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Showing papers on "Algorithmic trading published in 2010"


Posted Content
TL;DR: Based on within-stock variation, it is found that algorithmic trading and liquidity are positively related and quoted and effective spreads narrow under autoquote and adverse selection declines, indicating that algorithms do causally improve liquidity.
Abstract: Algorithmic trading has sharply increased over the past decade Does it improve market quality, and should it be encouraged? We provide the first analysis of this question The NYSE automated quote dissemination in 2003, and we use this change in market structure that increases algorithmic trading as an exogenous instrument to measure the causal effect of algorithmic trading on liquidity For large stocks in particular, algorithmic trading narrows spreads, reduces adverse selection, and reduces trade-related price discovery The findings indicate that algorithmic trading improves liquidity and enhances the informativeness of quotes

1,190 citations


Journal ArticleDOI
TL;DR: The US equity market has changed dramatically in recent years Increasing automation and the entry of new trading platforms has resulted in intense competition among trading platforms Despite these changes, traders still face the same challenges as before They seek to minimize the total cost of trading including commissions, bid/ask spreads, and market impact as discussed by the authors.
Abstract: The US equity market changed dramatically in recent years Increasing automation and the entry of new trading platforms has resulted in intense competition among trading platforms Despite these changes, traders still face the same challenges as before They seek to minimize the total cost of trading including commissions, bid/ask spreads, and market impact New technologies allow traders to implement traditional strategies more effectively For example, dark pools and indications of interest are just an updated form of tactics that NYSE floor traders used search for counterparties while minimizing the exposure of their clients’ trading interest to prevent front running Virtually every measurable dimension of US equity market quality has improved Execution speeds and retail commission have fallen Bid-ask spreads have fallen and remain low, although they spiked upward along with volatility during the recent financial crisis Market depth has increased Studies of institutional transactions costs find US costs among the lowest in the world Unlike during the Crash of 1987, the US equity market mechanism handled the increase in trading volume and volatility without disruption However, our markets lack a market-wide risk management system that would deal with computer generated chaos in real time, and our regulators should address this “Make or take” pricing, the charging of access fees to market orders that “take” liquidity and paying rebates to limit orders that “make” liquidity, causes distortions that should be corrected Such charges are not reflected in the quotations used for the measurement of best execution Direct access by non-brokers to trading platforms requires appropriate risk management Front running orders in correlated securities should be banned

231 citations


Journal ArticleDOI
TL;DR: In this article, the authors assess empirically whether speculation affects oil price dynamics and find strong evidence that oil price shifts are negatively related to stock price and exchange rate changes and that a complex web of time-varying first and second order conditional moment interactions affects both the CAPM and feedback trading components of the model.

222 citations


Journal ArticleDOI
TL;DR: This article found that pairs trading performs strongly during periods of prolonged turbulence, including the recent global financial crisis, and that alternative algorithms combined with other measures enhance trading profits considerably, by 22 bps a month for bank stocks.
Abstract: Despite confirming the continuing downward trend in profitability of pairs trading, this study found that the strategy performs strongly during periods of prolonged turbulence, including the recent global financial crisis. Moreover, alternative algorithms combined with other measures enhance trading profits considerably, by 22 bps a month for bank stocks.

208 citations


Journal ArticleDOI
TL;DR: In this article, the authors examined the performance of trend-following trading strategies in commodity futures markets using a monthly dataset spanning 48 years and 28 markets, and found that all parameterizations of the dual moving average crossover and channel strategies that they implement yield positive mean excess returns net of transactions costs in at least 22 of the 28 markets.
Abstract: This paper examines the performance of trend-following trading strategies in commodity futures markets using a monthly dataset spanning 48 years and 28 markets. We find that all parameterizations of the dual moving average crossover and channel strategies that we implement yield positive mean excess returns net of transactions costs in at least 22 of the 28 markets. When we pool our results across markets, we show that all of the trading rules earn hugely significant positive returns that prevail over most subperiods of the data as well. These results are robust with respect to the set of commodities the trading rules are implemented with, distributional assumptions, data-mining adjustments and transactions costs, and help resolve divergent evidence in the extant literature regarding the performance of momentum and pure trend-following strategies that is otherwise difficult to explain.

