Results 11  20
of
330
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 ..."
Abstract

Cited by 22 (4 self)
 Add to MetaCart
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.
A limit theorem for financial markets with inert investors
 Mathematics of Operations Research
, 2003
"... We study the effect of investor inertia on stock price fluctuations with a market microstructure model comprising many small investors who are inactive most of the time. It turns out that semiMarkov processes are tailor made for modeling inert investors. With a suitable scaling, we show that when t ..."
Abstract

Cited by 18 (2 self)
 Add to MetaCart
(Show Context)
We study the effect of investor inertia on stock price fluctuations with a market microstructure model comprising many small investors who are inactive most of the time. It turns out that semiMarkov processes are tailor made for modeling inert investors. With a suitable scaling, we show that when the price is driven by the market imbalance, the log price process is approximated by a process with long range dependence and nonGaussian returns distributions, driven by a fractional Brownian motion. Consequently, investor inertia may lead to arbitrage opportunities for sophisticated ‘third parties’. The mathematical contributions are a functional central limit theorem for stationary semiMarkov processes, and approximation results for stochastic integrals of continuous semimartingales with respect to fractional Brownian motion.
Price Dynamics in a Markovian Limit Order Market
 SIAM Journal for Financial Mathematics
"... We propose and study a simple stochastic model for the dynamics of a limit order book, in which arrivals of market order, limit orders and order cancellations are described in terms of a Markovian queueing system. Through its analytical tractability, the model allows to obtain analytical expressions ..."
Abstract

Cited by 18 (0 self)
 Add to MetaCart
We propose and study a simple stochastic model for the dynamics of a limit order book, in which arrivals of market order, limit orders and order cancellations are described in terms of a Markovian queueing system. Through its analytical tractability, the model allows to obtain analytical expressions for various quantities of interest such as the distribution of the duration between price changes, the distribution and autocorrelation of price changes, and the probability of an upward move in the price, conditional on the state of the order book. We study the diffusion limit of the price process and express the volatility of price changes in terms of parameters describing the arrival rates of buy and sell orders and cancelations. These analytical results provide some insight into the relation between order flow and price dynamics in orderdriven markets. Key words: limit order book, market microstructure, queueing, diffusion limit, highfrequency data, liquidity, duration analysis, point process.
FORECASTING VOLATILITY WITH THE MULTIFRACTAL RANDOM WALK MODEL
, 801
"... Abstract. We study the problem of forecasting volatility for the multifractal random walk model. In order to avoid the ill posed problem of estimating the correlation length T of the model, we introduce a limiting object defined in a quotient space; formally, this object is an infinite range logvola ..."
Abstract

Cited by 17 (3 self)
 Add to MetaCart
(Show Context)
Abstract. We study the problem of forecasting volatility for the multifractal random walk model. In order to avoid the ill posed problem of estimating the correlation length T of the model, we introduce a limiting object defined in a quotient space; formally, this object is an infinite range logvolatility. For this object and the non limiting object, we obtain precise prediction formulas and we apply them to the problem of forecasting volatility and pricing options with the MRW model in the absence of a reliable estimate of σ and T.
Long range dependence in financial markets
 Fractals in Engineering
"... The notions of selfsimilarity, scaling, fractional processes and long range dependence have been repeatedly used to describe properties of financial time series: stock prices, foreign exchange rates, market indices and commodity prices. We discuss the relevance of these concepts in the context of ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
The notions of selfsimilarity, scaling, fractional processes and long range dependence have been repeatedly used to describe properties of financial time series: stock prices, foreign exchange rates, market indices and commodity prices. We discuss the relevance of these concepts in the context of financial modelling, their relation with the basic principles of financial theory and possible economic explanations for their presence in financial time series.
Minimal agent based model for financial markets II: statistical properties of the linear and multiplicative dynamics. to be submitted
, 2008
"... We introduce a minimal Agent Based Model for financial markets to understand the nature and SelfOrganization of the Stylized Facts. The model is minimal in the sense that we try to identify the essential ingredients to reproduce the main most important deviations of price time series from a Random ..."
Abstract

Cited by 13 (3 self)
 Add to MetaCart
(Show Context)
We introduce a minimal Agent Based Model for financial markets to understand the nature and SelfOrganization of the Stylized Facts. The model is minimal in the sense that we try to identify the essential ingredients to reproduce the main most important deviations of price time series from a Random Walk behavior. We focus on four essential ingredients: fundamentalist agents which tend to stabilize the market; chartist agents which induce destabilization; analysis of price behavior for the two strategies; herding behavior which governs the possibility of changing strategy. Bubbles and crashes correspond to situations dominated by chartists, while fundamentalists provide a long time stability (on average). The Stylized Facts are shown to correspond to an intermittent behavior which occurs only for a finite value of the number of agents N. Therefore they correspond to finite size effect which, however, can occur at different time scales. We propose a new mechanism for the SelfOrganization of this state which is linked to the existence of a threshold for the agents to be active or not active. The feedback between price fluctuations and number of active agents represent a crucial element for this state of SelfOrganizedIntermittency. The model can be easily generalized to consider more realistic variants. 1
A Heterogeneous, Endogenous and Coevolutionary GPbased Financial Market
"... Stock markets are very important in modern societies and their behaviour have serious implications in a wide spectrum of the world’s population. Investors, governing bodies and the society as a whole could benefit from better understanding of the behavior of stock markets. The traditional approach t ..."
Abstract

Cited by 12 (5 self)
 Add to MetaCart
Stock markets are very important in modern societies and their behaviour have serious implications in a wide spectrum of the world’s population. Investors, governing bodies and the society as a whole could benefit from better understanding of the behavior of stock markets. The traditional approach to analyze such systems is the use of analytical models. However, the complexity of financial markets represents a big challenge to the analytical approach. Most analytical models make simplifying assumptions, such as perfect rationality and homogeneous investors, which threaten the validity of analytical results. This motivates alternative methods. In this work, we developed an artificial financial market and used it to study the behavior of stock markets. In this market, we model technical, fundamental and noise traders. The technical traders are sophisticated genetic programming based agents that coevolve (by means of their fitness function) by predicting investment opportunities in the market using technical analysis as the main tool. With this endogenous artificial market, we identified conditions under which the statistical properties of price series in the artificial market resembles those of the real financial markets. Additionally, we modeled the pressure to beat the market by a behavioral constraint imposed on the agents reflecting the Red Queen principle in evolution. We have demonstrated how evolutionary computation could play a key role in studying stock markets.
Exchange rate dynamics: a nonlinear survey
 In B. Rosser Jr (Ed.) Handbook of research on complexity
, 2009
"... According to the chartistfundamentalist approach, exchange rate fluctuations are at least partially driven by the interactions of heterogeneous boundedly rational speculators who use different trading strategies to determine their orders. This framework is guided by the observation that professiona ..."
Abstract

Cited by 11 (8 self)
 Add to MetaCart
According to the chartistfundamentalist approach, exchange rate fluctuations are at least partially driven by the interactions of heterogeneous boundedly rational speculators who use different trading strategies to determine their orders. This framework is guided by the observation that professional foreign exchange market participants indeed rely on both technical and fundamental analysis rules. Our goal is to survey such models and discuss some key mechanisms which may produce endogenous complex exchange rate dynamics.
Characterizations of joint distributions, copulas, information, dependence and decoupling, with applications to time series
 IMS LECTURE NOTES–MONOGRAPH SERIES
, 2006
"... ..."