Dynamic Semiparametric Factor Model Research Articles

Modelling and Forecasting Liquidity Supply Using Semiparametric Factor Dynamics

We model the dynamics of ask and bid curves in a limit order book market using a dynamic semiparametric factor model. The shape of the curves is captured by a factor structure which is estimated nonparametrically. Corresponding factor loadings are assumed to follow multivariate dynamics and are modelled using a vector autoregressive model. Applying the framework to four stocks traded at the Australian Stock Exchange (ASX) in 2002, we show that the suggested model captures the spatial and temporal dependencies of the limit order book. Relating the shape of the curves to variables reflecting the current state of the market, we show that the recent liquidity demand has the strongest impact. In an extensive forecasting analysis we show that the model is successful in forecasting the liquidity supply over various time horizons during a trading day. Moreover, it is shown that the model’s forecasting power can be used to improve optimal order execution strategies.

High Dimensional Nonstationary Time Series Modelling with Generalized Dynamic Semiparametric Factor Model

(High dimensional) time series which reveal nonstationary and possibly periodic behavior occur frequently in many scientic elds. In this article, we separate the modeling of high dimensional time series to time propagation of low dimensional time series and high dimensional time invariant functions via functional factor analysis. We propose a two-step estimation procedure. At the rst step, we detect the deterministic trends of the time series by incorporating time basis selected by the group Lasso-type technique and choose the space basis based on smoothed functional principal component analysis. We show properties of this estimator under various situations extending current variable selection studies. At the second step, we obtain the detrended low dimensional stochastic process. However an important issue arises: is it justied, from an inferential point of view, to base further statistical inference on the estimated stochastic time series? We show that the dierence between the inference based on the estimated time series and true unobserved time series is asymptotically negligible, which ultimately allows one to study the dynamics of the whole high-dimensional system with a low dimensional representation together with the deterministic trend. We apply the method to our motivating empirical problems: studies of the dynamic behavior of temperatures (further used for pricing weather derivatives), implied volatilities and risk patterns and correlated brain activities (neuro-economics related) using fMRI data, where a panel version model is also presented.

The Dynamics of Hourly Electricity Prices

The dynamics of hourly electricity prices in day-ahead markets is an important element of competitive power markets that were only established in the last decade. In electricity markets, the market micro-structure does not allow for continuous trading, since operators require advance notice in order to verify that the schedule is feasible and lies within transmission constraints. Instead agents have to submit their bids and offers for delivery of electricity for all hours of the next day before a specified market closing time. We suggest the use of dynamic semi-parametric factor models (DSFM) for the behavior of hourly electricity prices. We find that a model with three factors is able to explain already a high proportion of the variation in hourly electricity prices. Our analysis also provides insights into the characteristics of the market, in particular with respect to the driving factors of hourly prices and their dynamic behavior through time.

Dynamic semiparametric factor models in risk neutral density estimation

Dynamic semiparametric factor models (DSFM) simultaneously smooth in space and are parametric in time, approximating complex dynamic structures by time invariant basis functions and low dimensional time series. In contrast to traditional dimension reduction techniques, DSFM allows the access of the dynamics embedded in high dimensional data through the lower dimensional time series. In this paper, we study the time behavior of risk assessments from investors facing random financial payoffs. We use DSFM to estimate risk neutral densities from a dataset of option prices on the German stock index DAX. The dynamics and term structure of risk neutral densities are investigated by Vector Autoregressive (VAR) methods applied on the estimated lower dimensional time series.

A Joint Analysis of the KOSPI 200 Option and ODAX Option Markets Dynamics

As a function of strike and time to maturity the implied volatility estimation is a challenging task in nancial econometrics. Dynamic Semiparametric Factor Models (DSFM) are a model class that allows for the estimation of the implied volatility surface (IVS) in a dynamic context, employing semiparametric factor functions and time-varying loadings. Because nancial asset volatilities move over time, across assets and over markets, this paper analyses volatility interaction between German and Korean stock markets. As proxy for the volatility, factor loadings series derived from a DSFM application on option prices are employed. We examine volatility transmission between the markets under the vector autoregressive (VAR) model framework. Our results show that a shock in the volatility of one market may not translate directly into greater uncertainty in another market and it is unlikely that portfolio investors can benet from diversication among these markets due to cointegration.

A semiparametric factor model for electricity forward curve dynamics

In this paper we introduce the dynamic semiparametric factor model (DSFM) for electricity forward curves. The biggest advantage of our approach is that it not only leads to smooth, seasonal forward curves extracted from exchange traded futures and forward electricity contracts, but also to a parsimonious factor representation of the curve. Using closing prices from the Nordic power market Nord Pool we provide empirical evidence that the DSFM is an efficient tool for approximating forward curve dynamics.

