Continuous time and nonparametric modelling of U.S. interest rate models

In this paper we compare the forecasting performance of different models of interest rates using parametric and nonparametric estimation methods. In particular, we use three popular nonparametric methods, namely, artificial neural networks (ANN), k-nearest neighbour (k-NN), and local linear regression (LL). These are compared with forecasts obtained from two-factor continuous time interest rate models, namely, Chan, Karolyi, Longstaff, and Sanders [CKLS, J. Finance 47 (1992) 1209]; Cos, Ingersoll, and Ross [CIR, Econometrica 53 (1985) 385]; Brennan and Schwartz [BR-SC, J. Financ. Quant. Anal. 15 (1980) 907]; and Vasicek [J. Financ. Econ. 5 (1977) 177]. We find that while the parametric continuous time method, specifically Vasicek, produces the most successful forecasts, the nonparametric k-NN performed well.     

Universal price impact functions of individual trades in an order-driven market

The trade size ω has a direct impact on the price formation of the stock traded. Econophysical analyses of transaction data for the US and Australian stock markets have uncovered market-specific scaling laws, where a master curve of price impact can be obtained in each market when stock capitalization C is included as an argument in the scaling relation. However, the rationale of introducing stock capitalization in the scaling is unclear and the anomalous negative correlation between price change r and trade size ω for small trades is unexplained. Here we show that these issues can be addressed by taking into account the aggressiveness of orders that result in trades together with a proper normalization technique. Using order book data from the Chinese market, we show that trades from filled and partially filled limit orders have very different price impacts. The price impact of trades from partially filled orders is constant when the volume is not too large, while that of filled orders shows power-law behavior r?～?ω^α with α?≈?2/3. When returns and volumes are normalized by stock-dependent averages, capitalization-independent scaling laws emerge for both types of trades. However, no scaling relation in terms of stock capitalization can be constructed. In addition, the relation α?=?α_ω/α _r is verified for some individual stocks and for the whole data set containing all stocks using partially filled trades, where α_ω and α _r are the tail exponents of trade sizes and returns. These observations also enable us to explain the anomalous negative correlation between r and ω for small-size trades.     

Empirically based modeling in financial economics and beyond, and spurious stylized facts

The discovery of the dynamics of a time series requires construction of the transition density. We explain why 1-point densities and scaling exponents cannot determine the class of stochastic dynamics. Time series require some sort of underlying statistical regularity to provide a basis for analysis, and we construct an exhaustive list of such tests. The condition for stationary increments, not scaling, determines the existence of long time pair autocorrelations. We conjecture that for a selfsimilar process neither the pair correlations 〈x(t)x(s)〉 nor the 2-point density scales in both times t and s except in a pathological case, and give examples using three well-known Gaussian processes. An incorrect assumption of stationary increments can generate spurious stylized facts, including fat tails. When a sliding window is applied to nonstationary, uncorrelated increments then a Hurst exponent H_s = 1 / 2 is generated by that procedure even if the underlying model scales with a Hurst exponent H ≠ 1/2. We explain how this occurs dynamically. The nonstationarity arises from systematic unevenness in the traders' behavior in real time. Spurious stylized facts arise mathematically from using a log increment with a ‘sliding window’ to read the series. In addition, we show that nonstationary processes are generally not globally transformable to stationary ones. We also present a more detailed explanation of our recent FX data analysis and modeling.     

Completion time structures of stock price movements

Summary This paper proposes to model movements in more than a century of daily US stock prices as the outcome of a multi-state marked point process and studies the time it takes for stock prices to complete an up or a down move of a certain size. We present a new econometric specification for a class of dynamic models that account for autoregressive conditional duration effects. We also present a method to account for the effect of time-varying state variables that may change within a duration.We find strong evidence of dynamic dependencies in the direction and speed of stock price movements. Past interest rates are also found to affect the speed and direction of completion times. Out-of-sample prediction results show that forecasts of the direction of moves in stock prices can be greatly improved by including covariates such as interest rates and allowing for dynamics in the econometric specification.We thank an anonymous referee, an associate editor, Rob Engle, Mark Machina and Ruth Williams for helpful conversations. We are grateful to INQUIRE UK for financial support for this research.     

内在投资价值理论在中国股市的有效性检验

用F-O模型对深发展1991～2010年的内在价值进行测算,然后实证分析股价和内在价值之间的协整关系,发现在过去的20年中,两变量间并不存在协整关系。这说明中国股市是无效市场。通过计算泡沫值发现,20世纪90年代,深发展的泡沫值非常高,进入21世纪后泡沫值逐渐降低,反映出中国股市逐渐走向价值回归之路。     

Pricing futures on geometric indexes: A discrete time approach

Several futures contracts are written against an underlying asset that is a geometric, rather than arithmetic, index. These contracts include: the US Dollar Index futures, the CRB-17 futures, and the Value Line geometric index futures. Due to the geometric averaging, the standard cost-of-carry futures pricing formula is improper for pricing these futures contracts. We assume that asset prices are lognormally distributed, and capital markets are complete. Using the concepts of equivalent martingale measure and the risk-neutral valuation relationships in conjunction with discrete time methodology, we derive closed-form pricing formulas for these contracts. Our pricing formulas are consistent with the ones obtained via a continuous time paradigm.

The moments of the time to ruin in dependent Sparre Andersen models with Coxian claim sizes

A very general class of dependent Sparre Andersen models with Coxian claim sizes (e.g. Landriault et al. 2014) is considered in this paper. The moments of the time to ruin are studied under this class. An analytical form is provided for the moments, which involves solving linear systems of equations. Numerical examples are then considered to further study the properties of the mean and variance of the time to ruin.     

