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Heterogeneous agent models in economics and finance
 IN HANDBOOK OF COMPUTATIONAL ECONOMICS (EDS
, 2005
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Agentbased computational finance
 in Handbook of Computational Economics, Agentbased Computational Economics
, 2006
"... This paper surveys research on computational agentbased models used in finance. It will concentrate on models where the use of computational tools is critical in the process of crafting models which give insights into the importance and dynamics of investor heterogeneity in many financial settings. ..."
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Cited by 81 (3 self)
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This paper surveys research on computational agentbased models used in finance. It will concentrate on models where the use of computational tools is critical in the process of crafting models which give insights into the importance and dynamics of investor heterogeneity in many financial settings.
GAUSSIAN MULTIPLICATIVE CHAOS REVISITED
, 807
"... Abstract. In this article, we extend the theory of multiplicative chaos for positive definite functions in Rd of the form f(x) = λ2 + T ln x + g(x) where g is a continuous and bounded function. The construction is simpler and more general than the one defined by Kahane in 1985. As main applicatio ..."
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Abstract. In this article, we extend the theory of multiplicative chaos for positive definite functions in Rd of the form f(x) = λ2 + T ln x + g(x) where g is a continuous and bounded function. The construction is simpler and more general than the one defined by Kahane in 1985. As main application, we give a rigorous mathematical meaning to the KolmogorovObukhov model of energy dissipation in a turbulent flow.
Leverage causes fat tails and clustered volatility. Preprint. Traders’ collective portfolio optimization with transaction costs
"... We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called “value investing”, i.e. systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are normal ..."
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We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called “value investing”, i.e. systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are normally distributed and uncorrelated across time. All this changes when the funds are allowed to leverage, i.e. borrow from a bank, to purchase more assets than their wealth would otherwise permit. During good times competition drives investors to funds that use more leverage, because they have higher profits. As leverage increases price fluctuations become heavy tailed and display clustered volatility, similar to what is observed in real markets. Previous explanations of fat tails and clustered volatility depended on “irrational behavior”, such as trend following. Here instead this comes from the fact that leverage limits cause funds to sell into a falling market: A prudent bank makes itself locally safer by putting a limit to leverage, so when a fund exceeds its leverage limit, it must partially repay its loan by selling the asset. Unfortunately this sometimes happens to all the funds simultaneously when the price is already falling. The resulting nonlinear feedback amplifies large downward price movements. At the extreme this causes crashes, but the effect is seen at every time scale, producing a power law of price disturbances. A standard (supposedly more sophisticated) risk control policy in which individual banks base leverage limits on volatility causes leverage to rise during periods of low volatility, and to contract more quickly when volatility gets high, making these extreme fluctuations even worse.
Stock price jumps: news and volume play a minor role. ArXiv eprints
"... In order to understand the origin of stock price jumps, we crosscorrelate highfrequency time series of stock returns with different news feeds. We find that neither idiosyncratic news nor market wide news can explain the frequency and amplitude of price jumps. We find that the volatility patterns a ..."
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Cited by 26 (4 self)
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In order to understand the origin of stock price jumps, we crosscorrelate highfrequency time series of stock returns with different news feeds. We find that neither idiosyncratic news nor market wide news can explain the frequency and amplitude of price jumps. We find that the volatility patterns around jumps and around news are quite different: jumps are followed by increased volatility, whereas news tend on average to be followed by lower volatility levels. The shape of the volatility relaxation is also markedly different in the two cases. Finally, we provide direct evidence that large transaction volumes are not responsible for large price jumps. We conjecture that most price jumps are induced by order flow fluctuations close to the point of vanishing liquidity. Why do stock prices change? The traditional answer, within the theory of efficient markets, is that prices move because some new piece of information becomes
Random walks, liquidity molasses and critical response in financial markets, Quantitative Finance
, 2006
"... Stock prices are observed to be random walks in time despite a strong, long term memory in the signs of trades (buys or sells). Lillo and Farmer have recently suggested that these correlations are compensated by opposite long ranged fluctuations in liquidity, with an otherwise permanent market impac ..."
