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Showing papers in "Quantitative Finance in 2013"


Journal ArticleDOI
TL;DR: In this paper, the authors introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 and 2 for a single asset and a pair of assets.
Abstract: We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point pro- cesses and relies on linear self and mutually exciting stochastic inten- sities as introduced by Hawkes. We associate a counting process with the positive and negative jumps of an asset price. By coupling suitably the stochastic intensities of upward and downward changes of prices for several assets simultaneously, we can reproduce microstructure noise (i.e. strong microscopic mean reversion at the level of seconds to a few minutes) and the Epps effect (i.e. the decorrelation of the increments in microscopic scales) while preserving a standard Brownian diffusion behaviour on large scales. More effectively, we obtain analytical closed-form formulae for the mean signature plot and the correlation of two price increments that enable to track across scales the effect of the mean-reversion up to the diffusive limit of the model. We show that the theoretical results are consistent with empirical fits on futures Euro-Bund and Euro-Bobl in several situations.

315 citations


Journal ArticleDOI
TL;DR: A survey of empirical and theoretical studies of limit order books can be found in this article. But, the authors highlight several key unresolved questions about LOBs, and also illustrate that many such models poorly resemble real LBOs and that several well-established empirical facts have yet to be reproduced satisfactorily.
Abstract: Limit order books (LOBs) match buyers and sellers in more than half of the world’s financial markets. This survey highlights the insights that have emerged from the wealth of empirical and theoretical studies of LOBs. We examine the findings reported by statistical analyses of historical LOB data and discuss how several LOB models provide insight into certain aspects of the mechanism. We also illustrate that many such models poorly resemble real LOBs and that several well-established empirical facts have yet to be reproduced satisfactorily. Finally, we identify several key unresolved questions about LOBs.

216 citations


Journal ArticleDOI
TL;DR: In this paper, the authors propose a framework for studying optimal market-making policies in a limit order book (LOB) and model the bid-ask spread of the LOB by a tick-valued continuous-time Markov chain.
Abstract: We propose a framework for studying optimal market-making policies in a limit order book (LOB). The bid–ask spread of the LOB is modeled by a tick-valued continuous-time Markov chain. We consider a small agent who continuously submits limit buy/sell orders at best bid/ask quotes, and may also set limit orders at best bid (resp. ask) plus (resp. minus) a tick for obtaining execution order priority, which is a crucial issue in high-frequency trading. The agent faces an execution risk since her limit orders are executed only when they meet counterpart market orders. She is also subject to inventory risk due to price volatility when holding the risky asset. The agent can then also choose to trade with market orders, and therefore obtain immediate execution, but at a less favorable price. The objective of the market maker is to maximize her expected utility from revenue over a short-term horizon by a trade-off between limit and market orders, while controlling her inventory position. This is formulated as a mi...

157 citations


Journal ArticleDOI
TL;DR: Kahneman as discussed by the authors argued that the very same biological machinery that enables us to reason fast and slow is also the same machinery that allows us to think fast and slowly, which is the same mechanism that enables humans to reason quickly and slow.
Abstract: Thinking, Fast and Slow, by D. Kahneman, Farrar, Straus & Giroux, New York (2011), 499 pp., $30. ISBN-10 0385676514, ISBN-13 978-0385676519 The very same biological machinery that enables us to rea...

118 citations


Journal ArticleDOI
TL;DR: In this article, a mathematical definition of fragility and antifragility is proposed, defined as negative or positive sensitivity to a semi-measure of dispersion and volatility, and examined the link to nonlinear effects.
Abstract: We provide a mathematical definition of fragility and antifragility as negative or positive sensitivity to a semi-measure of dispersion and volatility (a variant of negative or positive "vega") and examine the link to nonlinear effects. We integrate model error (and biases) into the fragile or antifragile context. Unlike risk, which is linked to psychological notions such as subjective preferences (hence cannot apply to a coffee cup) we offer a measure that is universal and concerns any object that has a probability distribution (whether such distribution is known or, critically, unknown). We propose a detection of fragility, robustness, and antifragility using a single "fast-and-frugal", model-free, probability free heuristic that also picks up exposure to model error. The heuristic lends itself to immediate implementation, and uncovers hidden risks related to company size, forecasting problems, and bank tail exposures (it explains the forecasting biases). While simple to implement, it improves on stress testing and bypasses the cillib flaws in Value-at-Risk.

