Bid-offer Spread Research Articles

INFORMATION-BASED TRADING

We consider a pair of traders in a market where the information available to the second trader is a strict subset of the information available to the first trader. The traders make prices based on information concerning a security that pays a random cash flow at a fixed time T in the future. Market information is modeled in line with the scheme of Brody, Hughston, and Macrina. The risk-neutral distribution of the cash flow is known to the traders, who make prices with a fixed multiplicative bid-offer spread and report their prices to a game master who declares that a trade has been made when the bid price of one of the traders crosses the offer price of the other. We prove that the value of the first trader’s position is strictly greater than that of the second. The results are analyzed by use of simulation studies and generalized to situations where (a) there is a hierarchy of traders, (b) there are multiple successive trades, and (c) there is inventory aversion. In these settings, we show that information is superior to strategy.

Nonlocal Diffusions and the Quantum Black-Scholes Equation: Modelling the Market Fear Factor

In this paper, we establish a link between quantum stochastic processes, and nonlocal diffusions. We demonstrate how the non-commutative Black-Scholes equation of Accardi & Boukas (Luigi Accardi, Andreas Boukas, 'The Quantum Black-Scholes Equation', Jun 2007, available at arXiv:0706.1300v1) can be written in integral form. This enables the application of the Monte-Carlo methods adapted to McKean stochastic differential equations (H. P. McKean, 'A class of Markov processes associated with nonlinear parabolic equations', Proc. Natl. Acad. Sci. U.S.A., 56(6):1907-1911, 1966) for the simulation of solutions. We show how unitary transformations can be applied to classical Black-Scholes systems to introduce novel quantum effects. These have a simple economic interpretation as a market `fear factor', whereby recent market turbulence causes an increase in volatility going forward, that is not linked to either the local volatility function or an additional stochastic variable. Lastly, we extend this system to 2 variables, and consider Quantum models for bid-offer spread dynamics.

Liquidity and risk premia in electricity futures

Research on electricity futures markets has to date not explored the role that market liquidity may play in determining risk premia. Further, no detailed empirical examination of both liquidity and risk premia in the New Zealand electricity futures market are discernible. Using data from October 2009 to December 2015, we address these gaps in the literature. We find that liquidity has been gradually increasing and that a policy intervention to impose a maximum bid-offer spread was associated with liquidity-enhancing structural breaks, but this was evident only in the nearest-to-maturity futures contracts. Further, we develop models to explain risk premia that include a range of risk factors, which we categorise as either statistical, physical market, production cost or liquidity variables. From this analysis, we document significant time-varying premia that are driven by potentially inefficient behaviour. Finally, we find that liquidity risk does affect risk premia, but generally only in the case of longer-dated futures.

Nonlocal Diffusions and the Quantum Black-Scholes Equation: Modelling the Market Fear Factor

In this paper, we establish a link between quantum stochastic processes, and non-local diffusions. We demonstrate how the non-commutative Black-Scholes equation of Accardi & Boukas (Luigi Accardi, Andreas Boukas, The Quantum Black-Scholes Equation, Global Journal of Pure and Applied Mathematics, vol.2, no.2, pp.155-170, 2006) can be written in integral form. This enables the application of the Monte-Carlo methods adapted to McKean stochastic differential equations for the simulation of solutions. We show how unitary transformations can be applied to classical Black-Scholes systems to introduce novel quantum effects. These have a simple economic interpretation as a market 'fear factor', whereby recent market turbulence causes an increase in volatility going forward, that is not linked to either the local volatility function or an additional stochastic variable. Lastly, we extend this system to 2 variables, and consider Quantum models for bid-offer spread dynamics.

Optimal Microstructure Trading with a Long-Term Utility Function

We combine Almgren--Chriss optimal execution with market microstructure in a framework where passive (joining the queue in a limit order book) or aggressive (willing to cross the bid-offer spread) modes of execution are allowed. To achieve this, we represent the Almgren--Chriss strategy within the framework of Hamiltonian dynamics. We then show that if a risk-neutral agent has expected returns equal to Hamilton's generalized momenta, then such agent repeatedly solving a myopic wealth-maximization problem reproduces the Almgren and Chriss solution. Hence the vector of generalized momenta, p, represents effective microstructure alphas, and also is the gradient of the Bellman value function. We demonstrate that our formulation is computationally efficient and provide a practical algorithm, accompanied by a numerical example which illustrates what can go wrong in the naive approach.

