Narrow Results

We analyze a stochastic volatility market model in which volatility is correlated with return and is represented by an Ornstein-Uhlenbeck process. In the framework of this model we exactly calculate the leverage effect and other stylized facts, such as mean reversion, leptokurtosis and negative skewness. We also obtain a close analytical expression for the characteristic function and study the heavy tails of the probability distribution.

This paper reviews extant research on commodity price dynamics and commodity derivative pricing models. In the first half, we provide an overview of key characteristics of commodity price behavior that have been explored and documented in the theoretical and empirical literature. In the second half, we review existing derivative pricing models and discuss how the peculiarities of commodity markets have been integrated in these models. We conclude the paper with a brief outlook on various important research questions that need to be addressed in the future.

We study the optimal timing strategies for trading a mean-reverting price process with a finite deadline to enter and a separate finite deadline to exit the market. The price process is modeled by a diffusion with an affine drift that encapsulates a number of well-known models, including the Ornstein–Uhlenbeck (OU) model, Cox–Ingersoll–Ross (CIR) model, Jacobi model, and inhomogeneous geometric Brownian motion (IGBM) model. We analyze three types of trading strategies: (i) the long–short (long to open, short to close) strategy; (ii) the short–long (short to open, long to close) strategy, and (iii) the chooser strategy whereby the trader has the added flexibility to enter the market by taking either a long or short position, and subsequently close the position. For each strategy, we solve an optimal double stopping problem with sequential deadlines, and determine the optimal timing of trades. Our solution methodology utilizes the local time-space calculus of [Peskir (2005) A change-of-variable formula with local time on curves, Journal of Theoretical Probability18, 499–535] to derive nonlinear integral equations of Volterra-type that uniquely characterize the trading boundaries. The numerical implementation of the integral equations provides examples of the optimal trading boundaries.

Cointegration tests and ex ante trading rules are applied to study cross-market linkages between the Taiwan Index futures contracts listed on the Singapore Exchange and the Taiwan Stock Exchange Capitalization-weighted Stock Index futures contracts listed on the Taiwan Futures Exchange. The exchange rate-adjusted returns of the two futures series do not differ significantly in mean but in variances, and show significant mean-reverting tendencies between them. Our trading strategies are able to generate statistically significant, if economically insignificant, profits, while our Granger causality tests demonstrate that information flows primarily from the Singapore market to the Taiwan market, a result confirming other research.

The heart beat RR intervals extracted from the electrocardiogram recorded during the stress test show a non stationary profile consisting of a decreasing trend during the exercise phase, an increasing trend during the recovery and a global minimum (acme). In addition this time series exhibits a time-varying variance. We decompose the series into a deterministic trend and random fluctuation. The trend is obtained as an exponential fit of the data; the fluctuation is modeled as a mean reverting process driven by the trend, in which the random innovation has a time-varying variance. Data analysis, performed on ambulatory recorded electrocardiograms of 10 healthy subjects, shows that the model describes correctly the data series on a scale of at least 300 beats.

We aim at detecting stress in newborns by observing heart rate variability (HRV). The HRV features nonlinearities. Fractal dynamics is a usual way to model them and the Hurst exponent summarizes the fractal information. In our framework, we have observations of short duration, for which usual estimators of the Hurst exponent, like detrended fluctuation analysis (DFA), are not adapted. Moreover, we observe that the Hurst exponent does not vary much between stress and rest phases, but its decomposition in memory and underlying properties of the probability distribution leads to satisfactory diagnostic tools. This decomposition of the Hurst exponent is in addition embedded in a mean-reverting model. The resulting model is a mean-reverting fractional Lévy stable motion (FLSM). We estimate it and use its parameters as diagnostic tools of neonatal stress. Indeed, the value of the speed of reversion parameter is a significant indicator of stress. The evolution of both parameters in which the Hurst exponent is decomposed provides us with significant indicators as well. On the contrary, the Hurst exponent itself does not bear useful information.

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.

A new short-rate model and a new explicit instantaneous mean reversion formula are introduced. The introduction is presented via a comparison of various short-rate one factor models, which are calibrated and analyzed numerically via a Monte Carlo simulation. Two variance reduction techniques, Stratified Sampling and the Sobol Algorithm, are compared. An empirical comparison is constructed using criteria of goodness-of-fit, in five exchange rates. The data is ex-ante ultimately measuring the predictability of the stochastic models and variance reduction.

We investigate the effect of using an optimized exit rule on pairs trading. For every asset pair, we optimize the positions so that resulting intraday portfolio value is best fitted to an Ornstein–Uhlenbeck (OU) process through maximum likelihood estimation. Using various asset pairs, we examine the risks and returns of pairs trading strategies with and without an optimize exit rule. We provide empirical evidence that using an optimized exit rule improves the profitability of the trades and reduces turnovers.

Consider a partially informed trader who does not observe the true drift of a financial asset. Under Gaussian price dynamics with stochastic unobserved drift, including cases of mean-reversion and momentum dynamics, we take a filtering approach to solve explicitly for trading strategies which maximize expected logarithmic, exponential and power utility. We prove that the optimal strategies depend on current price and an exponentially weighted moving average (EMA) price, and in some cases current wealth, not on any other stochastic variables. We establish optimality over all price-history-dependent strategies satisfying integrability criteria, not just EMA-type strategies. Thus the condition that the optimal trading strategy reduces to a function of EMA and current price is not an assumption but rather a consequence of our analysis. We solve explicitly for the optimal parameters of the EMA-type strategies and verify optimality rigorously.

This chapter finds that the intraday Nikkei futures returns exhibit different patterns of momentum or mean reversion when changing observation intervals. Using a Markov chains methodology, a significant return momentum was found at 1-min observation interval. However, a significant return mean reversion was found at 10-min observation interval. This switching pattern of momentum to mean reversion is robust to intraday seasonality. Further, the sources that contribute to the high-frequency momentum and mean reversion are explored and it is concluded that large limit orders and the bid-ask effect can play the role.

In this chapter, we explore how long-run mean reversion in stock returns could have significant implication on the forecast or predictability of such returns.

In this chapter, we shall study bonds and their term structures. Bonds are a major class of investment assets distinct from equities, and they have salient features that will be explained. Continuous time stochastic processes are briefly introduced in this chapter to show their usage in modelling bond prices and therefore the resulting credit spreads and yields. Multiple regression analyses involving explanation of credit spreads and of bond returns are described.