Arbitrage violations and implied valuations: the option market

The ideas presented in this paper are those of the authors and not necessarily reflect the views of the National bank of Canada. Both authors thank the National Bank of Canada and the SSHRC of Canada for their help. Thanks are also due to Professor Y. Tian for his comments, and for participating, together with students of the Financial Engineering program at York University, in the data preparation and the execution of the Matlab programs. In this paper, we propose a necessary and sufficient condition for bid and ask prices of European options to be free of arbitrage, and derive from it an efficient numerical methodology to determine its satisfaction by a given set of prices. If the bid and ask prices satisfy the no-arbitrage (NA) condition, our methodology produces a vector of NA prices that lie between the bid and ask prices. Otherwise, our methodology generates a vector of arbitrage-free prices that is as close as possible, in some sense, to the bid–ask strip. The arbitrage-free prices detected by our methodology render the commonly used practice of using mid-points and then ‘cleaning’ arbitrage from them as unnecessary. Moreover, a vector of ‘cleaned’ prices obtained from mid-point prices may be outside the bid–ask spread even in an arbitrage-free market and, hence, in this case will not be representative of the current market. A new procedure of estimating implied valuation operators is also suggested here. This procedure is rooted in the economic properties of put and call prices and is based on Phillips and Taylor's approximation of a convex function. This approach is superior to common estimation techniques in that it produces an analytical expression for the implied valuation operator and is not data intensive as some other studies. Empirical findings for the new methods are documented and their economic implications are discussed.     

关于非银行金融机构参与外汇市场问题的研究

相比国际外汇市场,我国非银行金融机构参与外汇市场程度较低,这与外汇市场长期以来坚持实需交易原则有关,可考虑从适度放开自营交易、丰富产品等方面拓宽非银行金融机构参与外汇市场。     

Impact of liquidity on stock returns: an empirical investigation of the Tunisian stock market

This paper investigates the return–liquidity relationship on one Middle East and North Africa frontier market, the Tunisian Stock Exchange (TSE). The findings provide evidence that there is a significant and positive premium for companies with high price impact and low trading frequency. However, Tunisian investors appreciate more low spread stocks. We show, also, a non-linear relation between potential delays of execution and stock returns. In addition, we find that Tunisian investors require a premium to compensate past cumulative illiquidity risk (high price impact, low turnover and high potential delay of execution) over the prior three to 12 months and to compensate past cumulative spread over 12 months. We point out also that these effects are seasonal.     

Firm size,ownership structure,and systematic liquidity risk: The case of an emerging market

Previous studies support the hypothesis that institutional ownership leads to an enhanced systematic liquidity risk by increasing the commonality in liquidity. By using a proprietary database of all incoming orders and ownership structure in an emerging stock market, we show that institutional ownership leads to an increase in commonality in liquidity for mid- to-large cap firms; however, only individual ownership can lead to such an increase for small cap firms, revealing a new source of systematic liquidity risk for a specific group of firms. We also reveal that commonality decreases with the increasing number of investors (for both individual and institutional) at any firm size level; suggesting that as the investor base gets larger, views of market participants become more heterogeneous, which provides an alternative way to decrease the systematic liquidity risk.     

An approximation pricing algorithm in an incomplete market: A differential geometric approach

The minimal distance equivalent martingale measure (EMM) defined in Goll and Rüschendorf (2001) is the arbitrage-free equilibrium pricing measure. This paper provides an algorithm to approximate its density and the fair price of any contingent claim in an incomplete market. We first approximate the infinite dimensional space of all EMMs by a finite dimensional manifold of EMMs. A Riemannian geometric structure is shown on the manifold. An optimization algorithm on the Riemannian manifold becomes the approximation pricing algorithm. The financial interpretation of the geometry is also given in terms of pricing model risk.Received: February 2004, Mathematics Subject Classification (2000): 62P05, 91B24, 91B28JEL Classification: G11, G12, G13Yuan Gao: Present address Block 617, Bukit Panjang Ring Road, 16-806,Singapore 670617. I am currently working in a major investment bank.This paper is based on parts of my doctoral dissertation Gao (2002),which isavailable upon request.Part of the research was done during my visit to HumboldtUniversity in 2002 and was partially supported by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 373. I am especially thankful to Professor Hans Föllmer for the invitation and helpful discussions.We would like to thank Professor Martin Schweizer,the associate editor and the referee for their constructive comments.     