92 citations


Journal ArticleDOI
TL;DR: In this article, the pointwise regularity of multifractional Brownian motion, assumed as a model of stock price dynamics, is estimated for three stock indices: the Dow Jones Industrial Average, the FTSE 100 and the Nikkei 225.
Abstract: This paper deals with the problem of estimating the pointwise regularity of multifractional Brownian motion, assumed as a model of stock price dynamics. We (a) correct the shifting bias affecting a class of absolute moment-based estimators and (b) build a data-driven algorithm in order to dynamically check the local Gaussianity of the process. The estimation is therefore performed for three stock indices: the Dow Jones Industrial Average, the FTSE 100 and the Nikkei 225. Our findings show that, after the correction, the pointwise regularity fluctuates around 1/2 (the sole value consistent with the absence of arbitrage), but significant deviations are also observed.

82 citations


Journal ArticleDOI
TL;DR: McGrayne et al. as mentioned in this paper argued that the scientific world is not immune from having different schools of thought or attitudes or attitudes, and pointed out the need for diversity in the scientific community.
Abstract: by Sharon Bertsch McGrayne, Yale University Press, New Haven, CT (2011), 336 pp., $27.50. ISBN 978-0-300-16969-0. The scientific world is not immune from having different schools of thought or attr...

81 citations


Journal ArticleDOI
TL;DR: Wang et al. as discussed by the authors used firm-level data to examine whether investors follow each other into and out of the same industries in China's A-share markets and found that stock return dispersions from the information technology sector play a significant role in explaining the other sectors' herding activity.
Abstract: This paper uses firm-level data to examine whether investors follow each other into and out of the same industries in China’s A-share markets Our study is a significant addition to the literature that investigates herding behaviour in an industry context with asymmetric herding effects with respect to different market states, different stock exchanges, and the role of the information technology sector Using recent daily data from 17 May 2001 through 16 May 2011, we demonstrate strong evidence of industry herding in the A-share markets Evidence further supports that stock return dispersions from the information technology sector play a significant role in explaining the other sectors’ herding activity After examining bull and bear markets, herding is more profound in some sectors during a bull market Finally, industry herding is more prevalent in the Shenzhen stock exchange, while for some sectors in the Shanghai stock exchange herding is more prevalent during a bull market state

67 citations


Journal ArticleDOI
TL;DR: In this article, the authors presented a set of closed-form exact solutions for pricing discretely sampled variance swaps and volatility swaps, based on the Heston stochastic volatility model with regime switching.
Abstract: This study presents a set of closed-form exact solutions for pricing discretely sampled variance swaps and volatility swaps, based on the Heston stochastic volatility model with regime switching. In comparison with all the previous studies in the literature, this research, which obtains closed-form exact solutions for variance and volatility swaps with discrete sampling times, serves several purposes. (1) It verifies the degree of validity of Elliott et al.'s [Appl. Math. Finance, 2007, 14(1), 41–62] continuous-sampling-time approximation for variance and volatility swaps of relatively short sampling periods. (2) It examines the effect of ignoring regime switching on pricing variance and volatility swaps. (3) It contributes to bridging the gap between Zhu and Lian's [Math. Finance, 2011, 21(2), 233–256] approach and Elliott et al.'s framework. (4) Finally, it presents a semi-Monte-Carlo simulation for the pricing of other important realized variance based derivatives.