Do Information Releases Diminish Equity Bid-Offer Spreads?

Stock market makers are afraid that informed insiders will take advantage of them in trade. To protect themselves, they may increase the bid-offer spread to include a fee for the adverse selection risk . If set correctly, market makers will share in profits from others trading on private information and can distribute the remaining costs among other market participants. If market makers protect themselves this way, then when the risk of informed trading is relatively low, the bid-offer spread should decline. The risk of informed trading will be relatively low when the difference in public and private information shrinks. Filings with the Securities and Exchange Commission (SEC) and conference calls where corporate earnings are announced and discussed should be events that diminish this difference. Because smaller companies attract less scrutiny, they may experience relatively larger changes in this information distance after these releases. This paper finds weak evidence that spreads diminish when this information is released and a weak size effect. It hypothesizes that the bid-offer spread seems to the spread is smaller than has previously been estimated does or possibly does not exist. Estimates of this spread are actually a statistical illusion created by the structural form of earlier estimation techniques.

Investigating the determinants of dividend policy in emerging markets using a combination of exploratory variables

s. The authors analyze the factors causing dividend policy by utilizing agency cost theory of dividend and transaction cost of dividend by using blue chips companies stock listed in the Indonesian Stock Exchange (IDX) from 2004-2013. They also examine the transaction costs of bid-offer spread and commission as the proxies with agency cost factors of insider ownership and shareholder dispersion. The authors observe that the independent variables affected the dividend policy simultaneously. In addition, they find that the bid-offer spread as a new proxy also had significant effects on the dividend policy

Liquidity and Risk Premia in Electricity Futures

Research on electricity futures markets has to date not explored the role that market liquidity may play in determining risk premia. Further, no detailed empirical examination of both liquidity and risk premia in the New Zealand electricity futures market are discernible. Using data from October 2009 to December 2015, we address these gaps in the literature. We find that liquidity has been gradually increasing and that a policy intervention to impose a maximum bid-offer spread was associated with liquidity-enhancing structural breaks, but this was evident only in the nearest-to-maturity futures contracts. Further, we develop models to explain risk premia that include a range of risk factors which we categorise as either statistical, physical market, production cost, investor behaviour or liquidity variables. From this analysis, we document significant time-varying premia which are driven by potentially inefficient behaviour. Finally, we find that liquidity risk does affect risk premia, but generally only in the case of longer-dated futures.

Futures Convexity Adjustment with Continuously and Discretely Compounded Rates

With analytical results we quality and quantify the difference between futures convexity adjustment for continuously and discretely compounded forward rates, respectively. We find that the use of continuously compounded rates can underestimate the futures convexity adjustment by more than the typical bid-offer spread in a liquid market. Analytical formulas for futures convexity adjustment are derived. The Ho-Lee model is used as the calculation framework.

Algorithmic Trading vs. Bid-Offer Spreads, Volatility, and the Distribution of Profits and Losses: A Simulation

Algorithmic trading leads to contradictory conclusions of market participants and observers: While the former blame it to break the market, the latter find it makes it better. To explain these contradictory views, we create a few-type market simulation in a discrete-time, one-asset world. We analyse both the observable factors average bid-offer spread and volatility as well as the unobservable distribution of profits and losses of the market participants. We conclude that regarding HFT, market observers and market participants talk at cross-purposes.

Depicting the Bid-Offer Spread

In a number of financial market texts the bid-offer spread in flow markets is not well depicted. In such markets the demand and supply curves to the left of the equilibrium point cannot exist. This article offers an alternative depiction: only the curves to the right of the equilibrium point exist and the spread is the differential between the highest bid (the superior) price on the demand curve and the lowest (the superior) price on the supply curve. There are inferior bid and offer prices, represented by the downward-sloping demand curve and upward-sloping supply curve, respectively. The alternative depiction offered applies to both quote-driven and order-driven markets.