207 citations


Journal ArticleDOI
Frank Zhang1
TL;DR: In this article, the authors examined the implication of high-frequency trading for stock price volatility and price discovery in the U.S. capital market, and found that highfrequency trading is negatively related to the market's ability to incorporate information about firm fundamentals into asset prices.
Abstract: High-frequency trading has become a dominant force in the U.S. capital market, accounting for over 70% of dollar trading volume. This study examines the implication of high-frequency trading for stock price volatility and price discovery. I find that high-frequency trading is positively correlated with stock price volatility after controlling for firm fundamental volatility and other exogenous determinants of volatility. The positive correlation is stronger among the top 3,000 stocks in market capitalization and among stocks with high institutional holdings. The positive correlation is also stronger during periods of high market uncertainty. Furthermore, I find that high-frequency trading is negatively related to the market’s ability to incorporate information about firm fundamentals into asset prices. Stock prices tend to overreact to fundamental news when high-frequency trading is at a high volume. Overall, this paper demonstrates that high-frequency trading may potentially have some harmful effects for the U.S. capital market.

187 citations


Journal ArticleDOI
TL;DR: The authors review, synthesize, and critique the capital market literature examining trading volume around earnings announcements and other financial reports, and suggest directions for future research, concluding that existing research just scratches the surface of what trading volume can reveal about the characteristics of financial disclosures and the effects of these disclosures on investors.
Abstract: This paper reviews, synthesizes, and critiques the capital market literature examining trading volume around earnings announcements and other financial reports. Our purposes are to assess what we have learned from examining trading volume around these announcements and to suggest directions for future research. We conclude that researchers have yet to realize the potential Beaver (1968) identified for trading volume to yield unique insights regarding the nature of earnings announcements and other financial reports, and the effects of these announcements on market participants. This state of the literature is attributable to a dearth of volume theory early on, and more recently to a disconnect between theoretical development and empirical research. Thus, we begin by briefly summarizing developments in trading volume theory since Beaver (1968). We also discuss unique measurement challenges in trading volume research, including identifying appropriate proxies for abnormal trading volume and for individual investors’ beliefs. In light of theory and empirical measurement issues, we interpret the current literature and identify directions for future research. We conclude that extant research just scratches the surface of what trading volume can reveal about the characteristics of financial disclosures and the effects of these disclosures on investors.

163 citations


Journal ArticleDOI
TL;DR: In this article, the efficient market hypothesis (EMH) in the market for CO2 emission allowances in Phase I and Phase II of the European Union Emissions Trading Scheme (EU ETS) was tested.

144 citations


Posted ContentDOI
01 Apr 2010
TL;DR: In this article, a time series of the aggregate commission rate of NYSE trading for the period 1980-2003 is developed, and the authors find a positive relation between market returns and the aggregate rate.
Abstract: A quarterly time series of the aggregate commission rate of NYSE trading for the period 1980-2003 is developed. The aggregate commission rate is of significant size, captures trading cost, and reflects market illiquidity. Consistent with financial theory, I find a positive relation between market returns and the aggregate commission rate. The impact of the aggregate commission rate on market returns survives a number of robustness checks and is significant after controlling for interest-rate factors, trading volume, and the variability of trading volume. Overall, the findings suggest that market-wide liquidity is a state variable important for asset pricing.

127 citations


Journal ArticleDOI
TL;DR: In this paper, the authors derived distributions of transaction prices in limit order markets populated by low frequency traders (humans) before and after the entrance of a high frequency trader (machine) and found that the presence of a machine is likely to change the average transaction price, even in the absence of new information.
Abstract: Do high frequency traders affect transaction prices? In this paper we derive distributions of transaction prices in limit order markets populated by low frequency traders (humans) before and after the entrance of a high frequency trader (machine). We find that the presence of a machine is likely to change the average transaction price, even in the absence of new information. We also find that in a market with a high frequency trader, the distribution of transaction prices has more mass around the center and thinner far tails. With a machine, mean intertrade duration decreases in proportion to the increase in the ratio of the human order arrival rates with and without the presence of the machine; trading volume goes up by the same rate. We show that the machine makes positive expected profits by "sniping" out human orders somewhat away from the front of the book. This explains the shape of the transaction price density. In fact, we show that in a special case, the faster humans submit and vary their orders, the more profits the machine makes.