65 citations


Journal ArticleDOI
TL;DR: In this paper, the authors performed an empirical study of a set of large institutional orders executed in the US equity market and found that large trades are drawn from a distribution with tail exponent of roughly 3/2 and that market impact approximately increases as the square root of trade duration.
Abstract: We perform an empirical study of a set of large institutional orders executed in the US equity market. Our results validate the hidden order arbitrage theory proposed by Farmer et al. [How efficiency shapes market impact, 2013] of the market impact of large institutional orders. We find that large trades are drawn from a distribution with tail exponent of roughly 3/2 and that market impact approximately increases as the square root of trade duration. We examine price reversion after the completion of a trade, finding that permanent impact is also a square root function of trade duration and that its ratio to the total impact observed at the last fill is roughly 2/3. Additionally, we confirm empirically that the post-trade price reverts to a level consistent with a fair pricing condition of Farmer et al. (2013). We study the relaxation dynamics of market impact and find that impact decay is a multi-regime process, approximated by a power law in the first few minutes after order completion and subsequently ...

65 citations


Journal ArticleDOI
TL;DR: In this article, the authors study the stochastic behavior of the prices and volatilities of a sample of six of the most important commodity markets and compare these properties with those of the equity market.
Abstract: In this paper we study the stochastic behavior of the prices and volatilities of a sample of six of the most important commodity markets and we compare these properties with those of the equity market. we observe a substantial degree of heterogeneity in the behavior of the series. Our findings show that it is inappropriate to treat different kinds of commodities as a single asset class as is frequently the case in the academic literature and in the industry. We demonstrate that commodities can be a useful diversifier of equity volatility as well as equity returns. Options pricing and hedging applications exemplify the economic impacts of the differences across commodities and between model specifications.

Journal ArticleDOI
TL;DR: In this paper, a stochastic volatility market model for which an explicit candidate solution to the problem of maximizing the utility function of terminal wealth is obtained is obtained. And a verification result and a martingale representation of the solution are provided for the Heston model.
Abstract: In this paper, first we study a stochastic volatility market model for which an explicit candidate solution to the problem of maximizing the utility function of terminal wealth is obtained. Applying this result, we present a complete solution for the Heston model, which is a particular case of the general model. A verification result and a martingale representation of the solution are provided for the Heston model. Finally, the same techniques are used to study a stochastic interest rate model and a necessary and sufficient condition for exploding growth is presented.

Journal ArticleDOI
TL;DR: In this article, the authors developed a theory for the market impact of large trading orders, which they call metaorders because they are typically split into small pieces and executed incrementally, and showed that at equilibrium the distribution of trading volume adjusts to reflect information, and dictates the shape of the impact function.
Abstract: We develop a theory for the market impact of large trading orders, which we call metaorders because they are typically split into small pieces and executed incrementally. Market impact is empirically observed to be a concave function of metaorder size, i.e. the impact per share of large metaorders is smaller than that of small metaorders. We formulate a stylized model of an algorithmic execution service and derive a fair pricing condition, which says that the average transaction price of the metaorder is equal to the price after trading is completed. We show that at equilibrium the distribution of trading volume adjusts to reflect information, and dictates the shape of the impact function. The resulting theory makes empirically testable predictions for the functional form of both the temporary and permanent components of market impact. Based on the commonly observed asymptotic distribution for the volume of large trades, it says that market impact should increase asymptotically roughly as the square root ...

Journal ArticleDOI
TL;DR: In this article, the authors investigate the dynamics of the bivariate relationship between gold and silver prices and find that the presence of a fractal structure is measured using statistical techniques based on rescaled range analysis after accommodating short-term autocorrelated innovations in the return process.
Abstract: The price dynamics of gold and silver have long been a matter of popular concern and fascination. The objective of this study is to investigate the dynamics of the bivariate relationship between gold and silver prices. First, we investigate the spread, measured as the price difference between gold and silver trading as a futures contract. Then the presence of a fractal structure is measured using statistical techniques based on rescaled range analysis after accommodating short-term autocorrelated innovations in the return process. To highlight the economic consequences of fractality, we apply trading rules based upon the Hurst coefficient to the time series data. Importantly, we find that these rules out-perform simple buy-hold and moving-average strategies over varying holding periods.