Bias in an Empirical Approach to Determining Bond and Mortgage Risk Premiums

Empirical studies of bond and commercial mortgage performance often quantify a required risk premium by examining the difference between the promised yield and the realized yield as adjusted for default occurrence. These studies omit the effects of various other sources of risk, however, including collateral asset market risk, interest rate risk, and possibly call risk. These omissions downwardly bias the empirical risk premium estimate on the debt. In this paper, we disentangle and quantify the sources of this bias by modeling secured coupon debt (the commercial mortgage) as used in the calculation of a realized investment return. We consider deterministic and stochastic interest rate economies with mortgage contracts that are either noncallable or subject to a temporary prepayment lockout period. Given realistic parameter values associated with the term structure, underlying asset dynamics, and debt contracting, we show that the magnitude of the bias can be significant.     

The Cross-Section of Expected Stock Returns: New Evidence from an Emerging Market

Over 300 factors have been found to explain the cross-section of expected stock returns. Empirical studies also show that findings from multifactor asset-pricing models have not been consistent in an emerging market. Using DuPont analysis and a residual income valuation model for 284 nonfinancial companies on Ho Chi Minh Stock Exchange during the period 2008–2014, findings suggest that the return on equity and its change are informative for stock returns in Vietnam. In addition, the level of capital turnover, financial cost ratio (FCR), and changes in capital and in the FCR contain incremental explanatory power for stock returns.     

Linear beta pricing with inefficient benchmarks in a given factor structure*

ABSTRACT

We show the equivalence between the zero-beta version of a multi-factor arbitrage pricing model and a linear pricing model utilizing undiversified inefficient benchmarks in a given factor structure. The resulting linear model is a two-beta model, with one beta related to the inefficient benchmark and another adjusting for its inefficiency. This linear model shows that there are only two distinctive and computable sources of risk, affecting security expected returns, despite the existence of several risk factors. In a short empirical example we demonstrate that the model can be employed to provide guidance and allow researchers to test for the validity of their selection of the underlying risk factors driving variations in security returns.     

Pairs trading in the UK equity market: risk and return

In this paper, we provide the first comprehensive UK evidence on the profitability of the pairs trading strategy. Evidence suggests that the strategy performs well in crisis periods, so we control for both risk and liquidity to assess performance. To evaluate the effect of market frictions on the strategy, we use several estimates of transaction costs. We also present evidence on the performance of the strategy in different economic and market states. Our results show that pairs trading portfolios typically have little exposure to known equity risk factors such as market, size, value, momentum and reversal. However, a model controlling for risk and liquidity explains a far larger proportion of returns. Incorporating different assumptions about bid-ask spreads leads to reductions in performance estimates. When we allow for time-varying risk exposures, conditioned on the contemporaneous equity market return, risk-adjusted returns are generally not significantly different from zero.     

Liquidity,liquidity risk,and information flow: Lessons from an emerging market

This paper examines the role of public and private information flows in intraday liquidity and intraday liquidity risk in the Tunisian stock market. Our empirical results are based on ARMA and GARCH-type models and show that, for major Tunisian stocks, gradually elapsed public information together with gradually elapsed private information in the market is the dominant factor in liquidity improvements in the Tunisian stock market. Liquidity improvements are generated by a decrease in the bid-ask spread accompanied by an increase in the depth at best limit. Our results clearly indicate that the arrival of public information in a sequential manner is the dominant factor generating increases in liquidity risk related to the bid-ask spread, while the advent of private information in a contemporaneous manner is the dominant factor generating increases in liquidity risk related to the depth at best limit. Additionally, our results show that liquidity risk persistence disappears when trading volume and order imbalance are included as explanatory variables in the conditional variance equation.     

