markov process, coupled with a mean-reverting stochastic process of spread levels under fixed regimes, in order to obtain S-CoCo prices through simulation. The paper uses the pricing model in a Longstaff–Schwartz American option pricing framework to compute future state contingent S-CoCo prices for risk management. Dual trigger pricing is also discussed using the idiosyncratic CDS spread for the sovereign debt together with a broad market index. Numerical results are reported using S-CoCo designs for Greece, Italy and Germany with both the pricing and contingent pricing models.

In this paper, the pricing problem of variance and volatility swaps is discussed under a two-factor stochastic volatility model. This model can be treated as a two-factor Heston model with one factor following the CIR process and another characterized by a Markov chain, with the motivation originating from the popularity of the Heston model and the strong evidence of the existence of regime switching in real markets. Based on the derived forward characteristic function of the underlying price, analytical pricing formulae for variance and volatility swaps are presented, and numerical experiments are also conducted to compare swap prices calculated through our formulae and those obtained under the Heston model to show whether the introduction of the regime switching factor would lead to any significant difference.

The American option pricing problem is examined in this work using a regime switching finite moment log-stable model. The option prices under this model are governed by a coupled system of fractional partial differential equations. Combination of the coupled system and the spatial-fractional derivative makes it extremely difficult to find an analytic solution. We have constructed a numerical algorithm to numerically solve such problems. The developed predictor-corrector type method is highly efficient and reliable in solving coupled system in each regime having different volatility and interest rates. Two-sided Riesz space fractional diffusion term is approximated using fractional finite difference scheme whereas the classical space derivative term is approximated using central difference formula. Splitting technique is utilized to construct a highly efficient scheme which can also be implemented on parallel processors. Stability and error analysis of the scheme is proved analytically and demonstrated through numerical experiments. Effect of the order of the fractional derivative (also called tail index) on the option prices is shown through graphs by performing numerical experiments for different values of the tail index.

In this paper, I examine the ability of equity market illiquidity to predict Australian macroeconomic variables, between 1976 and 2010. In contrast to existing, U.S.-based, studies, I find that stock market illiquidity does not, on average, have much predictive power over economic growth. Consistent with the weak in-sample predictive power, economic growth forecasts from models that exclude stock illiquidity from the set of explanatory financial variables are statistically no worse than forecasts from models that include illiquidity. However, I find strong evidence that the predictive power of equity market illiquidity is state-contingent, with much higher predictability in states associated with economic and financial stress. The difference between the single-state and regime-switching models' results reflects the fact that, as the nonstressed states have been much more prevalent, parameter estimates from a single-state model averages over both stressed and non-stressed states thus lowering the statistical and economic significance of the estimates.

We model the returns of the convertible arbitrage strategy using a non-linear framework. This strategy has generated long periods of positive returns and low volatility, followed by shorter periods of extreme negative returns and high volatility, associated with market upheaval. We specify a smooth transition regression model to assess performance, a class of model particularly suited to this type of strategy as it allows gradual transition between risk regimes. We show that in alternate regimes, the strategy exhibits relatively high (low) exposure to risk factors and alpha is high (low). The evidence reported can account for abnormal returns demonstrated in previous studies.

This paper studies the optimal VIX futures trading problems under a regime-switching model. We consider the VIX as mean reversion dynamics with dependence on the regime that switches among a finite number of states. For the trading strategies, we analyze the timings and sequences of the investor’s market participation, which leads to several corresponding coupled system of variational inequalities. The numerical approach is developed to solve these optimal double stopping problems by using projected-successive-over-relaxation (PSOR) method with Crank–Nicolson scheme. We illustrate the optimal boundaries via numerical examples of two-state Markov chain model. In particular, we examine the impacts of transaction costs and regime-switching timings on the VIX futures trading strategies.

We study the problem of dynamically trading futures in a regime-switching market. Modeling the underlying asset price as a Markov-modulated diffusion process, we present a utility maximization approach to determine the optimal futures trading strategy. This leads to the analysis of the associated system of Hamilton–Jacobi–Bellman (HJB) equations, which are reduced to a system of linear ODEs. We apply our stochastic framework to two models, namely, the Regime-Switching Geometric Brownian Motion (RS-GBM) model and Regime-Switching Exponential Ornstein–Uhlenbeck (RS-XOU) model. Numerical examples are provided to illustrate the investor’s optimal futures positions and portfolio value across market regimes.

The smooth transition regression (STR) methodology was developed to model nonlinear relationships in the business cycle. We demonstrate the methodology can be used to analyse return series where exposure to financial market risk factors depends on market regime. The smooth transition between regimes inherent in STR is particularly appropriate for risk models as it allows for gradual transition of risk factor exposures. Variations in the methodology and tests its appropriateness are defined and discussed. We apply the STR methodology to model the risk of the return series of the convertible arbitrage (CA) hedge fund strategy. CA portfolios are comprised of instruments that have both equity and bond characteristics and alternate between the two depending on market level (state). The dual characteristics make the CA strategy a strong candidate for nonlinear risk models. Using the STR model, we confirm that the strategy’s risk factor exposure changes with market regime and, using this result, are able to account for the abnormal returns reported for the strategy in earlier studies.

We formulate a short-selling strategy of a stock and seek the optimal timing of short covering in the presence of a random recall and a loan fee rate in an illiquid stock loan market. The aim is to study how the optimal trading strategy of the short-seller is influenced by the relevant features of the stock loan market. We consider a regime-switching stock price model that captures the transition in between the bull and the bear markets. The solution to the optimal stopping problem is obtained in closed-form based on the techniques in Guo and Zhang (2005). We provide the numerical example to illustrate of importance of a regime-dependent stopping rule for the short-seller's problem.