Journal ArticleDOI
TL;DR: Computer trading in financial markets is a natural and inevitable consequence of technological progress, and is almost as old as computers themselves as mentioned in this paper. Computers facilitate basic market activities and are almost as good as computers.
Abstract: Computer trading in financial markets is a natural and inevitable consequence of technological progress, and is almost as old as computers themselves. Computers facilitate basic market activities s...

Journal ArticleDOI
TL;DR: Counterparty Credit Risk is a must-read for anyone interested or involved in counterparty credit risk as mentioned in this paper, and it is one of the first comprehensive, well-written books on this topic.
Abstract: Counterparty Credit Risk is a must-read for anyone interested or involved in counterparty credit risk (CCR); it is one of the first comprehensive, well-written books on this topic, which has become...

Journal ArticleDOI
TL;DR: In this paper, the relationship between gold prices and the U.S. Dollar has been investigated by using spot prices of gold and spot bilateral exchange rates against the Euro and the British Pound to study the pattern of volatility spillovers.
Abstract: We investigate how the relation between gold prices and the U.S. Dollar has been aected by the recent turmoil in financial markets. We use spot prices of gold and spot bilateral exchange rates against the Euro and the British Pound to study the pattern of volatility spillovers. We estimate the bivariate structural GARCH models proposed by Spargoli e Zagaglia (2008) to gauge the causal relations between volatility changes in the two assets. We also apply the tests for change of co-dependence of Cappiello, Gerard and Manganelli (2005). We document the ability of gold to generate stable comovements with the Dollar exchange rate that have survived the recent phases of market disruption. Our findings also show that exogenous increases in market uncertainty have tended to produce reactions of gold prices that are more stable than those of the U.S. Dollar.

Journal ArticleDOI
TL;DR: In this article, a wavelet coherency methodology with simulated confidence bounds was used to examine the short-term and long-term dependencies of the returns for S&P 500 and the SGSICI® commodity index.
Abstract: We utilize wavelet coherency methodology with simulated confidence bounds to examine the short-term and long-term dependencies of the returns for S&P 500 and the S&P GSCI® commodity index. Our results indicate no evidence of co-movement between S&P 500 total return and the S&P GSCI® commodity index total return in the short term, thereby suggesting diversification gains for equity investors. Importantly, this finding encompasses the onset of the current financial crisis. However, long-term diversification benefits, particularly after the onset of the recent financial crisis, are limited. We find, moreover, no consistent evidence of co-movements between S&P 500 and 10 individual sub-indexes of the S&P GSCI® commodity index. Of particular importance, we report weak co-movement of returns between S&P 500 and S&P GSCI® Precious Metals total return and S&P 500 and S&P GSCI® Softs at all frequencies, implying significant diversification gains both for short-term and long-term investors.

Journal ArticleDOI
TL;DR: The geometric Brownian motion assumption for the underlying asset price in the standard Black-Scholes model (1973) is known not to capture the accumulated empirical evidence as mentioned in this paper, and a main drawback of the...
Abstract: The geometric Brownian motion assumption for the underlying asset price in the standard Black–Scholes model (1973) is known not to capture the accumulated empirical evidence. A main drawback of the...

Journal ArticleDOI
TL;DR: In this paper, several statistical issues related to the log-normal continuous cascade model are studied and an approximation theory is developed in the limit of small intermittency λ 2 √ 1, i.e., when the degree of multifractality is small.
Abstract: Multifractal models and random cascades have been successfully used to model asset returns. In particular, the log-normal continuous cascade is a parsimonious model that has proven to reproduce most observed stylized facts. In this paper, several statistical issues related to this model are studied. We first present a quick, but extensive, review of its main properties and show that most of these properties can be studied analytically. We then develop an approximation theory in the limit of small intermittency λ2 ≪ 1, i.e. when the degree of multifractality is small. This allows us to prove that the probability distributions associated with these processes possess some very simple aggregation properties across time scales. Such a control of the process properties at different time scales allows us to address the problem of parameter estimation. We show that one has to distinguish two different asymptotic regimes: the first, referred to as the ‘low-frequency asymptotics’, corresponds to taking a sample who...