Electricity Pricing in New Zealand and the Australian State of Queensland: Accounting for the Impact of Sector Restructuring

The electricity industries of New Zealand (NZ) and the Australian state of Queensland have undergone substantial structural and regulatory reform with the common intent to improve economic efficiency. Deregulation and privatisation have been key elements of the reform but have been approached differently by each jurisdiction. This study traces the link between structural and regulatory regimes and asset valuation, profits and, ultimately, pricing. The study finds that key drivers in recent price increases are the government‐owned generation and retail sector in NZ and the government‐owned distribution sector in Queensland. It is concluded that, contrary to the rationale for the imposition of regulatory controls in a non‐market environment, the regulatory regimes appear to have contributed to higher rather than lower pricing structures.     

The short-term impact of director trading in UK closed-end funds

Most closed-end funds are transparent entities that hold securities that are actively traded in liquid markets. In such a setting, the argument that director transactions mitigate information asymmetry has very limited applicability. Our results provide support for the theory of Barber and Odean [2008. “All that Glitters: The Effect of Attention and News on the Buying Behavior of Individual and Institutional Investors.” Review of Financial Studies 21: 785–818]: retail investor decision-making is influenced by attention-grabbing events. Director purchases are one such attention-grabbing event and are associated with significant positive price returns – the magnitudes of which are linked to the size of the purchase, the size of the fund, and the investment mandate. Trading volumes increase at the time of the purchase but most of the initial price responses and trading volumes dissipate over the following 15 days.     

Asset Prices,Liquidity, and Monetary Policy in an Exchange Economy

I formulate a model in which money coexists with equity shares on a risky aggregate endowment. Agents can use equity as a means of payment, so shocks to equity prices translate into aggregate liquidity shocks that disrupt the mechanism of exchange. I characterize a family of optimal monetary policies and find that the resulting equity prices are independent of monetary considerations. I also study a perturbation of the family of optimal policies that targets a positive constant nominal interest rate and find that in this case the real equity return includes a liquidity return that depends on monetary considerations.     

Credit Availability and Asset Pricing Dynamics in Illiquid Markets: Evidence from Commercial Real Estate Markets

This article examines credit frictions and asset pricing in public and private markets with varying liquidity. We find that a tightening in credit availability is negatively related to subsequent price movements in private and public commercial real estate markets. Assets trading in illiquid segments of these markets are also susceptible to a feedback effect whereby changes in asset prices predict subsequent changes in credit availability. Controlling for investor demand, our findings suggest credit constraints play an economically significant asset pricing role in markets that are both highly levered and relatively illiquid.     

The impact of aggressive orders in an order-driven market: a simulation approach

This article investigates resiliency in an order-driven market. On basis of a vector autoregressive model capturing various dimensions of liquidity and their interactions, I simulate the effect of a large liquidity shock, measured by a very aggressive market order. I show that, despite the absence of market makers, the market is resilient. All dimensions of liquidity (spread, depth at the best prices and order book imbalances) revert to their steady-state values within 15 orders after the shock. For prices, a long run effect is found. Furthermore, different dimensions of liquidity interact. Immediately after a liquidity shock, the spread becomes wider than in the steady state, implying that one dimension of liquidity deteriorates, while at the same time, depth at the best prices increases, meaning an improvement of another liquidity dimension. In subsequent periods, the spread reverts back to the steady-state level but also depth decreases. Also, I find evidence for asymmetries in the impact of shocks on the ask and bid side. Shocks on the ask side have a stronger impact than shocks on the bid side. Finally, resiliency is higher for less-frequently traded stocks and stocks with a larger relative tick size.     