119 citations


Proceedings ArticleDOI
25 Jul 2010
TL;DR: A technique to derive the best offering strategy for a wind power producer in an electricity market that includes various trading floors is presented, which translates into a linear programming problem of moderate size which is readily solvable using commercially available software.
Abstract: This panel presentation is based on paper “J. M. Morales, A. J. Conejo, J. Perez-Ruiz, Short-Term Trading for a Wind Power Producer. IEEE Transactions on Power Systems, in press, 2010.” It presents a technique to derive the best offering strategy for a wind power producer in an electricity market that includes several trading floors. Uncertainty pertaining to wind availability, market prices at the different trading stages, and balancing energy needs are properly taken into account. Risk on profit variability is suitably controlled at the cost of a small reduction in expected profit. The proposed technique translates into a linear programming problem of moderate size, which is readily solvable using commercially available software.

Posted Content
TL;DR: The daily average foreign exchange market turnover reached $4 trillion in April 2010, 20% higher than in 2007 as mentioned in this paper, attributed largely to increased trading activity of other financial institutions, which contributed 85% of the higher turnover.
Abstract: Daily average foreign exchange market turnover reached $4 trillion in April 2010, 20% higher than in 2007. Growth owed largely to the increased trading activity of “other financial institutions”, which contributed 85% of the higher turnover. Within this customer category, the growth is driven by high-frequency traders, banks trading as clients of the biggest dealers, and online trading by retail investors. Electronic trading has been instrumental to this increase, particularly algorithmic trading.

Patent
15 Mar 2010
TL;DR: In this paper, a combination passive/aggressive trading strategy is used to execute trades of lists of securities or blocks of a single security within a desired time frame while taking advantage of dynamic market movement to realize price improvement.
Abstract: A computer-implemented system and method for executing trades of financial securities according to a combination passive/aggressive trading strategy that reliably executes trades of lists of securities or blocks of a single security within a desired time frame while taking advantage of dynamic market movement to realize price improvement for the trade within the desired time frame. A passive trading agent executes trades at advantageous prices by floating portions of the order at the bid or ask to maximize exposure to the inside market and attract market orders. An aggressive agent opportunistically takes liquidity as it arises, setting discretionary prices in accordance with historical trading data of the specified security.

Journal ArticleDOI
TL;DR: A dynamic model for intra-daily volumes that captures salient features of the series such as time series dependence, intra- daily periodicity and volume asymmetry is proposed.
Abstract: The explosion of algorithmic trading has been one of the most prominent recent trends in the financial industry. Algorithmic trading consists of automated trading strategies that attempt to minimize transaction costs by optimally placing orders. The key ingredient of many of these strategies are intra-daily volume proportions forecasts. This work proposes a dynamic model for intra-daily volumes that captures salient features of the series such as time series dependence, intra-daily periodicity and volume asymmetry. Moreover, we introduce a loss functions for the evaluation of proportions forecasts which retains both an operational and information theoretic interpretation. An empirical application on a set of widely traded index ETFs shows that the proposed methodology is able to significantly outperform common forecasting methods and delivers significantly more precise predictions for Volume Weighted Average Price trading.

Journal ArticleDOI
01 Sep 2010
TL;DR: In this paper, the authors present an efficient event processing platform for high-frequency and low-latency algorithmic trading, called fpga-to-pss (Toronto Publish/Subscribe System Family).
Abstract: In this demo, we present fpga-ToPSS (Toronto Publish/Subscribe System Family), an efficient event processing platform for high-frequency and low-latency algorithmic trading. Our event processing platform is built over reconfigurable hardware---FPGAs---to achieve line-rate processing. Furthermore, our event processing engine supports Boolean expression matching with an expressive predicate language that models complex financial strategies to autonomously buy and sell stocks based on real-time financial data.

Journal ArticleDOI
TL;DR: In this article, a trading strategy combining mean reversion and momentum in foreign exchange markets is proposed, which was originally designed for equity markets, but it also generates abnormal returns when applied to uncovered interest parity deviations for five countries.
Abstract: The literature on equity markets documents the existence of mean reversion and momentum phenomena. Researchers in foreign exchange markets find that foreign exchange rates also display behaviors akin to momentum and mean reversion. This paper implements a trading strategy combining mean reversion and momentum in foreign exchange markets. The strategy was originally designed for equity markets, but it also generates abnormal returns when applied to uncovered interest parity deviations for five countries. I find that the pattern for the positions thus created in the foreign exchange markets is qualitatively similar to that found in the equity markets. Quantitatively, this strategy performs better in foreign exchange markets than in equity markets. Also, it outperforms traditional foreign exchange trading strategies, such as carry trades and moving average rules.

