Linear and non-linear filtering in mathematical finance: a review

Date, Paresh; Ponomareva, Ksenia

doi:10.1093/imaman/dpq008

Cited by 35 publications

(21 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The financial modeller may choose from various algorithms to determine the initial parameters, some of which are described in Erlwein et al [24], Date and Ponomareva [25], and Date and Bustreo [26], amongst others. For the purpose of this study, a simple log-likelihood maximisation would suffice and the procedure in Date and Ponomareva [25] is adopted; this is also described in Hardy [27]. The data set is divided into two parts: one part as a training subset, and the remaining part is employed for the trading procedure and validation.…”

Section: Initialisation Of the Algorithmmentioning

confidence: 99%

A computing platform for pairs-trading online implementation via a blended Kalman-HMM filtering approach

Tenyakov

Mamon

2017

J Big Data

View full text Add to dashboard Cite

IntroductionPairs trading is an investment strategy used to exploit financial markets that are out of equilibrium. It consists of a long position in one security and a short position in another security at a predetermined ratio; see Elliott et al. [1]. Traders bet on the direction of the stocks relative to each other. Such a trading strategy is typically employed by hedge fund companies. Deviations in prices are monitored closely and used as basis for changing positions, taking advantage of market inefficiencies to obtain some profits. Hence, financial computing technologies with algorithmic trading capability, such as the one Abstract This paper addresses the problem of designing an efficient platform for pairs-trading implementation in real time. Capturing the stylised features of a spread process, i.e., the evolution of the differential between the returns from a pair of stocks, exhibiting a heavy-tailed mean-reverting process is also dealt with. Likewise, the optimal recovery of time-varying parameters in a return-spread model is tackled. It is important to solve such issues in an integrated manner to carry out the execution of trading strategies in a dynamic market environment. The Kalman and hidden Markov model (HMM) multiregime dynamic filtering approaches are fused together to provide a powerful method for pairs-trading actualisation. Practitioners' considerations are taken into account in the way the new filtering method is automated. The synthesis of the HMM's expectationmaximisation algorithm and Kalman filtering procedure gives rise to a set of self-updating optimal parameter estimates. The method put forward in this paper is a hybridisation of signal-processing algorithms. It highlights the critical role and beneficial utility of data fusion methods. Its appropriateness and novelty support the advancements of accurate predictive analytics involving big financial data sets. The algorithm's performance is tested on historical return spread between Coca-Cola and Pepsi Inc. 's equities. Through a back-testing trade, a hypothetical trader might earn a non-zero profit under the assumption of no transaction costs and bid-ask spreads. The method's success is illustrated by a trading simulation. The findings from this work show that there is high potential to gain when the transaction fees are low, and an investor is able to benefit from the proposed interplay of the two filtering methods. Tenyakov and Mamon J Big Data (2017) Data (2017) 4:46 put forward in this paper, are necessary for the efficient and successful implementation of a pairs trade. RESEARCHWhen the relative performance of the short position is better than that of the long position, this strategy is going to be profitable regardless of stock market regimes. So, a speculator who pairs a long position in a retail stock with a short position in a rival stock or an index ETF could end up with a profit. Pairs trading could be viewed alternatively as a mechanism to hedge both sector and market risks. When there is a financial crisis, two stoc...

show abstract

Section: Initialisation Of the Algorithmmentioning

confidence: 99%

A computing platform for pairs-trading online implementation via a blended Kalman-HMM filtering approach

Tenyakov

Mamon

2017

J Big Data

View full text Add to dashboard Cite

show abstract

“…Bayesian state estimation [1] is an established and flexible signal processing framework that can accommodate many real world problems such as target tracking and navigation [2], audio restoration [3], speech processing [4], and processing of financial data [5]. The main idea is to obtain a probabilistic description of a state x k by (sequentially) processing measurements y 1:l = {y 1 , .…”

Section: Introductionmentioning

confidence: 99%

Computation and visualization of posterior densities in scalar nonlinear and non-Gaussian Bayesian filtering and smoothing problems

Roth

Gustafsson

2017

2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

View full text Add to dashboard Cite

One-dimensional Bayesian filtering and smoothing problems can be solved numerically using a number of algorithms, even in nonlinear and non-Gaussian cases. In this educational paper we advocate for the benefits of visualizing the obtained posterior densities as complement to, e.g., estimation error analysis. In addition to a review of Bayesian filtering and smoothing and the respective point mass and particle solutions, we devise a novel algorithm for filtering when the likelihood cannot be evaluated. Several instructive examples are discussed and easily adjustable matlab code is provided as complement to this paper.

show abstract

“…Babbs and Nowman (1999) and Bolder (2001)), the estimation of the spot prices of commodities from the futures prices (see Schwartz (1997) and Manoliu and Tompaidis (2002)) and updating the uncertain drift parameters in the context of hedging in incomplete markets (Monoyios (2007)). A review of applications of filtering in financial mathematics is provided in Date and Ponomareva (2011).…”

Section: Introductionmentioning

confidence: 99%

Value-at-Risk for fixed-income portfolios: a Kalman filtering approach

Date

Bustreo

2015

IMA J Management Math

Self Cite

View full text Add to dashboard Cite

We propose a way of measuring the risk of a sovereign debt portfolio by using a simple two-factor short rate model. The model is calibrated from data and then the changes in the bond prices are simulated by using a Kalman filter. The bond prices being simulated remain arbitrage-free, in contrast with principal component analysis based strategies for simulation and risk measurement of debt portfolios. In liquid sovereign debt markets, a risk measurement methodology which allows the future bond price scenarios to be arbitrage-free may be seen as a potentially more realistic way of measuring the debt portfolio risk due to interest rate fluctuations. We demonstrate the performance of this methodology with calibration and backtesting, both on simulated data as well as on a real portfolio of US government bonds.

show abstract

Linear and non-linear filtering in mathematical finance: a review

Cited by 35 publications

References 55 publications

A computing platform for pairs-trading online implementation via a blended Kalman-HMM filtering approach

A computing platform for pairs-trading online implementation via a blended Kalman-HMM filtering approach

Computation and visualization of posterior densities in scalar nonlinear and non-Gaussian Bayesian filtering and smoothing problems

Value-at-Risk for fixed-income portfolios: a Kalman filtering approach

Contact Info

Product

Resources

About