Category Financial Econometrics and Empirical Market Microstructure

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 leading up to the December 1, 2008 stress event. Note the log scale, so any increase above linear is super-exponential.

The following is noteworthy:

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image217 image218

1. On February 27, PStress jumped by 170x from extremely low levels. It was a Black Swan. PStress (i. e., equity market volatility) had no predictive power. However, the extremely low level of volatility/implied stress could be viewed

Fig. 14 S&P 500 PStress

image219as a contrarian signal of high hidden risk and risk myopia/overconfldence as discussed earlier.

2...

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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 is that we have a regression model:

У* = x/0 + " (1)

where

y*—a latent variable, which is not observed, xi—a vector of independent variables,

"—a vector of constant coefficients,

"i—error term.

We observe a dichotomous variable yi defined by

l, if y* >0, 0, otherwise.

In other words, y; is the PD, taking the value 1 or zero. In the process of credit underwriting y* would be defined as a propensity to receive approval from a credit organization.

Подпись:1, if the borrower is defaulted, 0, otherwise.

The probit and logit models differ in the specification of distributional form of the erro...

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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. The tick-to-price ratio is a measure of an effective tick size. We find dramatic differences between distributions for assets with large and small tick-to-price ratio. The presence of returns clustering is evident for large tick size assets. The statistical differences between large and small tick size assets appear to reduce at higher time scales of observation. A possible way to explain returns dynamics for large tick size assets is the coupling of returns with bid-ask spread dynamics...

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Statistical Properties of MRW Process

In order to demonstrate distinctive feature of MRW process, one can compare its realization with realization of geometric Brownian motion (original random walk model of Bachelier), which sample increments and path are shown in Figs. 1 and 2. Sample realizations of increments and path of MRW are shown in Figs. 3 and 4.

Comparing Fig. 3 with Fig. 1, one can notice significant differences in the way, which each process goes. When dynamics of increments of random walk (Fig. 1) are very regular and one can not observe large deviations from the mean value, the dynamics of MRW (Fig. 3) is much more intermittent, one can easily spot volatility clustering and large excursions (extreme events).

o

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О І I I , , , I

‘ 0 2000 4000 6000 8000

n

Fig. 1 Increments of geometrical Brownian motion for a =...

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On Some Approaches to Managing Market Risk Using VaR Limits: A Note

Alexey Lobanov

Abstract Market risk has been traditionally considered in a single-period setting, with fixed positions in a static portfolio and losses caused by price volatility over a specified time horizon. In the real world, however, trading losses are generally a product of both position changes and adverse market movements. Market risk limits have been widely used in the industry for controlling both ex-ante and ex-post losses from traders’ actions, but the interplay of risk limits with risk measurement has been scarcely studied in the literature. This note aims to provide insights into the broad concepts of using limits in market risk management, as well as some approaches to setting and managing market risk limits in a dynamic setting.

Keywords Market risk • Positions limits • Tr...

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Time-Warped Longest Common Subsequence (T-WLCS)

The basic idea is to unite both DTW and LCSS approaches (Guo and Siegelmann 2004)

f 0, _if _i = 0 _or_j = 0

cij = max {a-i, j, ci, j_i, c,-_ij_i + 1 ,_if_i, j >0, Qt = Cj (5)

: max Ci_i, j, cij_i} , _if_i, j > 0, Qi ф Cj

Example 1.C = 41516171, Q = 4567, LCS(C, Q) = 4, T-WLCS(C, Q) = 4 Example 2. C = 44556677, Q = 4567, LCS(C, Q) = 4, T-WLCS(C, Q) = 8 Example 3. C = 4455661111177, Q = 4567, LCS(C, Q) = 4, T-WLCS(C, Q) = 8

4 Granger-Causality

A time series X is said to Granger-cause Y if it can be shown, usually through a series of t-tests and F-tests on lagged values of X (and with lagged values of Y also included), that those X-values provide statistically significant information about future values of Y (Granger 1969).

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