Journal ArticleDOI
TL;DR: In this paper, the authors employ a hidden Markov model to examine how the intra-day dynamics of the stock market have changed, and how to use this information to develop trading strategies at high frequencies.
Abstract: Algorithmic Trading (AT) and High Frequency (HF) trading, which are responsible for over 70\% of US stocks trading volume, have greatly changed the microstructure dynamics of tick-by-tick stock data. In this paper we employ a hidden Markov model to examine how the intra-day dynamics of the stock market have changed, and how to use this information to develop trading strategies at high frequencies. In particular, we show how to employ our model to submit limit-orders to profit from the bid-ask spread and we also provide evidence of how HF traders may profit from liquidity incentives (liquidity rebates). We use data from February 2001 and February 2008 to show that while in 2001 the intra-day states with shortest average durations (waiting time between trades) were also the ones with very few trades, in 2008 the vast majority of trades took place in the states with shortest average durations. Moreover, in 2008 the states with shortest durations have the smallest price impact as measured by the volatility of price innovations.

Journal ArticleDOI
TL;DR: In this article, the authors use two extremely liquid S&P 500 ETFs to analyze the prevailing trading conditions when mispricing allowing arbitrage opportunities is created, and they show that their minor differences are not responsible for the misprice.
Abstract: We use two extremely liquid S&P 500 ETFs to analyze the prevailing trading conditions when mispricing allowing arbitrage opportunities is created. While these ETFs are not perfect substitutes, we show that their minor differences are not responsible for the mispricing. Spreads increase just before arbitrage opportunities, consistent with a decrease in liquidity. Order imbalance increases as markets become more one-sided and spread changes become more volatile which suggests an increase in liquidity risk. The price deviations are economically significant (mean profit of 6.6% p.a. net of spreads) and are followed by a tendency to quickly correct back towards parity.

Journal ArticleDOI
TL;DR: The authors studied the profitability of Covered Interest Parity arbitrage violations and their relationship with market liquidity and credit risk using a novel and unique dataset of tick-by-tick firm quotes for all financial instruments involved in the arbitrage strategy.
Abstract: We study the profitability of Covered Interest Parity (CIP) arbitrage violations and their relationship with market liquidity and credit risk using a novel and unique dataset of tick-by-tick firm quotes for all financial instruments involved in the arbitrage strategy. The empirical analysis shows that positive CIP arbitrage deviations include a compensation for liquidity and credit risk. Once these risk premia are taken into account, small arbitrage profits only accrue to traders who are able to negotiate low trading costs. The results are robust to stale pricing and the nonsynchronous trading occurring in the markets involved in the arbitrage strategy.


Book ChapterDOI
TL;DR: A number of interesting agent-based financial market models have been proposed as mentioned in this paper, which successfully explain some important stylized facts of financial markets, such as bubbles and crashes, fat tails for the distribution of returns and volatility clustering.
Abstract: In the recent past, a number of interesting agent-based financial market models have been proposed. These models successfully explain some important stylized facts of financial markets, such as bubbles and crashes, fat tails for the distribution of returns and volatility clustering. These models, reviewed, for instance, in Chen, Chang, and Du (in press); Hommes (2006); LeBaron (2006); Lux (in press); Westerhoff (2009), are based on the observation that financial market participants use different heuristic trading rules to determine their speculative investment positions. Note that survey studies by Frankel and Froot (1986);Menkhoff (1997);Menkhoff and Taylor (2007); Taylor and Allen (1992) in fact reveal that market participants use technical and fundamental analysis to assess financial markets. Agent-based financial market models obviously have a strong empirical microfoundation.

Journal ArticleDOI
TL;DR: In this article, the authors examine two empirical issues regarding stock liquidity: (1) to what degree are different liquidity proxies correlated and (2) how are different proxies related to stocks' trading characteristics.

