A Partially Observed Model for Micromovement of Asset Prices with Bayes Estimation via Filtering

Zeng, Yong

doi:10.1111/1467-9965.t01-1-00022

Cited by 57 publications

(66 citation statements)

References 61 publications

(66 reference statements)

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“…Note that Theorem 5.1 is a filter approximation result for a model where signal and observation cannot be made independent via a measure transformation. This sets the result apart from filter approximation results as in Zeng (2003) which are based on general results by T. Kurtz and E. Goggins concerning weak convergence of conditional expectations. By the same token, Zeng (2003) obtains only weak convergence of the approximating filters, while here we obtain convergence in probability.…”

Section: A6mentioning

confidence: 60%

Pricing credit derivatives under incomplete information: a nonlinear-filtering approach

Frey

Runggaldier

2010

Finance Stoch

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This paper considers a general reduced form pricing model for credit derivatives where default intensities are driven by some factor process X. The process X is not directly observable for investors in secondary markets; rather, their information set consists of the default history and of noisy price observation for traded credit products. In this context the pricing of credit derivatives leads to a challenging nonlinear filtering problem. We provide recursive updating rules for the filter, derive a finite dimensional filter for the case where X follows a finite state Markov chain and propose a novel particle filtering algorithm. A numerical case study illustrates the properties of the proposed algorithms.

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Section: A6mentioning

confidence: 60%

Pricing credit derivatives under incomplete information: a nonlinear-filtering approach

Frey

Runggaldier

2010

Finance Stoch

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“…Bayesian ltering (BF) estimator (Zeng, 2003(Zeng, , 2004 Let X (t) be the latent continuous value process for our assets. We have the following model setup:…”

Section: Bias Correction Is Obtained By the Estimator For Noise Term Ementioning

confidence: 99%

Statistical and Algorithm Aspects of Optimal Portfolios

Shek

2010

SSRN Journal

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We address three key aspects of optimal portfolio construction: expected return, variancecovariance modeling and optimization in presence of cardinality constraints. On expected return modeling, we extend the self-excited point process framework to model conditional arrival intensities of bid and ask side market orders of listed stocks. The cross-excitation of market orders is modeled explicitly such that the ask side market order size and bid side probability weighted order book cumulative volume can aect the ask side order intensity, and vice versa. Dierent variations of the framework are estimated by using method of maximum likelihood estimation, based on a recursive application of the log-likelihood functions derived in this thesis. Results indicate that the self-excited point process framework is able to capture a signicant amount of the underlying trading dynamics of market orders, both in-sample and out-of-sample.A new framework is introduced, Realized GARCH, for the joint modeling of returns and realized measures of volatility. A key feature is a measurement equation that relates the realized measure to the conditional variance of returns. The measurement equation facilitates a simple modeling of the dependence between returns and future volatility. Realized GARCH models with a linear or log-linear specication have many attractive features. They are parsimonious, simple to estimate, and imply an ARMA structure for the conditional variance and the realized measure. An empirical application with DJIA stocks and an exchange traded index fund shows that a simple Realized GARCH structure leads to substantial improvements in the empirical t over standard GARCH models.Finally we describe a novel algorithm to obtain the solution of the optimal portfolio problem with NP-hard cardinality constraints. The algorithm is based on a local relaxation that exploits the inherent structure of the objective function. It solves a sequence of small, local, quadratic-programs by rst projecting asset returns onto a reduced metric space, followed by clustering in this space to identify sub-groups of assets that best accentuate a suitable measure of similarity amongst dierent assets. The algorithm can either be cold started using the centroids of initial clusters or be warm started based on the output of a previous result. Empirical result, using baskets of up to 3,000 stocks and with dierent cardinality constraints, indicates that the algorithm is able to achieve signicant performance gain over a sophisticated branchand-cut method. One key application of this local relaxation algorithm is in dealing with large scale cardinality constrained portfolio optimization under tight time constraint, such as for the purpose of index tracking or index arbitrage at high frequency.iv

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“…This is consistent with the fact that economic sources for clustering such as the trading activity of other investors are not directly observable. Markov modulated marked point processes with partial information (without price impact) were considered previously in the statistical modelling of high frequency data, see for instance Zeng [45], Cvitanic et al [26], or Cartea and Jaimungal [17]; however, we are the first to study optimal liquidation in such a setting.…”

Section: Introductionmentioning

confidence: 99%

Shall I Sell or Shall I Wait? Optimal Liquidation Under Partial Information with Price Impact

Colaneri

Eksi

Frey³

et al. 2016

SSRN Journal

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A Partially Observed Model for Micromovement of Asset Prices with Bayes Estimation via Filtering

Cited by 57 publications

References 61 publications

Pricing credit derivatives under incomplete information: a nonlinear-filtering approach

Pricing credit derivatives under incomplete information: a nonlinear-filtering approach

Statistical and Algorithm Aspects of Optimal Portfolios

Shall I Sell or Shall I Wait? Optimal Liquidation Under Partial Information with Price Impact

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