Journal ArticleDOI
TL;DR: In this paper, a non-parametric approach to pairs trading based on renko and kagi constructions which originated from Japanese charting indicators and were introduced to academic studies by Pastukhov was proposed.
Abstract: This research proposes a new non-parametric approach to pairs trading based on renko and kagi constructions which originated from Japanese charting indicators and were introduced to academic studies by Pastukhov The method exploits statistical information about the variability of the tradable process The approach does not find a long-run mean of the process and trade towards it like other methods of pairs trading The only assumption we need is that the statistical properties of the spread process volatility remain reasonably constant The theoretical profitability of the method has been demonstrated for the Ornstein–Uhlenbeck process Tests on the daily market data of American and Australian stock exchanges show statistically significant average excess returns ranging from 14 to 36% per month and annualized Sharpe ratio from 15 to 34

Journal ArticleDOI
TL;DR: Plen and Nicola Bruti-Liberati as mentioned in this paper presented numerical methods for stochastic differential equations (SDEs) with jumps via simulation, with the same authors as the present authors.
Abstract: by Eckhard Platen and Nicola Bruti-Liberati, Springer (2010). ISBN 978-3642120572. This book presents numerical methods for stochastic differential equations (SDEs) with jumps via simulation, with ...

Journal ArticleDOI
TL;DR: In this paper, the authors combine GARCH-type models with the extreme value theory to estimate the tails of three financial index returns (S&P 500, FTSE 100 and NIKKEI 225) representing three important financial areas in the world.
Abstract: Although stock prices fluctuate, the variations are relatively small and are frequently assumed to be normally distributed on a large time scale. But sometimes these fluctuations can become determinant, especially when unforeseen large drops in asset prices are observed that could result in huge losses or even in market crashes. The evidence shows that these events happen far more often than would be expected under the generalised assumption of normally distributed financial returns. Thus it is crucial to model distribution tails properly so as to be able to predict the frequency and magnitude of extreme stock price returns. In this paper we follow the approach suggested by McNeil and Frey in 2000 and combine GARCH-type models with the extreme value theory to estimate the tails of three financial index returns – S&P 500, FTSE 100 and NIKKEI 225 – representing three important financial areas in the world. Our results indicate that EVT-based conditional quantile estimates are more accurate than those from c...

Journal ArticleDOI
TL;DR: In this paper, the authors compare the performance of alternative methods for computing non-central chi-square distributions with an externally tested benchmark and present closed-form solutions for computing Greek measures under the unrestricted CEV option pricing model, thus being able to accommodate direct leverage effects and inverse leverage effects.
Abstract: Pricing options and evaluating Greeks under the constant elasticity of variance (CEV) model requires the computation of the non-central chi-square distribution function. In this article, we compare the performance, in terms of accuracy and computational time, of alternative methods for computing such probability distributions against an externally tested benchmark. In addition, we present closed-form solutions for computing Greek measures under the unrestricted CEV option pricing model, thus being able to accommodate direct leverage effects as well as inverse leverage effects that are frequently observed in options markets.

Journal ArticleDOI
TL;DR: In this paper, the authors define set-valued dynamic risk measures on with and with an image space in the power set and deduce primal and dual representations of the risk measures.
Abstract: Set-valued dynamic risk measures are defined on with and with an image space in the power set of . Primal and dual representations of dynamic risk measures are deduced. Definitions of different time consistency properties in the set-valued framework are given. It is shown that the recursive form for multivariate risk measures as well as an additive property for the acceptance sets is equivalent to a stronger time consistency property called multi-portfolio time consistency.