Measuring Changes in Liquidity Using the Bid-Offer Price Proxy: Determinants of Liquidity in the United Kingdom Gilt Market

Financial market liquidity is an important yardstick of value for investors and central monetary authorities. Secondary market liquidity itself cannot be observed directly and is instead measured using a number of different proxies. The most common proxy is the asset bid-off price spread. In this study we conduct time series analysis of the bid-offer spread in order to ascertain if the level of liquidity in a specified market has improved over a period of time. The market we select is the United Kingdom government bond market or gilt market. During the 1990s the UK monetary authorities introduced a number of structural reforms in the gilt market, designed to improve secondary market liquidity. We measure the success of the reforms by attempting to determine if liquidity levels improved in the post-reform period, via the examination of the bid-offer spread. We examine the determinants of this proxy measure, and estimate which of the explanatory variables carries the greatest weight in influencing liquidity levels. We conclude that a number of the independent variables that we examined, including bond issue size and maturity, are found to be significant determinants of liquidity. We conclude further that similar structural reforms should be considered by other central monetary authorities wishing to improve bond market liquidity levels, and that the determinant factors we cite should be reviewed during periods of market correction, when liquidity levels decrease.

Regulated Technology Diffusion: The SEC and the Impact of 'Penny Pricing' in Electronic Options Trading

The Securities Exchange Commission (SEC) implemented the first phase of a 'penny pricing' pilot in the exchange-traded equity options market in February 2007. The initial phase of this trial required the six United States options exchanges to reduce the minimum bid-offer spread from five or ten cents to a penny for the options corresponding to thirteen underlying equity securities. The catalyst for this pricing change was the improved electronic capabilities of the exchanges. Over the course of the preceding decade, the exchanges invested in the development of electronic trading systems that allowed for more efficient quoting and trading of options securities. The SEC's mandated pricing change effectively redistributes the gains of innovation from the exchanges' market makers to individual investors. his paper analyses the market impact of the Penny Pilot and highlights the SEC's central role in shaping the options market's innovations and competitive environment. Beyond a reduction in bid-offer spreads, the pricing pilot has stimulated a variety of changes in trading dynamics and market structure. These repercussions include thinner markets, changes in market maker fee structures, the introduction of alternative trading venues, and incentives for the exchanges to prioritize further technological innovation.

Measuring Bond Market Liquidity: Devising A Composite Aggregate Liquidity Score

The importance of liquidity in financial markets is emphasised strongly in the academic literature. There is more than one definition of liquidity, which can lead to confusion when attempting to measure liquidity levels. Hence liquidity is often measured through the use of proxy indicators such as the bid-offer spread. No single measure is completely satisfactory, and the use of proxy measures renders comparison across markets difficult. Our objective is to devise a composite aggregate measure of liquidity that makes use of a range of market factors, and which is applicable to any financial market. This study considers United Kingdom gilt securities during 1993–2002, a period of structural reform in the market. We devise a transparent, accessible and easy-to-implement method to measure liquidity level in a financial market, using an aggregate scoring system. This adopts a composite methodology, using components selected on the basis of their relative importance to promoting liquidity. Our research suggests that market liquidity improved in the gilt market during our observation period. Furthermore, the measurement methodology we propose may be employed by institutional investors to measure liquidity in any financial market, and enables them to make comparisons across different markets prior to making the investment decision. <b>TOPICS:</b>Statistical methods, VAR and use of alternative risk measures of trading risk, exchanges/markets/clearinghouses

FORWARD-RATE VOLATILITIES AND THE SWAPTION MATRIX: WHY NEITHER TIME-HOMOGENEITY NOR TIME-DEPENDENCE ARE ENOUGH

This work presents the first systematic analysis of the whole swaption matrix by fitting a parsimonious, nonlinear, financially-inspired volatility model to market data. The study uses several years of data spanning period of major market volatility. We find that the quality of the fits is good (on average of the same magnitude as the bid-offer spread), and better when a displaced-diffusion approach is chosen, but some systematic shortcomings are observed and discussed. The analysis suggests that a two-regime Markov chain approach may be more successful and better financially motivated. More generally, the present study highlights the shortcomings of purely time-dependent or time-homogenous approaches. These findings should be applicable to other option markets as well. Finally, we find that the present (nonlinear) model vastly outperforms PCA-based approaches when in comes to predicting moves in implied volatilities.