Journal ArticleDOI
TL;DR: In this article, the authors examine how high frequency trading is actually used and examine different notions of fairness, such as equal opportunity, fairness of outcomes, and fairness of market participants.
Abstract: Recent concern over "high frequency trading" (HFT) has called into question the fairness of the practice. What does it mean for a financial market to be "fair"? We first examine how high frequency trading is actually used. High frequency traders are often implementing traditional beneficial strategies such as market making and arbitrage, although computers can also be used for manipulative strategies as well. We then examine different notions of fairness. Procedural fairness can be viewed from the perspective of equal opportunity, in which all market participants are treated alike. The same rules apply to HFT as to other traders. Another approach to fairness is in the equality of outcomes. Many HFT strategies are beneficial to other market participants, so one cannot categorically denounce the practice as unfair. Other strategies, for both high and low frequency trading, are not. It is thus important to distinguish between the technology and the use of the technology to make judgments on fairness.

Journal ArticleDOI
TL;DR: Li et al. as discussed by the authors provided an empirical investigation aimed at uncovering the statistical properties of intricate stock trading networks based on the order flow data of a highly liquid stock (Shenzhen Development Bank) listed on Shenzhen Stock Exchange during the whole year of 2003.
Abstract: We provide an empirical investigation aimed at uncovering the statistical properties of intricate stock trading networks based on the order flow data of a highly liquid stock (Shenzhen Development Bank) listed on Shenzhen Stock Exchange during the whole year of 2003. By reconstructing the limit order book, we can extract detailed information of each executed order for each trading day and demonstrate that the trade size distributions for different trading days exhibit power-law tails and that most of the estimated power-law exponents are well within the Levy stable regime. Based on the records of order matching among investors, we can construct a stock trading network for each trading day, in which the investors are mapped into nodes and each transaction is translated as a direct edge from the seller to the buyer with the trade size as its weight. We find that all the trading networks comprise a giant component and have power-law degree distributions and disassortative architectures. In particular, the degrees are correlated with order sizes by a power-law function. By regarding the size of executed order as its fitness, the fitness model can reproduce the empirical power-law degree distribution.

Book ChapterDOI
TL;DR: In this article, the authors focus on the empirical characteristics of prices and volume in stock markets and derive a link between economic fundamentals and the dynamic properties of asset returns and volume, which can be used by all investors to hedge against changes in market conditions.
Abstract: Publisher Summary Trading volume is an important aspect of the economic interactions in financial markets among various investors. Both volume and prices are driven by underlying economic forces, and thus convey important information about the workings of the market. This chapter focuses on the empirical characteristics of prices and volume in stock markets. The interactions between prices and quantities in an equilibrium yield a rich set of implications for any asset pricing model, when an explicit link between economic fundamentals and the dynamic properties of asset returns and volume are derived. By exploiting the relation between prices and volume in the dynamic equilibrium model, one can identify and construct the hedging portfolio, which can be used by all investors to hedge against changes in market conditions. This hedging portfolio has considerable forecast power in predicting future returns of the market portfolio and its abilities to explain cross-sectional variation in expected returns is comparable to other popular risk factors such as market betas, the Fama and French SMB factor, and optimal forecast portfolios. The presence of market frictions, such as transactions costs, can influence the level of trading volume and serve as a bridge between the market microstructure literature and the broader equilibrium asset pricing literature.

28 Oct 2010
TL;DR: The massive increase in trading in commodity derivatives over the past decade has been documented in this paper, showing that the gross market value of OTC trading was an order of magnitude greater than that of organized exchanges and over-the-counter (OTC) trading.
Abstract: This article documents the massive increase in trading in commodity derivatives over the past decade—growth that far outstrips the growth in commodity production and the need for deriva tives to hedge risk by commercial producers and users of commodities. During the past decade, many institutional portfolio managers added commodity derivatives as an asset class to their port folios. This addition was part of a larger shift in portfolio strategy away from traditional equity investment and toward derivatives based on assets such as real estate and commodities. Institu tional investors’ use of commodity futures to hedge against stock market risk is a relatively recent phenomenon. Trading in commodity derivatives also increased along with the rapid expansion of trading in all derivative markets. This trading was directly related to the search for higher yields in a low interest rate environment. The growth was both in organized exchanges and over-thecounter (OTC) trading, but the gross market value of OTC trading was an order of magnitude greater. This growth is important to note because a critical factor in the recent crisis was counterparty failure in OTC trading of mortgage derivatives. (JEL G120, G130, G180)