Quadratic term structure models in discrete time

This paper extends the results on quadratic term structure models in continuous time to the discrete time setting. The continuous time setting can be seen as a special case of the discrete time one. Discrete time quadratic models have advantages over their continuous time counterparts as well as over discrete time affine models. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors, time-dependent parameters, regime changes and “jumps” in the underlying factors. In particular regime changes and “jumps” cannot so easily be accommodated in continuous time quadratic models. Pricing bond options requires simple integration and model estimation does not require a restrictive choice of the market price of risk.     

Price discovery in tick time

This paper develops a tick time model for the quote setting dynamics on Nasdaq. The model decomposes quotes into an efficient price, asymmetric information and noise. Both the evolution of the efficient price and the information contents of quotes depend on quote durations. New measures for the contribution to price discovery are defined within this model. When aggregated to fixed calendar time intervals, they relate closely to Hasbrouck [Hasbrouck, Joel, 1995, One security, many markets: determining the contribution to price discovery, Journal of Finance 50, 1175–1199] information shares. Empirical results for 20 Nasdaq stocks indicate that ECNs, in particular Island, contribute most to price discovery for active stocks. For less active stocks, wholesale market makers contribute most.     

Stylised facts of financial time series and hidden Markov models in continuous time

Hidden Markov models are often applied in quantitative finance to capture the stylised facts of financial returns. They are usually discrete-time models and the number of states rarely exceeds two because of the quadratic increase in the number of parameters with the number of states. This paper presents an extension to continuous time where it is possible to increase the number of states with a linear rather than quadratic growth in the number of parameters. The possibility of increasing the number of states leads to a better fit to both the distributional and temporal properties of daily returns.     

数据融合中的时间配准方法探究

时间配准是指应用内插、外推、拟合等算法对各传感器的观测序列进行处理,使得各传感器能在同一时刻提供对同一目标的观测数据.时间配准是数据融合中不可缺少的一个环节,本文主要概述了两种常用的时间配准法并列举了三次样条插值实例.     

A note on modelling economic growth determinants in the Dominican Republic

The article models economic growth determinants in the Dominican Republic. The exercise considers a panel of 25 candidate explanatory variables observed during the last three decades of the twentieth century. The time series are selected on the basis of economic theory and previous findings in the cross-country empirical growth literature. The modelling reveals that the annual growth rate of real gross domestic product per capita is, on average, inversely associated to a proxy for market distortions, and positively related to government expenditure, economic growth in the United States of America, and an index of globalization comprising international trade and migration variables.     

Robust reinsurance contracts in continuous time

We investigate reinsurance contract problems in a continuous-time principal-agent framework, where the reinsurer (principal) is concerned about potential model ambiguity in the claims process, but the insurer (agent) trusts the claims process, or vice versa. The reinsurer designs a robust reinsurance contract that maximizes his exponential utility of terminal wealth under the worst-case distribution, subject to the insurer’s incentive constraint. Optimal reinsurance contracts are explicitly derived in different ambiguity situations. We first show that the reinsurer’s robustness preference makes him become more conservative, which induces him to raise the reinsurance price, which then decreases the demand for reinsurance. However, the insurer’s robustness preference increases both the reinsurance price and the demand. Furthermore, the reinsurer continuously adjusts the reinsurance price, leading the insurer to always purchase a constant proportion of reinsurance, no matter who faces ambiguity, or whether ambiguity exists. Finally, the economic implications of model ambiguity are illustrated using numerical examples.     

Spatial modelling of claim frequency and claim size in non-life insurance

In this paper, models for claim frequency and average claim size in non-life insurance are considered. Both covariates and spatial random effects are included allowing the modelling of a spatial dependency pattern. We assume a Poisson model for the number of claims, while claim size is modelled using a Gamma distribution. However, in contrast to the usual compound Poisson model, we allow for dependencies between claim size and claim frequency. A fully Bayesian approach is followed, parameters are estimated using Markov Chain Monte Carlo (MCMC). The issue of model comparison is thoroughly addressed. Besides the deviance information criterion and the predictive model choice criterion, we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. We give an application to a comprehensive data set from a German car insurance company. The inclusion of spatial effects significantly improves the models for both claim frequency and claim size, and also leads to more accurate predictions of the total claim sizes. Further, we detect significant dependencies between the number of claims and claim size. Both spatial and number of claims effects are interpreted and quantified from an actuarial point of view.     

Asymmetric information and imperfect competition in a continuous time multivariate security model

This paper deals with the problem of price formation in a market with asymmetric information and several risky assets. We then extend the multivariate security model of Caballé and Krishnan (1994) to a continuous time framework, and general utility function. Our model enables us to observe some results which are specific to multi security markets such as Giffen effect. An application of the main result will be the non trivial generalizations of the models of Back (1992) and Cho (1997).Mathematics Subject Classification (1991): 49L10, 60G44, 90A15JEL Classification: G11, G12The author would like to thank his supervisor H. Pham, K. Back and an anonymous referee for useful comments and discussions.     

Sub-sequence incidence analysis within series of Bernoulli trials: application in characterisation of time series dynamics

ABSTRACT

This paper presents a new and widely applicable nonparametric approach to the characterisation of time series dynamics. The approach involves analysis of the incidence of occurrence of patterns in the direction of movement of the series, and may readily be applied to time series data measured on any scale. The paper includes derivations of analytic forms for two (infinite) families of distributions under the null hypothesis of random behaviour, and of a useful analytic form for the generation of the moments of these distributions. The distributions are asymptotically normal, so allowing for straightforward application of the approach presented in the paper too long series of high frequency and/or extended time period data. Areas of application in finance and accounting are suggested.