Modeling Financial Market Using Percolation Theory

Anastasiya Byachkova and Artem Simonov Abstract Econophysics is a relatively new discipline. It is one of the most interesting and promising trends in modeling complex economic systems such as financial …

Multifractal Formalism for Stochastic Processes

Original definition of fractal was proposed by Mandelbrot with respect to sets. He defined fractal as a mathematical set with fractal dimension is strictly larger than its topological dimension (Mandelbrot …

Adaptive Learning

Risk management is a core discipline in a rapidly changing world. From finance to ecology, we face unprecedented systemic risks from increasingly coupled global systems. Non-linearities render long term predictions …

Benchmarking

The website www. rogovindex. com was created in 2012-2013 to allow for viewing and, if desired, exporting into spreadsheet files the history of hourly, daily, weekly, monthly, or annual (the …

Jumps Identification

Before a price jump can be accounted for in an estimation stage, it first has to be identified. Surprisingly, but the literature up to now does not offer a consensus …

European Divergence Case Study

The European Divergence Scenario illustrates the Adaptive Stress Testing frame­work well. With the introduction of the Euro, credit spreads converged for all member countries and started an unsustainable cycle of …

Results

When buying or selling a security, investors typically are interested in the following three questions: How likely am I to transact? What price am I likely to receive? How much …

Recurrence Plot Approach

Two main problems with the correlation integral approach are: (1) considerable amount of data necessary for reliable estimates and (2) a priori choice of embedding parameters for reconstructed phase space. …

Models of Corporations and Sovereigns

The sample of corporations included information from different industries (oil and gas, utilities, retail, telecom, etc.) and countries. We considered the rated companies from these industries which also had financial …

Stress Grades Amplify Market Based Risk Signals

As volatility based metrics, StressGrades will not directly uncover hidden structural risk or predict Black Swans. StressGrades merely amplify existing market based signals of risk, as a seismograph amplifies geological …

Structural and Econometric Model

Demand-for-mortgage function can be represented by the following equation: ln L = PlD C ylC C SlF C VlP + д-lM C el (1) where L is usually the loan …

Percolation Model of Stock Market Prices

It is well known that we often observe “clustering” (or herding) phenomena in the financial markets—the situation when agents in the market prefer to make the same decisions. This behavior …

Multifractal Random Walk Model

1.1 Model Description As discussed above, continuous Multifractal Random Walk (MRW) (Bacry et al. 2000,2001) process is the only continuous stochastic stationary causal process with exact multifractal properties and Gaussian …

Seek Out the New: Harnessing Network Intelligence

Adaptive Stress Testing builds a creative tension between contrarian views of Innovators and the “wisdom of crowds” (Surowiecki 2004). Innovators are contrarians who perceive hidden risks that are not yet …

Time Series Data Mining vs. Risk Management

The major tasks considered by the time series data mining community (Ratanama- hatana et al. 2010) are as follows: - Indexing (Query by Content): Given a query time series Q, …

Model-Independent Price Jump Indicators

1. Extreme returns indicator: a price jump occurs at time t if the return at time t is above some threshold. The threshold value can be selected by two ways: …

U. S. Subprime Case Study: 2006-2008

Even Nassim Taleb admits that the U. S. subprime crisis was no Black Swan. The macro environment in 2006 was increasingly fragile. Classic macroeconomic imbalances built up over years: low …

Raising Issues About Impact of High Frequency Trading on Market Liquidity

Vladimir Naumenko Abstract The aim of this paper is to consider some problems with evaluation of the impact of high frequency trading on market liquidity. The first part is devoted …

Revisiting of Empirical Zero Intelligence Models

Vyacheslav Arbuzov Abstract This paper describes a zero-intelligence approach implementation for the modeling of financial markets. We construct a mechanism of order flow and market engine simulation. We analyze stylized …

Probability of Default Models

Here, and later in the paper, the default is understood as one of the following signals for its registration: • A bank’s capital sufficiency level falls below 2 %. • …

Backtesting StressGrades

Below we show several are early warning backtesting case studies on ETF’s representing major asset classes. We calibrated DStress for each ETF based on the largest daily drawdown dates (e. …

Sample Selection Bias in Mortgage Market Credit Risk Modeling

Agatha Lozinskaia Abstract The mortgage crisis that started in the U. S. in 2007 and lasted until 2009 was characterized by an unusually large number of defaults on the subprime …

Model Calibration

In order to understand this model’s properties and its advantages, it is necessary to analyze how the model can reflect real data conditions. Thus, there is an issue of calibration …

Numerical Simulation of the MRW Process

The bottleneck of numerical simulation of the MRW process (8) is simulation of logarithmically correlated noise! Дг [k]. Simulation of the discrete Gaussian noise process with given autocorrelation function (covariance …

Summary

Adaptive stress testing is a blend of art and science which continually integrates qualitative macro and quantitative micro perspectives. The first challenge in stress testing is to conceive of a …

Longest Common Subsequence Similarity (LCSS)

The basic idea is to match two sequences by allowing some elements to be unmatched or left out. (Sankoff and Kruskal 1983). Given a sequence C(m), and a sequence Q(n), …

Comparison of Portfolio Management Strategies

Despite the great potential of the developed models, most of them have not been applied to real data. To prove the usefulness of portfolio management models for practitioners, we apply …

Model-Dependent Price Jump Indicators

1. The Difference Between Bi-power Variance and Standard Deviation The method is based on two distinct measures of overall volatility, where the first one takes into account the entire price …

The Second Wave: HSBC’s February 2007 Loss

The second major jump in subprime volatility occurred on February 23, 2007, the day after HSBC announced a $10.5 bn loss in their US subprime holdings. It looked like a …

How to Disentangle the Impact of HFT on Market Liquidity from Other Factors?

There are a number of challenges for evaluation of the influence of HFT on market quality. First, it is very difficult to disentangle the impact of HFT on the market …

The Mike-Farmer Model (2008)

In the publication of Farmer et al. (2006) in the Future Enhancement chapter, there were announced important properties of the order flow for a future upgrade of the model. Parts …

System of Models and Synergy of Rating Estimations

Previously we considered the capabilities which were given to us by rating mappings and models. Later we will discuss the synergy of these approaches as instruments of the Joint Rating …

S&P 500 (SPY) Case Study

On December 1 ’08 SPY fell 9.6 % (log return), the biggest daily drop since Black Monday in 1987. Figure 14 shows a super-exponential increase in (Normal Distribution Implied) PStress …

Econometric Models for Credit Underwriting and Default

Traditional credit risk models on the mortgage market employ a parametric approach to estimate regression of the default probability. These are classical binary choice models (probit and logit). The idea …

How Tick Size Affects the High Frequency Scaling of Stock Return Distributions

Gianbiagio Curato and Fabrizio Lillo Abstract We study the high frequency scaling of the distributions of returns for stocks traded at NASDAQ market as a function of the tick-to-price ratio. …

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