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Cited by 26 (4 self)
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Stock prices are observed to be random walks in time despite a strong, long term memory in the signs of trades (buys or sells). Lillo and Farmer have recently suggested that these correlations are compensated by opposite long ranged fluctuations in liquidity, with an otherwise permanent market impact, challenging the scenario proposed in Quantitative Finance 4, 176 (2004), where the impact is transient, with a powerlaw decay in time. The exponent of this decay is precisely tuned to a critical value, ensuring simultaneously that prices are diffusive on long time scales and that the response function is nearly constant. We provide new analysis of empirical data that confirm and make more precise our previous claims. We show that the powerlaw decay of the bare impact function comes both from an excess flow of limit order opposite to the market order flow, and to a systematic anticorrelation of the bidask motion between trades, two effects that create a ‘liquidity molasses ’ which dampens market volatility. 1 1
V.: Gaussian multiplicative chaos and applications: a review, arxiv
"... In this article, we review the theory of Gaussian multiplicative chaos initially introduced by Kahane’s seminal work in 1985. Though this beautiful paper faded from memory until recently, it already contains ideas and results that are nowadays under active investigation, like the construction of th ..."
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In this article, we review the theory of Gaussian multiplicative chaos initially introduced by Kahane’s seminal work in 1985. Though this beautiful paper faded from memory until recently, it already contains ideas and results that are nowadays under active investigation, like the construction of the Liouville measure in 2dLiouville quantum gravity or thick points of the Gaussian Free Field. Also, we mention important extensions and generalizations of this theory that have emerged ever since and discuss a whole family of applications, ranging from finance, through the KolmogorovObukhov model of turbulence to 2dLiouville quantum gravity. This review also includes new results like the convergence of discretized Liouville measures on isoradial graphs (thus including the triangle and square lattices) towards the continuous Liouville measures (in the subcritical and critical case) or multifractal analysis of the measures in all dimensions.
t−statistic based correlation and heterogeneity Robust Inference
, 2008
"... We develop a general approach to robust inference about a scalar parameter when the data is potentially heterogeneous and correlated in a largely unknown way. The key ingredient is the following result of Bakirov and Székely (2005) concerning the small sample properties of the standard t−test: For a ..."
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Cited by 25 (0 self)
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We develop a general approach to robust inference about a scalar parameter when the data is potentially heterogeneous and correlated in a largely unknown way. The key ingredient is the following result of Bakirov and Székely (2005) concerning the small sample properties of the standard t−test: For a significance level of 5 % or lower, the t−test remains conservative for underlying observations that are independent and Gaussian with heterogenous variances. One might thus conduct robust large sample inference as follows: partition the data into q ≥ 2 groups, estimate the model for each group and conduct a standard t−test with the resulting q parameter estimators. This results in valid and in some sense efficient inference when the groups are chosen in a way that ensures the parameter estimators to be asymptotically independent, unbiased and Gaussian of possibly different variances. We provide examples of how to apply this approach to time series, panel, clustered and spatially correlated data.
Volatility clustering in financial markets: Empirical facts and agent based models
, 2004
"... Summary. Time series of financial asset returns often exhibit the volatility clustering property: large changes in prices tend to cluster together, resulting in persistence of the amplitudes of price changes. After recalling various methods for quantifying and modeling this phenomenon, we discuss se ..."
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Cited by 21 (0 self)
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Summary. Time series of financial asset returns often exhibit the volatility clustering property: large changes in prices tend to cluster together, resulting in persistence of the amplitudes of price changes. After recalling various methods for quantifying and modeling this phenomenon, we discuss several economic mechanisms which have been proposed to explain the origin of this volatility clustering in terms of behavior of market participants and the news arrival process. A common feature of these models seems to be a switching between low and high activity regimes with heavytailed durations of regimes. Finally, we discuss a simple agentbased model which links such variations in market activity to threshold behavior of market participants and suggests a link between volatility clustering and investor inertia. 1
Asymptotic formulas with error estimates for call pricing functions and the implied volatility at extreme strikes
, 2009
"... In this paper, we obtain asymptotic formulas with error estimates for the implied volatility associated with a European call pricing function. We show that these formulas imply Lee’s moment formulas for the implied volatility and the tailwing formulas due to Benaim and Friz. In addition, we analyze ..."
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Cited by 20 (4 self)
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In this paper, we obtain asymptotic formulas with error estimates for the implied volatility associated with a European call pricing function. We show that these formulas imply Lee’s moment formulas for the implied volatility and the tailwing formulas due to Benaim and Friz. In addition, we analyze Paretotype tails of stock price distributions in uncorrelated HullWhite, SteinStein, and Heston models and find asymptotic formulas with error estimates for call pricing functions in these models.