Bounding Bermudan swaptions in a swap-rate market model

We develop a new method for finding upper bounds for Bermudan swaptions in a swap-rate market model. By comparing with lower bounds found by exercise boundary parametrization, we find that the bounds are well within bid-offer spread. As an application, we study the dependence of Bermudan swaption prices on the number of instantaneous factors used in the model. We also establish an equivalence with LIBOR market models and show that virtually identical lower bounds for Bermudan swaptions are obtained.

Non-Equilibrium Patterns in the Space of the Stock Market Prices

Using a phenomenological approach, we analyse the formation and the propagation of the patterns (or ‘dissipative structures’) in the stock market, the spatial coordinate being the bid-offer spread y, as a function of which the spectrum φ of deals is modelled. The stock market will be considered a distributed active medium that is a set of active elements (the brokers) interacting with others through deals (typically a diffusion process). The physical model used is the reaction-diffusion model. The reactive part of the reaction-diffusion equation is developed from a hot-spot mechanism, with a characteristic jump when φ passes the critical value φc. Solving the stationary equation according to the Dirichlet boundary conditions, we find the ‘hot deals’ regions, meaning regions of speculative transactions which can be considered ‘dissipation’ as they do not contribute to the gross national product.

The Microstructure of Currency Markets: An Empirical Model of Intra-day Return and Bid-Ask Spread Behavior

This paper analyzes the intra-day relationship between bid-ask spreads and “market” return volatility for U.S. Dollar/Deutschemark quotes. We are able to identify a statistically and economically significant “Reverse U-shaped” pattern in the bid-offer spread in 1996. Tests of the stability and ordering of “market” volatility, performed across several different fractions of the day, reveal that variances of intra-day returns are heterogeneous and ordered, declining around the Asian lunch break, increasing steadily during the London morning trading hours, peaking at the opening of New York to subsequently fall with the closing of the European markets. Results also indicate that “market” volatility is significantly higher during intra-day versus overnight periods. Then, we introduce a structural model that attempts to explain those empirical regularities by capturing some currency-specific features of the data: possibly asymmetric and stochastic trading cost structure, discrete directional updates and parameters’ temporal heterogeneity, and by relating the bid-ask spread to different sources of random noise. We evaluate these parameters via GMM using a set of convenient unconditional intra-day moments implied by the basic configuration of the model. Analysis of the resulting estimated patterns reveals that trading costs play a significant role in explaining the intra-day variability of bid and offer currency returns. Inventory considerations appear to be more relevant in the trading morning, while the perceived risk of arrival of informed trades seems more likely to affect the dealers’ cost structure in the afternoon. The contribution of the “true” currency risk to the total variability of posted bid and ask quotes’ returns is not surprisingly highest with the opening of the European markets.

Scaling Laws for the Market Microstructure of the Interdealer Broker Markets

We discuss a series of simple models for microstructure of a double auction without intermediaries. We specialize to those markets, such as interdealer broker markets, which are dominated by professional traders, who trade mainly through limit orders, watch markets closely, and move their limit order prices frequently. We model these markets as a set of buyers and a set of sellers, whose numbers vary in time, and who diffuse in price space and interact through an annihilation interaction. We seek to compute the purely statistical effects of the presence of large numbers of traders, as scaling laws on various measures of liquidity, and to this end we allow our model very few parameters. We find that the bid-offer spread scales as 1 over the square root of the deal rate. In addition we investigate the scaling of other intuitive relationships, such as the relationship between the fluctuations of the best bid/offer and the density of buyers and sellers. We then study this model and its scaling laws under the influence of random disturbances to trader drift, volatility, and entrance rate. We also study possible extensions to the model, such as the addition of market order traders, and an interaction that models momentum-type trading. Finally, we discuss how simulations may be carried out to study scaling in all of these settings, and how the models may be tested in actual markets.

Calibrating Libor Market Models

The Libor Market Models arise from the general multi-factor Heath-Jarrow-Morton interest rate model. The Libor Market Models assume that, say, 3 months simple rates are log-normal. With pricing formulae for caps/floors and swaptions this makes the model easy to calibrate for a specific choice of volatility function. We describe how to calibrate the model using a non-parametric volatility function. We apply a smoothness criteria to the quality of fit used in calibration as erratic volatilities otherwise result from the calibration. We perform numerical studies using real market data from several markets to check the robustness of the implementation towards changes in model/calibration parameters. The implementation is indeed very robust and market quotes are matched within bid-offer spread.