Papers by Christopher Ting
Econometric Modeling: Derivatives eJournal, 2017
According to the Kyle (1985) model of informed trading, information in trade size is likely to ef... more According to the Kyle (1985) model of informed trading, information in trade size is likely to effect a permanent price impact. However, two prominent structural models in the literature do not include trade size in their framework. In this paper, we present a nesting relationship of major structural models and formulate a generalized model that includes all trade variables. A new measure to quantify the amount of information in the order flow is proposed. Our empirical analysis shows that it is indeed the “surprise” in trade size that contributes significantly in reflecting the price change of Nikkei and TOPIX futures. Key words: Market microstructure, volume information, futures market
May 1992 c = 1 Conformal Field Theory and the Fractional Quantum Hall Effect
We examine the application of c = 1 conformal field theory to the description of the fractional q... more We examine the application of c = 1 conformal field theory to the description of the fractional quantum Hall effect (FQHE). It is found that the Gaussian model together with an appropriate boundary condition for the order parameter furnishes an effective theory for the Laughlin type FQHE. The plateau formation condition corresponds to taking the chiral portion of the theory. e-mail: scip1005@nuscc.nus.sg e-mail: phylaich@nusvm.bitnet
We show that the S-shaped hyperbolic tangent function of signed volume is appropriate to model th... more We show that the S-shaped hyperbolic tangent function of signed volume is appropriate to model the price impact of a trade. This model enables an implied true price to be obtained without relying on the quotes. We compare this implied true price with the quotes’ midpoint. For the 1,748 common stocks traded on the NYSE in 1997, we find that the implied true price is superior than the midpoint in proxying for the unobservable true price. The difference between these two proxies is statistically and economically significant. In addition, there is evidence that the price impact function changes over time and relates to the information environment of the company. In light of our trade-based approach to estimating transaction costs, the quote-based effective spread is found to have an upward bias. In sum, this article reveals that both the midpoint and the effective spread are not as reliable as most researchers have implicitly predicated. ∗We would like to thank Liuren Wu for comments on...
On the Term Structure of Model-Free Volatilities and Volatility Risk Premium
An Introduction to Quantitative Finance
An Introduction to Quantitative Finance, 2015
This concise textbook provides a unique framework to introduce Quantitative Finance to advanced u... more This concise textbook provides a unique framework to introduce Quantitative Finance to advanced undergraduate and beginning postgraduate students. Inspired by Newton's three laws of motion, three principles of Quantitative Finance are proposed to help practitioners also to understand the pricing of plain vanilla derivatives and fixed income securities.
Journal of Financial Econometrics, 2009
• This paper applies the Asymmetric Autoregressive Conditional Duration (AACD) model to estimate ... more • This paper applies the Asymmetric Autoregressive Conditional Duration (AACD) model to estimate the probability of informed trading (PIN). • We model trade direction (buy versus sell orders) and the duration between trades jointly. • Extending the Easley, Hvidkjaer and O'Hara (2002) approach, which uses the aggregate numbers of daily buy and sell orders to estimate PIN, we use transaction data. • We allow for interactions between consecutive buy-sell orders. • We account for the duration between trades and the volume of trade.
Empirical Economics, 2005
We investigate the distribution of high-frequency price changes, conditional on trading volume an... more We investigate the distribution of high-frequency price changes, conditional on trading volume and duration between trades, on four stocks traded on the New York Stock Exchange. The conditional probabilities are estimated nonparametrically using local polynomial regression methods. We find substantial skewness in the distribution of price changes, with the direction of skewness dependent on the sign of trade. We also find that the probability of larger price changes increases with volume, but only for trades that occur with longer durations. The distribution of price changes vary with duration primarily when volume is high.
Physica A: Statistical Mechanics and its Applications, 2002
In this paper, we construct and analyze a prototypical model of microscopic chaos. In particular,... more In this paper, we construct and analyze a prototypical model of microscopic chaos. In particular, we extend the results of Beck and Shimizu to the case where the microscopic time scale is no longer small. The upshot is that a non-Ornstein-Uhlenbeck deterministic process can generate a Gaussian di usion process.
We examine the application of c=1 conformal field theory to the description of the fractional qua... more We examine the application of c=1 conformal field theory to the description of the fractional quantum Hall effect (FQHE). It is found that the Gaussian model together with an appropriate boundary condition for the order parameter furnishes an effective theory for the Laughlin type FQHE. The plateau formation condition corresponds to taking the chiral portion of the theory.
The braid group dynamics captures the fractional quantum Hall effect (FQHE) as a manifestation of... more The braid group dynamics captures the fractional quantum Hall effect (FQHE) as a manifestation of puncture phase. When the dynamics is generalized for particles on a multi-sheeted surface, we obtain new tools which determine the fractional charges, the quantum statistics, and the filling factors of the multi-layered FQHE. A many-quasihole wavefunction is proposed for the bilayered samples. We also predict a ν = 5/7 FQHE for triple-layered samples. The viability of 3-dimensional FQHE and the application of the concept of generalized duality to anyonic superconductivity are discussed. PACS numbers: 71.28, 71.10, 72.20M 1 Laughlin’s theory [1] of fractional quantum Hall effect (FQHE) elegantly describes the incompressibility of the 2-dimensional electronic system under the influence of a strong, uniform magnetic field. The theory is pivoted on an ansätz which is taken to be the ground state ψm of the many-body system displaying FQHE: ψm = ∏ (wa − wb) m exp( − 1 4ℓ2 ∑ |wa | 2), (1) a<...