Posted Content
TL;DR: The experiments show that the boosting approach is able to improve the predictive capacity when indicators are combined and aggregated as a single predictor, and the combination of indicators of different stocks demonstrated to be adequate in order to reduce the use of computational resources, and still maintain an adequate predictive capacity.
Abstract: We propose a multi-stock automated trading system that relies on a layered structure consisting of a machine learning algorithm, an online learning utility, and a risk management overlay. Alternating decision tree (ADT), which is implemented with Logitboost, was chosen as the underlying algorithm. One of the strengths of our approach is that the algorithm is able to select the best combination of rules derived from well-known technical analysis indicators and is also able to select the best parameters of the technical indicators. Additionally, the online learning layer combines the output of several ADTs and suggests a short or long position. Finally, the risk management layer can validate the trading signal when it exceeds a specified non-zero threshold and limit the application of our trading strategy when it is not profitable. We test the expert weighting algorithm with data of 100 randomly selected companies of the S&P 500 index during the period 2003–2005. We find that this algorithm generates abnormal returns during the test period. Our experiments show that the boosting approach is able to improve the predictive capacity when indicators are combined and aggregated as a single predictor. Even more, the combination of indicators of different stocks demonstrated to be adequate in order to reduce the use of computational resources, and still maintain an adequate predictive capacity.

Posted Content
TL;DR: In this paper, the authors study the use of trading strategies and their profitability in experimental asset markets with asymmetrically informed traders and find that insiders make most of their profits from trades which are initiated by their limit orders, especially at the beginning of a period when the change in their fundamental information is large.
Abstract: We study the use of trading strategies and their profitability in experimental asset markets with asymmetrically informed traders. We find that insiders make most of their profits from trades which are initiated by their limit orders -- especially at the beginning of a period and when the change in their fundamental information is large. The average informed lose most with market orders and their losses are highest at the beginning of a period when they can be exploited by insiders. Uninformed traders act as liquidity providers. They place the highest number of limit orders and end up with the market return.

Journal ArticleDOI
TL;DR: The authors found that trading volumes and return volatility are negatively correlated, implying a lack of support for the mixture of distributions hypothesis (MDH), and that short to medium term currency relationships may be dominated by trading dynamics and not by fundamentals.
Abstract: The relationship between trading volume and volatility in foreign exchange markets continues to be of much interest, especially given the higher than expected volatility of returns. Allowing for non-linearities, this paper tests competing hypotheses on the possible relationship between volatility and trading volume using data for three major currency futures contracts denominated in US dollars, namely the British pound, the Canadian dollar and the Japanese yen. We find that trading volumes and return volatility are negatively correlated, implying a lack of support for the mixture of distributions hypothesis (MDH). Using linear and nonlinear Granger causality tests, we document significant lead-lag relations between trading volumes and return volatility consistent with the sequential arrival of information (SAI) hypothesis. These findings are robust and not sample dependent or due to heterogeneity of beliefs as proxied by open interest. Furthermore, our results are insensitive to the modeling approach used to recover volatility measures. Overall, our findings support the contention that short to medium term currency relationships may be dominated by trading dynamics and not by fundamentals.

Proceedings ArticleDOI
06 Apr 2010
TL;DR: In this article, the conditions for viability of spectrum trading markets by considering scenarios with different market structures, number of trading participants and amount of tradable spectrum were determined, and agent-based computational economics (ACE) was used to analyze each market scenario and the behaviors of its participants.
Abstract: Spectrum trading markets are of growing interest to many spectrum management agencies. They are motivated by their desire to increase the use of market based mechanisms for spectrum management and reduce their emphasis on command and control methods. Despite the liberalization of regulations on spectrum trading in some countries, spectrum markets have not yet emerged as a key spectrum assignment component. The lack of liquidity in these markets is sometimes cited as a primary factor in this outcome. This work focuses on determining the conditions for viability of spectrum trading markets by considering scenarios with different market structures, number of trading participants and amount of tradable spectrum. We make use of Agent-Based Computational Economics (ACE) to analyze each market scenario and the behaviors of its participants. Our models indicate that spectrum markets can be viable in a service if sufficient numbers of market participants exist and the amount of tradable spectrum is balanced to the demand. We use the results of this analysis and the characteristics of the viable markets found to make recommendations for the design of spectrum trading markets. Further work will explore more complicated scenarios.