Journal ArticleDOI
TL;DR: Collins and Morten T. Hansen, 2011, 320 pp., $19.79, ISBN: 978-0062120991 as mentioned in this paper. But the authors do not discuss their work.
Abstract: by Jim Collins and Morten T. Hansen, Harper Business (2011), 320 pp., $19.79, ISBN: 978-0062120991. Financial quants and management consultants exist in parallel universes, seemingly without regard...

Journal ArticleDOI
TL;DR: It is shown that a worst-case coherent risk minimization leads to a penalized minimization of the empirical risk estimate, and a simplified version of this paper is applied to the factor model-based CVaR minimization, and it improves on the performance, achieving betterCVaR, turnover, standard deviation and Sharpe ratio than the empirical CVa R minimization and market benchmarks.
Abstract: The conditional value-at-risk (CVaR) has gained growing popularity in financial risk management due to the coherence property and tractability in its optimization. However, optimal solutions to the CVaR minimization are highly susceptible to estimation error of the risk measure because the estimate depends only on a small portion of sampled scenarios. The same is equally true of the other coherent measures. In this paper, by employing robust optimization modelling for minimizing coherent risk measures, we present a simple and practical way for making the solution robust over a certain range of estimation errors. More specifically, we show that a worst-case coherent risk minimization leads to a penalized minimization of the empirical risk estimate. The worst-case risk measure developed in this paper is different from the distributionally worst-case CVaR in Zhu and Fukushima's work of 2009, but these two worst-case risk measures can be simultaneously minimized. Additionally, inspired by Konno, Waki and Yuuk...

Journal ArticleDOI
TL;DR: In this paper, a simple iterative method was proposed to determine the optimal exercise boundary for American options, allowing us to compute the values of American options and their Greeks quickly and accurately.
Abstract: We introduce a simple iterative method to determine the optimal exercise boundary for American options, allowing us to compute the values of American options and their Greeks quickly and accurately. Following Little, Pant and Hou's idea (2000), we derive a new equation for the optimal exercise boundary containing a single integral. The proposed method is an iterative numerical method for finding its solution. Using it, we can calculate the entire optimal exercise boundary in a non-time-recursive way, in contrast to conventional methods. Extensive numerical results indicate that our method is computationally more efficient than the methods currently available, particularly for hedge ratios.

Journal ArticleDOI
TL;DR: This article studied the dependence of the magnitude of rate moves on the level of rates and found a universal relationship that holds across currencies and over a very extended period of time (almost 50 years).
Abstract: We look at the dependence of the magnitude of rate moves on the level of rates, and we find a universal relationship that holds across currencies and over a very extended period of time (almost 50 years). For the very low level of rates, we find a proportional behaviour; for rates of an intermediate level we find that the magnitude of moves becomes independent of the level. The linear dependence resumes, however, for very high rates. We find the results to be very robust across currencies, tenors and time periods. Even the data we have collected for the UK Consol yields going back to the XIX century conform closely to the same pattern. We discuss the importance of these findings for several theoretical and practical applications.

Journal ArticleDOI
TL;DR: In this paper, the authors show that log-periodic power-law (LPPL) functions are intrinsically very hard to fit to time series and that the fitting procedure must take into account the sloppy nature of this kind of model.
Abstract: We show that log-periodic power-law (LPPL) functions are intrinsically very hard to fit to time series. This comes from their sloppiness, the squared residuals depending very much on some combinations of parameters and very little on other ones. The time of singularity that is supposed to give an estimate of the day of the crash belongs to the latter category. We discuss in detail why and how the fitting procedure must take into account the sloppy nature of this kind of model. We then test the reliability of LPPLs on synthetic AR(1) data replicating the Hang Seng 1987 crash and show that even this case is borderline regarding the predictability of the divergence time. We finally argue that current methods used to estimate a probabilistic time window for the divergence time are likely to be over-optimistic.