Market Price of Trading Liquidity Risk and Market Depth
International Journal of Theoretical and Applied Finance
Price impact of a trade is an important element in pre-trade and post-trade analyses. We introduc... more Price impact of a trade is an important element in pre-trade and post-trade analyses. We introduce a framework to analyze the market price of liquidity risk, which allows us to derive an inhomogeneous Bernoulli ordinary differential equation. We obtain two closed form solutions, one of which reproduces the linear function of the order flow in Kyle (1985) for informed traders. However, when traders are not as asymmetrically informed, an S-shape function of the order flow is obtained. We perform an empirical intra-day analysis on Nikkei futures to quantify the price impact of order flow and compare our results with industry’s heuristic price impact functions. Our model of order flow yields a rich framework to not only estimate the liquidity risk parameters, but also to provide a plausible cause of why volatility and correlation are stochastic in nature. Finally, we find that the market depth encapsulates the market price of liquidity risk.
Information Contents of Trade and Quote Imbalances, and the Hypothesis of Reverse Liquidity: Evidence from a Fully Automated Exchange
SSRN Electronic Journal
... Exchange of Singapore and the Singapore International Monetary Exchange (SIMEX). Unlike ... F... more ... Exchange of Singapore and the Singapore International Monetary Exchange (SIMEX). Unlike ... Firstly, to unambiguously ex-amine the information content of trade imbalance, it is crucial to have transaction records with trading direction provided. ...
Variance Risk Premiums of Commodity ETFs
Journal of Futures Markets, 2016
The term structure of S&P 100 model-free volatilities
Quantitative Finance, 2012
ABSTRACT We develop an improved method to obtain the model-free volatility more accurately despit... more ABSTRACT We develop an improved method to obtain the model-free volatility more accurately despite the limitations of a finite number of options and large strike price intervals. Our method computes the model-free volatility from European-style S&amp;P 100 index options over a horizon of up to 450 days, the first time that this has been attempted, as far as we are aware. With the estimated daily term structure over the long horizon, we find that (i) changes in model-free volatilities are asymmetrically more positively impacted by a decrease in the index level than negatively impacted by an increase in the index level; (ii) the negative relationship between the daily change in model-free volatility and the daily change in index level is stronger in the near term than in the far term; and (iii) the slope of the term structure is positively associated with the index level, having a tendency to display a negative slope during bear markets and a positive slope during bull markets. These significant results have important implications for pricing and hedging index derivatives and portfolios.
A Common Measure of Liquidity Costs for Futures and Stock Exchanges
Handbook of Asian Finance, 2014
Eprint Arxiv Cond Mat 9207019, Jul 17, 1992
The braid group dynamics captures the fractional quantum Hall effect (FQHE) as a manifestation of... more The braid group dynamics captures the fractional quantum Hall effect (FQHE) as a manifestation of puncture phase. When the dynamics is generalized for particles on a multi-sheeted surface, we obtain new tools which determine the fractional charges, the quantum statistics, and the filling factors of the multi-layered FQHE. A many-quasihole wavefunction is proposed for the bilayered samples. We also predict a ν = 5/7 FQHE for triple-layered samples. The viability of 3-dimensional FQHE and the application of the concept of generalized duality to anyonic superconductivity are discussed.
We examine the application of c = 1 conformal field theory to the description of the fractional q... more We examine the application of c = 1 conformal field theory to the description of the fractional quantum Hall effect (FQHE). It is found that the Gaussian model together with an appropriate boundary condition for the order parameter furnishes an effective theory for the Laughlin type FQHE. The plateau formation condition corresponds to taking the chiral portion of the theory.
Microscopic chaos and non-chaotic structural disorder are two contending candidates to shed light... more Microscopic chaos and non-chaotic structural disorder are two contending candidates to shed light on the origin of Brownian motion. In this paper, we construct and analyze prototypical models of microscopic chaos and structural disorder. These models exhibit standard statistical physics related to the equipartition theorem, Einstein's diffusion law, Green-Kubo equation, and the inverse-square power spectrum. We have also proved that the models follow the Wiener process, even when the microscopic time scale τ is not small. Our study suggests that microscopic chaos can be construed as a special case of structural disorder.
Magnocellular pathway for rotation invariant Neocognitron
International journal of neural systems, 1993
In the mammalian visual system, magnocellular pathway and parvocellular pathway cooperatively pro... more In the mammalian visual system, magnocellular pathway and parvocellular pathway cooperatively process visual information in parallel. The magnocellular pathway is more global and less particular about the details while the parvocellular pathway recognizes objects based on the local features. In many aspects, Neocognitron may be regarded as the artificial analogue of the parvocellular pathway. It is interesting then to model the magnocellular pathway. In order to achieve "rotation invariance" for Neocognitron, we propose a neural network model after the magnocellular pathway and expand its roles to include surmising the orientation of the input pattern prior to recognition. With the incorporation of the magnocellular pathway, a basic shift in the original paradigm has taken place. A pattern is now said to be recognized when and only when one of the winners of the magnocellular pathway is validified by the parvocellular pathway. We have implemented the magnocellular pathway ...
Uploads
Papers by Christopher Ting