Pursuing Value Through Liquidity in IPOs: Underpricing,Share Retention,Lockup, and Trading Volume Relationships

We argue that in an initial public offering (IPO), pre-IPO owners make decisions regarding underpricing, share retention, and share lockup simultaneously and optimally to maximize aftermarket liquidity. We predict that underpricing fosters higher trading volume in both the short run and the long run. Also, liquidity is negatively related to the proportion of shares retained by pre-IPO owners, ceteris paribus, so IPO underpricing should be positively related to the proportion of shares retained, as an offset. We document evidence consistent with these predictions. In addition, we find that, for IPOs with a lockup restriction, underpricing is more substantial and the positive relation between share retention and underpricing is much stronger. We also find that the relationship between underpricing and trading volume is stronger for IPOs with lockup. IPOs with lockup have higher trading volume, and a significant portion of this difference is associated with the effect of underpricing.JEL Classification: G10, G14, G24     

Nonlinear asset pricing in Chinese stock market: A deep learning approach

The redesign of asset pricing models failed to integrate the frequent financial phenomenon that stock markets exhibit a non-linear long- and short-term memory structure. The difficulty lies in developing a nonlinear pricing structure capable of depicting the memory influence of the pricing variable. This paper presents a Long- and Short-Term Memory Neural Network Model (LSTM) to capture the non-linear pricing structure among five elements in the Chinese stock market, including market portfolio return, market capitalisation, book-to-market ratio, earnings factor, and investment factor. The long–short-term memory structure implies that the autocorrelation function of the stock return series decays slowly and has a long-term characteristic. The LSTM model surpasses the standard Fama–French five-factor model in terms of out-of-sample goodness-of-fit and long–short strategy performance. The empirical findings indicate that the LSTM nonlinear model properly represents the nonlinear relationships between the five components.     

The effect of ownership and control on market valuation: Evidence from initial public offerings in The Netherlands

This study examines whether ownership and control variables influence market valuation at the time of the initial public offering (IPO). Using a sample of 118 IPOs on Euronext Amsterdam during the period 1984-2001, we find support for this conjecture. Management stock ownership, the proportion of independent supervisory directors, and board monitoring by large nonmanagement hareholders are positively related to IPO firm value. These factors are successful in reducing agency costs. We also find that supermajority management stock ownership and takeover defenses lower IPO firm value. Therefore, these mechanisms increase agency costs, resulting in a lower price that investors are willing to pay for IPO shares.     

Numerical solutions to an integro-differential parabolic problem arising in the pricing of financial options in a Levy market

We study the numerical solutions for an integro-differential parabolic problem modeling a process with jumps and stochastic volatility in financial mathematics. We present two general algorithms to calculate numerical solutions. The algorithms are implemented in PDE2D, a general-purpose, partial differential equation solver.     

Adaptive Learning in an Expectational Difference Equation with Several Lags: Selecting among Learnable REE

It is demonstrated that adaptive learning in the least squares sense may be incapable of satisfactorily reducing the number of attainable equilibria in a rational expectations model when focusing on the forward‐solutions to the model. The model examined, as an illustration, is a basic asset pricing model for exchange rate determination that is augmented with technical trading in the currency market in the form of moving averages since it is the most commonly used technique according to questionnaire surveys. The forward‐solutions to such a model are preferable to the backward‐solutions that are normally utilized since announcement effects is an important feature in currency trade. Because of technical trading in foreign exchange, the current exchange rate depends on j _max lags of the exchange rate, meaning that the model has j _max+1 rational expectations equilibria, where several of them are adaptively learnable in the least squares sense. However, since past exchange rates should not affect the current exchange rate when technical trading is absent, it is possible to single out a unique equilibrium among the adaptively learnable equilibria that is economically meaningful. It is worth noting that the model examined can also be viewed as a model for stock price determination in which the forward‐solutions to the model are preferable to the backward‐solutions since the importance of announcement effects is a common characteristic for currency and stock markets.