Dynamic Semiparametric Factor Models in Risk Neutral Density Estimation

Dimension reduction techniques for functional data analysis model and approximate smooth random functions by lower dimensional objects. In many applications the focus of interest lies not only in dimension reduction but also in the dynamic behaviour of the lower dimensional objects. The most prominent dimension reduction technique - functional principal components analysis - however, does not model time dependences embedded in functional data. In this paper we use dynamic semiparametric factor models (DSFM) to reduce dimensionality and analyse the dynamic structure of unknown random functions by means of inference based on their lower dimensional representation. We apply DSFM to estimate the dynamic structure of risk neutral densities implied by prices of option on the DAX stock index.

Long memory persistence in the factor of Implied volatility dynamics

The volatility implied by observed market prices as a function of the strike and time to maturity form an Implied Volatility Surface (IV S). Practical applications require reducing the dimension and characterize its dynamics through a small number of factors. Such dimension reduction is summarized by a Dynamic Semiparametric Factor Model (DSFM) that characterizes the IV S itself and their movements across time by a multivariate time series of factor loadings. This paper focuses on investigating long range dependence in the factor loadings series. Our result reveals that shocks to volatility persist for a very long time, affecting significantly stock prices. For appropriate representation of the series dynamics and the possibility of improved forecasting, we model the long memory in levels and absolute returns using the class of fractional integrated volatility models that provide flexible structure to capture the slow decaying autocorrelation function reasonably well.

Statistics of risk aversion

Information about risk preferences from investors is essential for modelling a wide range of quantitative finance applications. Valuable information related to preferences can be extracted from option prices through pricing kernels. In this paper, pricing kernels and their term structure are estimated in a time varying approach from DAX and ODAX data using dynamic semiparametric factor model (DSFM). DSFM smooths in time and space simultaneously, approximating complex dynamic structures by basis functions and a time series of loading coefficients. Contradicting standard risk aversion assumptions, the estimated pricing kernels indicate risk proclivity in certain levels of return. The analysis of the time series of loading coefficients allows a better understanding of the dynamic behaviour from investors preferences towards risk.

Long Memory Persistence in the Factor of Implied Volatility Dynamics

The volatility implied by observed market prices as a function of the strike and time to maturity form an Implied Volatility Surface (IV S). Practical applications require reducing the dimension and characterize its dynamics through a small number of factors. Such dimension reduction is summarized by a Dynamic Semiparametric Factor Model (DSFM) that characterizes the IV S itself and their movements across time by a multivariate time series of factor loadings. This paper focuses on investigating long range dependence in the factor loadings series. Our result reveals that shocks to volatility persist for a very long time, affecting significantly stock prices. For appropriate representation of the series dynamics and the possibility of improved forecasting, we model the long memory in levels and absolute returns using the class of fractional integrated volatility models that provide flexible structure to capture the slow decaying autocorrelation function reasonably well.

A Dynamic Semiparametric Factor Model for Implied Volatility String Dynamics

A primary goal in modelling the implied volatility surface (IVS) for pricing and hedging aims at reducing complexity. For this purpose one fits the IVS each day and applies a principal component analysis using a functional norm. This approach, however, neglects the degenerated string structure of the implied volatility data and may result in a modelling bias. We propose a dynamic semiparametric factor model (DSFM), which approximates the IVS in a finite dimensional function space. The key feature is that we only fit in the local neighborhood of the design points. Our approach is a combination of methods from functional principal component analysis and backfitting techniques for additive models. The model is found to have an approximate 10% better performance than a sticky moneyness model. Finally, based on the DSFM, we devise a generalized vega-hedging strategy for exotic options that are priced in the local volatility framework. The generalized vega-hedging extends the usual approaches employed in the local volatility framework.

DSFM Fitting of Implied Volatility Surfaces

The implied volatility became one of the key issues in modern quantitative finance, since the plain vanilla option prices contain vital information for pricing and hedging of exotic and illiquid options. European plain vanilla options are nowadays widely traded, which results in a great amount of high-dimensional data especially on an intra day level. The data reveal a degenerated string structure. Dynamic Semiparametric Factor Models (DSFM) are tailored to handle complex, degenerated data and yield low dimensional representation of the implied volatility surface (IVS). We discuss estimation issues of the model and apply it to DAX option prices.

Implied Volatility String Dynamics

A primary goal in modelling the dynamics of implied volatility surfaces (IVS) aims at reducing complexity. For this purpose one fits the IVS each day and applies a principal component analysis using a functional norm. This approach, however, neglects the degenerated string structure of the implied volatility data and may result in a severe modelling bias. We propose a dynamic semiparametric factor model, which approximates the IVS in a finite dimensional function space. The key feature is that we only fit in the local neighborhood of the design points. Our approach is a combination of methods from functional principal component analysis and backfitting techniques for additive models. The model is found to have an approximate 10% better performance than the typical naive trader models. The model can be a backbone in risk management serving for value at risk computations and scenario analysis.